rating, ranking, betting and mathematics r vittal rao
TRANSCRIPT
![Page 2: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/2.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”Ed: “Hi Mark”Mark: “Eduardo”Ed: “You and Erica splt up?”Mark: “How did you know that?”Ed: “It is on your blog”Mark: “Yeah”Ed:“Are you alright?”Mark: “I need you”Ed: “I am here for you”Mark: “No, I need your algorithm to rank chess players”
![Page 3: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/3.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.
Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”Ed: “Hi Mark”Mark: “Eduardo”Ed: “You and Erica splt up?”Mark: “How did you know that?”Ed: “It is on your blog”Mark: “Yeah”Ed:“Are you alright?”Mark: “I need you”Ed: “I am here for you”Mark: “No, I need your algorithm to rank chess players”
![Page 4: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/4.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”
Ed: “Hi Mark”Mark: “Eduardo”Ed: “You and Erica splt up?”Mark: “How did you know that?”Ed: “It is on your blog”Mark: “Yeah”Ed:“Are you alright?”Mark: “I need you”Ed: “I am here for you”Mark: “No, I need your algorithm to rank chess players”
![Page 5: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/5.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”Ed: “Hi Mark”
Mark: “Eduardo”Ed: “You and Erica splt up?”Mark: “How did you know that?”Ed: “It is on your blog”Mark: “Yeah”Ed:“Are you alright?”Mark: “I need you”Ed: “I am here for you”Mark: “No, I need your algorithm to rank chess players”
![Page 6: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/6.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”Ed: “Hi Mark”Mark: “Eduardo”
Ed: “You and Erica splt up?”Mark: “How did you know that?”Ed: “It is on your blog”Mark: “Yeah”Ed:“Are you alright?”Mark: “I need you”Ed: “I am here for you”Mark: “No, I need your algorithm to rank chess players”
![Page 7: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/7.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”Ed: “Hi Mark”Mark: “Eduardo”Ed: “You and Erica splt up?”
Mark: “How did you know that?”Ed: “It is on your blog”Mark: “Yeah”Ed:“Are you alright?”Mark: “I need you”Ed: “I am here for you”Mark: “No, I need your algorithm to rank chess players”
![Page 8: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/8.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”Ed: “Hi Mark”Mark: “Eduardo”Ed: “You and Erica splt up?”Mark: “How did you know that?”
Ed: “It is on your blog”Mark: “Yeah”Ed:“Are you alright?”Mark: “I need you”Ed: “I am here for you”Mark: “No, I need your algorithm to rank chess players”
![Page 9: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/9.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”Ed: “Hi Mark”Mark: “Eduardo”Ed: “You and Erica splt up?”Mark: “How did you know that?”Ed: “It is on your blog”
Mark: “Yeah”Ed:“Are you alright?”Mark: “I need you”Ed: “I am here for you”Mark: “No, I need your algorithm to rank chess players”
![Page 10: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/10.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”Ed: “Hi Mark”Mark: “Eduardo”Ed: “You and Erica splt up?”Mark: “How did you know that?”Ed: “It is on your blog”Mark: “Yeah”
Ed:“Are you alright?”Mark: “I need you”Ed: “I am here for you”Mark: “No, I need your algorithm to rank chess players”
![Page 11: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/11.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”Ed: “Hi Mark”Mark: “Eduardo”Ed: “You and Erica splt up?”Mark: “How did you know that?”Ed: “It is on your blog”Mark: “Yeah”Ed:“Are you alright?”
Mark: “I need you”Ed: “I am here for you”Mark: “No, I need your algorithm to rank chess players”
![Page 12: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/12.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”Ed: “Hi Mark”Mark: “Eduardo”Ed: “You and Erica splt up?”Mark: “How did you know that?”Ed: “It is on your blog”Mark: “Yeah”Ed:“Are you alright?”Mark: “I need you”
Ed: “I am here for you”Mark: “No, I need your algorithm to rank chess players”
![Page 13: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/13.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”Ed: “Hi Mark”Mark: “Eduardo”Ed: “You and Erica splt up?”Mark: “How did you know that?”Ed: “It is on your blog”Mark: “Yeah”Ed:“Are you alright?”Mark: “I need you”Ed: “I am here for you”
Mark: “No, I need your algorithm to rank chess players”
![Page 14: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/14.jpg)
A Scene
Eduardo is entering a dorm room in Harvard University, as Mark isat his laptop.Mark:“Done! Perfect timing. Eduardo is here and he is going tohave the key ingredient”Ed: “Hi Mark”Mark: “Eduardo”Ed: “You and Erica splt up?”Mark: “How did you know that?”Ed: “It is on your blog”Mark: “Yeah”Ed:“Are you alright?”Mark: “I need you”Ed: “I am here for you”Mark: “No, I need your algorithm to rank chess players”
![Page 15: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/15.jpg)
Ed: “Are you OK?”
Mark: “We are ranking girls”Ed: “You mean the other students”Mark: “Yeah”Ed: “Do you think it is such a good idea?”Mark: “I need your algorithm - I need your algorithm”Ed: “With each girl’s base rating 1400...”Ed proceeds to write the formulae (on a window with a crayon)
![Page 16: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/16.jpg)
Ed: “Are you OK?”Mark: “We are ranking girls”
Ed: “You mean the other students”Mark: “Yeah”Ed: “Do you think it is such a good idea?”Mark: “I need your algorithm - I need your algorithm”Ed: “With each girl’s base rating 1400...”Ed proceeds to write the formulae (on a window with a crayon)
![Page 17: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/17.jpg)
Ed: “Are you OK?”Mark: “We are ranking girls”Ed: “You mean the other students”
Mark: “Yeah”Ed: “Do you think it is such a good idea?”Mark: “I need your algorithm - I need your algorithm”Ed: “With each girl’s base rating 1400...”Ed proceeds to write the formulae (on a window with a crayon)
![Page 18: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/18.jpg)
Ed: “Are you OK?”Mark: “We are ranking girls”Ed: “You mean the other students”Mark: “Yeah”
Ed: “Do you think it is such a good idea?”Mark: “I need your algorithm - I need your algorithm”Ed: “With each girl’s base rating 1400...”Ed proceeds to write the formulae (on a window with a crayon)
![Page 19: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/19.jpg)
Ed: “Are you OK?”Mark: “We are ranking girls”Ed: “You mean the other students”Mark: “Yeah”Ed: “Do you think it is such a good idea?”
Mark: “I need your algorithm - I need your algorithm”Ed: “With each girl’s base rating 1400...”Ed proceeds to write the formulae (on a window with a crayon)
![Page 20: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/20.jpg)
Ed: “Are you OK?”Mark: “We are ranking girls”Ed: “You mean the other students”Mark: “Yeah”Ed: “Do you think it is such a good idea?”Mark: “I need your algorithm - I need your algorithm”
Ed: “With each girl’s base rating 1400...”Ed proceeds to write the formulae (on a window with a crayon)
![Page 21: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/21.jpg)
Ed: “Are you OK?”Mark: “We are ranking girls”Ed: “You mean the other students”Mark: “Yeah”Ed: “Do you think it is such a good idea?”Mark: “I need your algorithm - I need your algorithm”Ed: “With each girl’s base rating 1400...”
Ed proceeds to write the formulae (on a window with a crayon)
![Page 22: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/22.jpg)
Ed: “Are you OK?”Mark: “We are ranking girls”Ed: “You mean the other students”Mark: “Yeah”Ed: “Do you think it is such a good idea?”Mark: “I need your algorithm - I need your algorithm”Ed: “With each girl’s base rating 1400...”Ed proceeds to write the formulae (on a window with a crayon)
![Page 23: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/23.jpg)
Eduardo’s Formula!
Ea =1
1 + 10 (Rb−Ra)400
Eb =1
1 + 10 (Ra−Rb)400
![Page 24: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/24.jpg)
Eduardo’s Formula!
Ea =1
1 + 10 (Rb−Ra)400
Eb =1
1 + 10 (Ra−Rb)400
![Page 25: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/25.jpg)
Eduardo’s Formula!
Ea =1
1 + 10 (Rb−Ra)400
Eb =1
1 + 10 (Ra−Rb)400
![Page 26: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/26.jpg)
Mark’s Observation
Mark:“When any two girls are matched up there’s an expectation ofwhich will win based on their current rating, right?And all those expectations are expressed this way”
![Page 27: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/27.jpg)
Mark’s Observation
Mark:“When any two girls are matched up
there’s an expectation ofwhich will win based on their current rating, right?And all those expectations are expressed this way”
![Page 28: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/28.jpg)
Mark’s Observation
Mark:“When any two girls are matched up there’s an expectation ofwhich will win
based on their current rating, right?And all those expectations are expressed this way”
![Page 29: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/29.jpg)
Mark’s Observation
Mark:“When any two girls are matched up there’s an expectation ofwhich will win based on their current rating, right?
And all those expectations are expressed this way”
![Page 30: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/30.jpg)
Mark’s Observation
Mark:“When any two girls are matched up there’s an expectation ofwhich will win based on their current rating, right?And all those expectations are expressed this way”
![Page 31: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/31.jpg)
The Social Network
Movie relesed in the USA on October 01, 2010 by ColumbiaPicturesAdapted from the 2009 book “The accidental Billionnaires” byBen MezrichThe film portrays the founding of the social networking websiteFACEBOOK and the ensuing legal battles
CAST:Jesse Eisenberg as Mark Zuckerberg (founder of Facebook)Andrew Garfield as Eduardo Saverin (cofounder)Justin Timblelake as Sean Parker (cofounder)
![Page 32: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/32.jpg)
The Social Network
Movie relesed in the USA on October 01, 2010 by ColumbiaPictures
Adapted from the 2009 book “The accidental Billionnaires” byBen MezrichThe film portrays the founding of the social networking websiteFACEBOOK and the ensuing legal battles
CAST:Jesse Eisenberg as Mark Zuckerberg (founder of Facebook)Andrew Garfield as Eduardo Saverin (cofounder)Justin Timblelake as Sean Parker (cofounder)
![Page 33: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/33.jpg)
The Social Network
Movie relesed in the USA on October 01, 2010 by ColumbiaPicturesAdapted from the 2009 book “The accidental Billionnaires” byBen Mezrich
The film portrays the founding of the social networking websiteFACEBOOK and the ensuing legal battles
CAST:Jesse Eisenberg as Mark Zuckerberg (founder of Facebook)Andrew Garfield as Eduardo Saverin (cofounder)Justin Timblelake as Sean Parker (cofounder)
![Page 34: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/34.jpg)
The Social Network
Movie relesed in the USA on October 01, 2010 by ColumbiaPicturesAdapted from the 2009 book “The accidental Billionnaires” byBen MezrichThe film portrays the founding of the social networking websiteFACEBOOK and the ensuing legal battles
CAST:Jesse Eisenberg as Mark Zuckerberg (founder of Facebook)Andrew Garfield as Eduardo Saverin (cofounder)Justin Timblelake as Sean Parker (cofounder)
![Page 35: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/35.jpg)
The Social Network
Movie relesed in the USA on October 01, 2010 by ColumbiaPicturesAdapted from the 2009 book “The accidental Billionnaires” byBen MezrichThe film portrays the founding of the social networking websiteFACEBOOK and the ensuing legal battles
CAST:
Jesse Eisenberg as Mark Zuckerberg (founder of Facebook)Andrew Garfield as Eduardo Saverin (cofounder)Justin Timblelake as Sean Parker (cofounder)
![Page 36: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/36.jpg)
The Social Network
Movie relesed in the USA on October 01, 2010 by ColumbiaPicturesAdapted from the 2009 book “The accidental Billionnaires” byBen MezrichThe film portrays the founding of the social networking websiteFACEBOOK and the ensuing legal battles
CAST:Jesse Eisenberg as Mark Zuckerberg (founder of Facebook)
Andrew Garfield as Eduardo Saverin (cofounder)Justin Timblelake as Sean Parker (cofounder)
![Page 37: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/37.jpg)
The Social Network
Movie relesed in the USA on October 01, 2010 by ColumbiaPicturesAdapted from the 2009 book “The accidental Billionnaires” byBen MezrichThe film portrays the founding of the social networking websiteFACEBOOK and the ensuing legal battles
CAST:Jesse Eisenberg as Mark Zuckerberg (founder of Facebook)Andrew Garfield as Eduardo Saverin (cofounder)
Justin Timblelake as Sean Parker (cofounder)
![Page 38: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/38.jpg)
The Social Network
Movie relesed in the USA on October 01, 2010 by ColumbiaPicturesAdapted from the 2009 book “The accidental Billionnaires” byBen MezrichThe film portrays the founding of the social networking websiteFACEBOOK and the ensuing legal battles
CAST:Jesse Eisenberg as Mark Zuckerberg (founder of Facebook)Andrew Garfield as Eduardo Saverin (cofounder)Justin Timblelake as Sean Parker (cofounder)
![Page 39: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/39.jpg)
Awards
8 Nominations for Academy Awards includingBest Picture, Best Director and Best ActorWon ThreeBest Adapted Screenplay, Best Original Score, and Best FilmEditingIn 68th Golden Globe Awards won the award forBest Moion Picture, Best Diector, Best Screenplay and BestOriginal Score
![Page 40: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/40.jpg)
Awards
8 Nominations for Academy Awards including
Best Picture, Best Director and Best ActorWon ThreeBest Adapted Screenplay, Best Original Score, and Best FilmEditingIn 68th Golden Globe Awards won the award forBest Moion Picture, Best Diector, Best Screenplay and BestOriginal Score
![Page 41: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/41.jpg)
Awards
8 Nominations for Academy Awards includingBest Picture, Best Director and Best Actor
Won ThreeBest Adapted Screenplay, Best Original Score, and Best FilmEditingIn 68th Golden Globe Awards won the award forBest Moion Picture, Best Diector, Best Screenplay and BestOriginal Score
![Page 42: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/42.jpg)
Awards
8 Nominations for Academy Awards includingBest Picture, Best Director and Best ActorWon Three
Best Adapted Screenplay, Best Original Score, and Best FilmEditingIn 68th Golden Globe Awards won the award forBest Moion Picture, Best Diector, Best Screenplay and BestOriginal Score
![Page 43: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/43.jpg)
Awards
8 Nominations for Academy Awards includingBest Picture, Best Director and Best ActorWon ThreeBest Adapted Screenplay, Best Original Score, and Best FilmEditing
In 68th Golden Globe Awards won the award forBest Moion Picture, Best Diector, Best Screenplay and BestOriginal Score
![Page 44: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/44.jpg)
Awards
8 Nominations for Academy Awards includingBest Picture, Best Director and Best ActorWon ThreeBest Adapted Screenplay, Best Original Score, and Best FilmEditingIn 68th Golden Globe Awards won the award for
Best Moion Picture, Best Diector, Best Screenplay and BestOriginal Score
![Page 45: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/45.jpg)
Awards
8 Nominations for Academy Awards includingBest Picture, Best Director and Best ActorWon ThreeBest Adapted Screenplay, Best Original Score, and Best FilmEditingIn 68th Golden Globe Awards won the award forBest Moion Picture, Best Diector, Best Screenplay and BestOriginal Score
![Page 46: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/46.jpg)
RATING and RANKING
![Page 47: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/47.jpg)
Rating
Given n objects a Rating assigns n REAL NUMBERS (positive ornegative), (preferably distinct), one each to these n objects
![Page 48: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/48.jpg)
Rating
Given n objects
a Rating assigns n REAL NUMBERS (positive ornegative), (preferably distinct), one each to these n objects
![Page 49: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/49.jpg)
Rating
Given n objects a Rating assigns n REAL NUMBERS
(positive ornegative), (preferably distinct), one each to these n objects
![Page 50: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/50.jpg)
Rating
Given n objects a Rating assigns n REAL NUMBERS (positive ornegative),
(preferably distinct), one each to these n objects
![Page 51: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/51.jpg)
Rating
Given n objects a Rating assigns n REAL NUMBERS (positive ornegative), (preferably distinct),
one each to these n objects
![Page 52: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/52.jpg)
Rating
Given n objects a Rating assigns n REAL NUMBERS (positive ornegative), (preferably distinct), one each to these n objects
![Page 53: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/53.jpg)
Ranking
Given n objects a Ranking assigns the n positive integers1, 2, 3, · · · , n, one each to these n objectsEvery Rating creates a Ranking by arranging the ratings indescending order
![Page 54: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/54.jpg)
Ranking
Given n objects
a Ranking assigns the n positive integers1, 2, 3, · · · , n, one each to these n objectsEvery Rating creates a Ranking by arranging the ratings indescending order
![Page 55: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/55.jpg)
Ranking
Given n objects a Ranking assigns
the n positive integers1, 2, 3, · · · , n, one each to these n objectsEvery Rating creates a Ranking by arranging the ratings indescending order
![Page 56: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/56.jpg)
Ranking
Given n objects a Ranking assigns the n positive integers1, 2, 3, · · · , n,
one each to these n objectsEvery Rating creates a Ranking by arranging the ratings indescending order
![Page 57: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/57.jpg)
Ranking
Given n objects a Ranking assigns the n positive integers1, 2, 3, · · · , n, one each to these n objects
Every Rating creates a Ranking by arranging the ratings indescending order
![Page 58: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/58.jpg)
Ranking
Given n objects a Ranking assigns the n positive integers1, 2, 3, · · · , n, one each to these n objectsEvery Rating creates a Ranking by arranging the ratings indescending order
![Page 59: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/59.jpg)
Pairwise Comparison
It is well known that human beings have difficulty ranking any setof items of size bigger than fiveHowever we are all particularly adept at pairwise comparisonSuch pairwise comparisons are at the heart of most of the methodsof rating and ranking
![Page 60: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/60.jpg)
Pairwise Comparison
It is well known that human beings have difficulty ranking any setof items of size bigger than five
However we are all particularly adept at pairwise comparisonSuch pairwise comparisons are at the heart of most of the methodsof rating and ranking
![Page 61: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/61.jpg)
Pairwise Comparison
It is well known that human beings have difficulty ranking any setof items of size bigger than fiveHowever we are all particularly adept at pairwise comparison
Such pairwise comparisons are at the heart of most of the methodsof rating and ranking
![Page 62: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/62.jpg)
Pairwise Comparison
It is well known that human beings have difficulty ranking any setof items of size bigger than fiveHowever we are all particularly adept at pairwise comparisonSuch pairwise comparisons are at the heart of most of the methodsof rating and ranking
![Page 63: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/63.jpg)
General Mathematical Techniques
Most of the rating system use one or more of the following:
I Linear Algebra - Linear Systems of Equations, eigenvalues andEigenvectors)
I Optimization
I Statistics (Markov techniques)
I Game Theory
![Page 64: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/64.jpg)
General Mathematical Techniques
Most of the rating system use one or more of the following:
I Linear Algebra - Linear Systems of Equations, eigenvalues andEigenvectors)
I Optimization
I Statistics (Markov techniques)
I Game Theory
![Page 65: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/65.jpg)
General Mathematical Techniques
Most of the rating system use one or more of the following:
I Linear Algebra - Linear Systems of Equations, eigenvalues andEigenvectors)
I Optimization
I Statistics (Markov techniques)
I Game Theory
![Page 66: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/66.jpg)
General Mathematical Techniques
Most of the rating system use one or more of the following:
I Linear Algebra - Linear Systems of Equations, eigenvalues andEigenvectors)
I Optimization
I Statistics (Markov techniques)
I Game Theory
![Page 67: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/67.jpg)
General Mathematical Techniques
Most of the rating system use one or more of the following:
I Linear Algebra - Linear Systems of Equations, eigenvalues andEigenvectors)
I Optimization
I Statistics (Markov techniques)
I Game Theory
![Page 68: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/68.jpg)
ARROW’s IMPOSSIBILITY THEOREM
![Page 69: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/69.jpg)
Arrow’s Four Criteria
I Every voter should be free to rank the candidates in any orderhe or she likes(This criterion is known as the Unrestricted Domain criterion)
I If only a subset of the candidates is considered the rankingorder within the subset should not change(Independence of Irrelevant Alternatives)
I If all voters choose candidate A over candidate B, then thevoting system should rank A ahead of B(Pereto Principle)
I No single voter should have disproportionate control over anelection(Non − dictatorship)
![Page 70: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/70.jpg)
Arrow’s Four Criteria
I Every voter should be free to rank the candidates in any orderhe or she likes
(This criterion is known as the Unrestricted Domain criterion)
I If only a subset of the candidates is considered the rankingorder within the subset should not change(Independence of Irrelevant Alternatives)
I If all voters choose candidate A over candidate B, then thevoting system should rank A ahead of B(Pereto Principle)
I No single voter should have disproportionate control over anelection(Non − dictatorship)
![Page 71: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/71.jpg)
Arrow’s Four Criteria
I Every voter should be free to rank the candidates in any orderhe or she likes(This criterion is known as the Unrestricted Domain criterion)
I If only a subset of the candidates is considered the rankingorder within the subset should not change(Independence of Irrelevant Alternatives)
I If all voters choose candidate A over candidate B, then thevoting system should rank A ahead of B(Pereto Principle)
I No single voter should have disproportionate control over anelection(Non − dictatorship)
![Page 72: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/72.jpg)
Arrow’s Four Criteria
I Every voter should be free to rank the candidates in any orderhe or she likes(This criterion is known as the Unrestricted Domain criterion)
I If only a subset of the candidates is considered the rankingorder within the subset should not change
(Independence of Irrelevant Alternatives)
I If all voters choose candidate A over candidate B, then thevoting system should rank A ahead of B(Pereto Principle)
I No single voter should have disproportionate control over anelection(Non − dictatorship)
![Page 73: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/73.jpg)
Arrow’s Four Criteria
I Every voter should be free to rank the candidates in any orderhe or she likes(This criterion is known as the Unrestricted Domain criterion)
I If only a subset of the candidates is considered the rankingorder within the subset should not change(Independence of Irrelevant Alternatives)
I If all voters choose candidate A over candidate B, then thevoting system should rank A ahead of B(Pereto Principle)
I No single voter should have disproportionate control over anelection(Non − dictatorship)
![Page 74: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/74.jpg)
Arrow’s Four Criteria
I Every voter should be free to rank the candidates in any orderhe or she likes(This criterion is known as the Unrestricted Domain criterion)
I If only a subset of the candidates is considered the rankingorder within the subset should not change(Independence of Irrelevant Alternatives)
I If all voters choose candidate A over candidate B, then thevoting system should rank A ahead of B
(Pereto Principle)
I No single voter should have disproportionate control over anelection(Non − dictatorship)
![Page 75: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/75.jpg)
Arrow’s Four Criteria
I Every voter should be free to rank the candidates in any orderhe or she likes(This criterion is known as the Unrestricted Domain criterion)
I If only a subset of the candidates is considered the rankingorder within the subset should not change(Independence of Irrelevant Alternatives)
I If all voters choose candidate A over candidate B, then thevoting system should rank A ahead of B(Pereto Principle)
I No single voter should have disproportionate control over anelection(Non − dictatorship)
![Page 76: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/76.jpg)
Arrow’s Four Criteria
I Every voter should be free to rank the candidates in any orderhe or she likes(This criterion is known as the Unrestricted Domain criterion)
I If only a subset of the candidates is considered the rankingorder within the subset should not change(Independence of Irrelevant Alternatives)
I If all voters choose candidate A over candidate B, then thevoting system should rank A ahead of B(Pereto Principle)
I No single voter should have disproportionate control over anelection
(Non − dictatorship)
![Page 77: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/77.jpg)
Arrow’s Four Criteria
I Every voter should be free to rank the candidates in any orderhe or she likes(This criterion is known as the Unrestricted Domain criterion)
I If only a subset of the candidates is considered the rankingorder within the subset should not change(Independence of Irrelevant Alternatives)
I If all voters choose candidate A over candidate B, then thevoting system should rank A ahead of B(Pereto Principle)
I No single voter should have disproportionate control over anelection(Non − dictatorship)
![Page 78: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/78.jpg)
Arrow’s Theorem (1951)
The four criteria seem to be obvious or self evident - or just PlainCommon Sensebut his result is notArrow’s Impossibility Theorem:
It is IMPOSSIBLE for any
voting system to satisfy all four
common sense criteria simultaneously
(NOBEL PRIZE IN ECONOMICS - 1972)
![Page 79: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/79.jpg)
Arrow’s Theorem (1951)
The four criteria seem to be obvious or self evident - or just PlainCommon Sense
but his result is notArrow’s Impossibility Theorem:
It is IMPOSSIBLE for any
voting system to satisfy all four
common sense criteria simultaneously
(NOBEL PRIZE IN ECONOMICS - 1972)
![Page 80: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/80.jpg)
Arrow’s Theorem (1951)
The four criteria seem to be obvious or self evident - or just PlainCommon Sensebut his result is not
Arrow’s Impossibility Theorem:
It is IMPOSSIBLE for any
voting system to satisfy all four
common sense criteria simultaneously
(NOBEL PRIZE IN ECONOMICS - 1972)
![Page 81: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/81.jpg)
Arrow’s Theorem (1951)
The four criteria seem to be obvious or self evident - or just PlainCommon Sensebut his result is notArrow’s Impossibility Theorem:
It is IMPOSSIBLE for any
voting system to satisfy all four
common sense criteria simultaneously
(NOBEL PRIZE IN ECONOMICS - 1972)
![Page 82: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/82.jpg)
Arrow’s Theorem (1951)
The four criteria seem to be obvious or self evident - or just PlainCommon Sensebut his result is notArrow’s Impossibility Theorem:
It is IMPOSSIBLE for any
voting system to satisfy all four
common sense criteria simultaneously
(NOBEL PRIZE IN ECONOMICS - 1972)
![Page 83: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/83.jpg)
Arrow’s Theorem (1951)
The four criteria seem to be obvious or self evident - or just PlainCommon Sensebut his result is notArrow’s Impossibility Theorem:
It is IMPOSSIBLE for any
voting system to satisfy all four
common sense criteria simultaneously
(NOBEL PRIZE IN ECONOMICS - 1972)
![Page 84: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/84.jpg)
Arrow’s Theorem (1951)
The four criteria seem to be obvious or self evident - or just PlainCommon Sensebut his result is notArrow’s Impossibility Theorem:
It is IMPOSSIBLE for any
voting system to satisfy all four
common sense criteria simultaneously
(NOBEL PRIZE IN ECONOMICS - 1972)
![Page 85: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/85.jpg)
Arrow’s Theorem (1951)
The four criteria seem to be obvious or self evident - or just PlainCommon Sensebut his result is notArrow’s Impossibility Theorem:
It is IMPOSSIBLE for any
voting system to satisfy all four
common sense criteria simultaneously
(NOBEL PRIZE IN ECONOMICS - 1972)
![Page 86: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/86.jpg)
Arrow’s Theorem (1951)
The four criteria seem to be obvious or self evident - or just PlainCommon Sensebut his result is notArrow’s Impossibility Theorem:
It is IMPOSSIBLE for any
voting system to satisfy all four
common sense criteria simultaneously
(NOBEL PRIZE IN ECONOMICS - 1972)
![Page 87: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/87.jpg)
BCS (Bowl Championship Series)
In place since 1998Since its inception in 1998, the NCAA’s Bowl Championship Serieshas weathered criticism from nearly all directions.
![Page 88: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/88.jpg)
BCS (Bowl Championship Series)
In place since 1998
Since its inception in 1998, the NCAA’s Bowl Championship Serieshas weathered criticism from nearly all directions.
![Page 89: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/89.jpg)
BCS (Bowl Championship Series)
In place since 1998Since its inception in 1998, the NCAA’s Bowl Championship Serieshas weathered criticism from nearly all directions.
![Page 90: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/90.jpg)
Massey System
Proposed by Kenneth Massey in 1997 (as an undergraduatestudent)Basically based on Least Square Solution of a Linear SystemModified version used in BCS (BOWL CHAMPIONSHIPSERIES)
![Page 91: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/91.jpg)
Massey System
Proposed by Kenneth Massey in 1997 (as an undergraduatestudent)
Basically based on Least Square Solution of a Linear SystemModified version used in BCS (BOWL CHAMPIONSHIPSERIES)
![Page 92: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/92.jpg)
Massey System
Proposed by Kenneth Massey in 1997 (as an undergraduatestudent)Basically based on Least Square Solution of a Linear System
Modified version used in BCS (BOWL CHAMPIONSHIPSERIES)
![Page 93: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/93.jpg)
Massey System
Proposed by Kenneth Massey in 1997 (as an undergraduatestudent)Basically based on Least Square Solution of a Linear SystemModified version used in BCS (BOWL CHAMPIONSHIPSERIES)
![Page 94: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/94.jpg)
Colley’s Winning Proportion Ranking
At the beginning each team is given an equal ranking of 12
Dynamically adjust the ranking as the turnament progressesAt some stage if Team Ti has played ni games and won wi gamesand lost `i games then define
ri =1 + wi
2 + niNote:We have wi + `i = niIf Ti has played 2k games and won exactly half of these, namely kgames, then
ri =1 + k
2 + 2k
=1
2
![Page 95: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/95.jpg)
Colley’s Winning Proportion Ranking
At the beginning each team is given an equal ranking of 12
Dynamically adjust the ranking as the turnament progressesAt some stage if Team Ti has played ni games and won wi gamesand lost `i games then define
ri =1 + wi
2 + niNote:We have wi + `i = niIf Ti has played 2k games and won exactly half of these, namely kgames, then
ri =1 + k
2 + 2k
=1
2
![Page 96: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/96.jpg)
Colley’s Winning Proportion Ranking
At the beginning each team is given an equal ranking of 12
Dynamically adjust the ranking as the turnament progresses
At some stage if Team Ti has played ni games and won wi gamesand lost `i games then define
ri =1 + wi
2 + niNote:We have wi + `i = niIf Ti has played 2k games and won exactly half of these, namely kgames, then
ri =1 + k
2 + 2k
=1
2
![Page 97: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/97.jpg)
Colley’s Winning Proportion Ranking
At the beginning each team is given an equal ranking of 12
Dynamically adjust the ranking as the turnament progressesAt some stage if Team Ti has played ni games
and won wi gamesand lost `i games then define
ri =1 + wi
2 + niNote:We have wi + `i = niIf Ti has played 2k games and won exactly half of these, namely kgames, then
ri =1 + k
2 + 2k
=1
2
![Page 98: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/98.jpg)
Colley’s Winning Proportion Ranking
At the beginning each team is given an equal ranking of 12
Dynamically adjust the ranking as the turnament progressesAt some stage if Team Ti has played ni games and won wi games
and lost `i games then define
ri =1 + wi
2 + niNote:We have wi + `i = niIf Ti has played 2k games and won exactly half of these, namely kgames, then
ri =1 + k
2 + 2k
=1
2
![Page 99: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/99.jpg)
Colley’s Winning Proportion Ranking
At the beginning each team is given an equal ranking of 12
Dynamically adjust the ranking as the turnament progressesAt some stage if Team Ti has played ni games and won wi gamesand lost `i games
then define
ri =1 + wi
2 + niNote:We have wi + `i = niIf Ti has played 2k games and won exactly half of these, namely kgames, then
ri =1 + k
2 + 2k
=1
2
![Page 100: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/100.jpg)
Colley’s Winning Proportion Ranking
At the beginning each team is given an equal ranking of 12
Dynamically adjust the ranking as the turnament progressesAt some stage if Team Ti has played ni games and won wi gamesand lost `i games then define
ri =1 + wi
2 + ni
Note:We have wi + `i = niIf Ti has played 2k games and won exactly half of these, namely kgames, then
ri =1 + k
2 + 2k
=1
2
![Page 101: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/101.jpg)
Colley’s Winning Proportion Ranking
At the beginning each team is given an equal ranking of 12
Dynamically adjust the ranking as the turnament progressesAt some stage if Team Ti has played ni games and won wi gamesand lost `i games then define
ri =1 + wi
2 + niNote:
We have wi + `i = niIf Ti has played 2k games and won exactly half of these, namely kgames, then
ri =1 + k
2 + 2k
=1
2
![Page 102: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/102.jpg)
Colley’s Winning Proportion Ranking
At the beginning each team is given an equal ranking of 12
Dynamically adjust the ranking as the turnament progressesAt some stage if Team Ti has played ni games and won wi gamesand lost `i games then define
ri =1 + wi
2 + niNote:We have wi + `i = ni
If Ti has played 2k games and won exactly half of these, namely kgames, then
ri =1 + k
2 + 2k
=1
2
![Page 103: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/103.jpg)
Colley’s Winning Proportion Ranking
At the beginning each team is given an equal ranking of 12
Dynamically adjust the ranking as the turnament progressesAt some stage if Team Ti has played ni games and won wi gamesand lost `i games then define
ri =1 + wi
2 + niNote:We have wi + `i = niIf Ti has played 2k games and won exactly half of these, namely kgames, then
ri =1 + k
2 + 2k
=1
2
![Page 104: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/104.jpg)
Colley’s Winning Proportion Ranking
At the beginning each team is given an equal ranking of 12
Dynamically adjust the ranking as the turnament progressesAt some stage if Team Ti has played ni games and won wi gamesand lost `i games then define
ri =1 + wi
2 + niNote:We have wi + `i = niIf Ti has played 2k games and won exactly half of these, namely kgames, then
ri =1 + k
2 + 2k
=1
2
![Page 105: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/105.jpg)
Controversies and Obama
2008 U.S. Presidential Election CampaignObama wa asked to describe one thing about sports he wouldchange, andObama mentioned his disgust with using BCS rating sytem todetermine bowl-game participants2009:“We need a playoff,” President Elect Obama told reporters afterbeing asked about Florida’s 24-14 victory over Oklahoma in BCSchampionship game. “If I’m Utah, or if I’m USC or if I’m Texas, Imight still have some quibbles.”Senator Orrin Hatch of Utah asked the US Justice Department toreview the legality of the BCS for possible violation of antitrustlaws
![Page 106: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/106.jpg)
Controversies and Obama
2008 U.S. Presidential Election Campaign
Obama wa asked to describe one thing about sports he wouldchange, andObama mentioned his disgust with using BCS rating sytem todetermine bowl-game participants2009:“We need a playoff,” President Elect Obama told reporters afterbeing asked about Florida’s 24-14 victory over Oklahoma in BCSchampionship game. “If I’m Utah, or if I’m USC or if I’m Texas, Imight still have some quibbles.”Senator Orrin Hatch of Utah asked the US Justice Department toreview the legality of the BCS for possible violation of antitrustlaws
![Page 107: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/107.jpg)
Controversies and Obama
2008 U.S. Presidential Election CampaignObama wa asked to describe one thing about sports he wouldchange, and
Obama mentioned his disgust with using BCS rating sytem todetermine bowl-game participants2009:“We need a playoff,” President Elect Obama told reporters afterbeing asked about Florida’s 24-14 victory over Oklahoma in BCSchampionship game. “If I’m Utah, or if I’m USC or if I’m Texas, Imight still have some quibbles.”Senator Orrin Hatch of Utah asked the US Justice Department toreview the legality of the BCS for possible violation of antitrustlaws
![Page 108: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/108.jpg)
Controversies and Obama
2008 U.S. Presidential Election CampaignObama wa asked to describe one thing about sports he wouldchange, andObama mentioned his disgust with using BCS rating sytem todetermine bowl-game participants
2009:“We need a playoff,” President Elect Obama told reporters afterbeing asked about Florida’s 24-14 victory over Oklahoma in BCSchampionship game. “If I’m Utah, or if I’m USC or if I’m Texas, Imight still have some quibbles.”Senator Orrin Hatch of Utah asked the US Justice Department toreview the legality of the BCS for possible violation of antitrustlaws
![Page 109: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/109.jpg)
Controversies and Obama
2008 U.S. Presidential Election CampaignObama wa asked to describe one thing about sports he wouldchange, andObama mentioned his disgust with using BCS rating sytem todetermine bowl-game participants2009:
“We need a playoff,” President Elect Obama told reporters afterbeing asked about Florida’s 24-14 victory over Oklahoma in BCSchampionship game. “If I’m Utah, or if I’m USC or if I’m Texas, Imight still have some quibbles.”Senator Orrin Hatch of Utah asked the US Justice Department toreview the legality of the BCS for possible violation of antitrustlaws
![Page 110: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/110.jpg)
Controversies and Obama
2008 U.S. Presidential Election CampaignObama wa asked to describe one thing about sports he wouldchange, andObama mentioned his disgust with using BCS rating sytem todetermine bowl-game participants2009:“We need a playoff,”
President Elect Obama told reporters afterbeing asked about Florida’s 24-14 victory over Oklahoma in BCSchampionship game. “If I’m Utah, or if I’m USC or if I’m Texas, Imight still have some quibbles.”Senator Orrin Hatch of Utah asked the US Justice Department toreview the legality of the BCS for possible violation of antitrustlaws
![Page 111: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/111.jpg)
Controversies and Obama
2008 U.S. Presidential Election CampaignObama wa asked to describe one thing about sports he wouldchange, andObama mentioned his disgust with using BCS rating sytem todetermine bowl-game participants2009:“We need a playoff,” President Elect Obama told reporters
afterbeing asked about Florida’s 24-14 victory over Oklahoma in BCSchampionship game. “If I’m Utah, or if I’m USC or if I’m Texas, Imight still have some quibbles.”Senator Orrin Hatch of Utah asked the US Justice Department toreview the legality of the BCS for possible violation of antitrustlaws
![Page 112: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/112.jpg)
Controversies and Obama
2008 U.S. Presidential Election CampaignObama wa asked to describe one thing about sports he wouldchange, andObama mentioned his disgust with using BCS rating sytem todetermine bowl-game participants2009:“We need a playoff,” President Elect Obama told reporters afterbeing asked about Florida’s 24-14 victory over Oklahoma in BCSchampionship game.
“If I’m Utah, or if I’m USC or if I’m Texas, Imight still have some quibbles.”Senator Orrin Hatch of Utah asked the US Justice Department toreview the legality of the BCS for possible violation of antitrustlaws
![Page 113: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/113.jpg)
Controversies and Obama
2008 U.S. Presidential Election CampaignObama wa asked to describe one thing about sports he wouldchange, andObama mentioned his disgust with using BCS rating sytem todetermine bowl-game participants2009:“We need a playoff,” President Elect Obama told reporters afterbeing asked about Florida’s 24-14 victory over Oklahoma in BCSchampionship game. “If I’m Utah, or if I’m USC or if I’m Texas, Imight still have some quibbles.”
Senator Orrin Hatch of Utah asked the US Justice Department toreview the legality of the BCS for possible violation of antitrustlaws
![Page 114: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/114.jpg)
Controversies and Obama
2008 U.S. Presidential Election CampaignObama wa asked to describe one thing about sports he wouldchange, andObama mentioned his disgust with using BCS rating sytem todetermine bowl-game participants2009:“We need a playoff,” President Elect Obama told reporters afterbeing asked about Florida’s 24-14 victory over Oklahoma in BCSchampionship game. “If I’m Utah, or if I’m USC or if I’m Texas, Imight still have some quibbles.”Senator Orrin Hatch of Utah asked the US Justice Department toreview the legality of the BCS for possible violation of antitrustlaws
![Page 115: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/115.jpg)
Controversies and Obama
2008 U.S. Presidential Election CampaignObama wa asked to describe one thing about sports he wouldchange, andObama mentioned his disgust with using BCS rating sytem todetermine bowl-game participants2009:“We need a playoff,” President Elect Obama told reporters afterbeing asked about Florida’s 24-14 victory over Oklahoma in BCSchampionship game. “If I’m Utah, or if I’m USC or if I’m Texas, Imight still have some quibbles.”Senator Orrin Hatch of Utah asked the US Justice Department toreview the legality of the BCS for possible violation of antitrustlaws
![Page 116: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/116.jpg)
End of the Road for BCS
2011:The BCS was put on notice that they are being scrutinized by theUS Justice Dpertment2012:On June 26, 2012, it was announced that the Bowl ChampionshipSeries will be replaced by a four-team playoff, effective for the2014-15 season to be known as the College Football Playoff.
![Page 117: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/117.jpg)
End of the Road for BCS
2011:
The BCS was put on notice that they are being scrutinized by theUS Justice Dpertment2012:On June 26, 2012, it was announced that the Bowl ChampionshipSeries will be replaced by a four-team playoff, effective for the2014-15 season to be known as the College Football Playoff.
![Page 118: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/118.jpg)
End of the Road for BCS
2011:The BCS was put on notice that they are being scrutinized by theUS Justice Dpertment
2012:On June 26, 2012, it was announced that the Bowl ChampionshipSeries will be replaced by a four-team playoff, effective for the2014-15 season to be known as the College Football Playoff.
![Page 119: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/119.jpg)
End of the Road for BCS
2011:The BCS was put on notice that they are being scrutinized by theUS Justice Dpertment2012:
On June 26, 2012, it was announced that the Bowl ChampionshipSeries will be replaced by a four-team playoff, effective for the2014-15 season to be known as the College Football Playoff.
![Page 120: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/120.jpg)
End of the Road for BCS
2011:The BCS was put on notice that they are being scrutinized by theUS Justice Dpertment2012:On June 26, 2012, it was announced that the Bowl ChampionshipSeries will be replaced by a four-team playoff, effective for the2014-15 season to be known as the College Football Playoff.
![Page 121: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/121.jpg)
Elo’s Rating
![Page 122: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/122.jpg)
Chess Rating
Arpad Elo (1903-1992)An avid Chess PlayerCreated an efficient method to rate and rank chess playersHis system was approved byUSCF (United States Chess Federation)FIDE (Federaton Internationale des Eches) - The World ChessFederationBecame popular outside chess world and adapted to rate othersports and competitive situations
![Page 123: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/123.jpg)
Chess Rating
Arpad Elo (1903-1992)
An avid Chess PlayerCreated an efficient method to rate and rank chess playersHis system was approved byUSCF (United States Chess Federation)FIDE (Federaton Internationale des Eches) - The World ChessFederationBecame popular outside chess world and adapted to rate othersports and competitive situations
![Page 124: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/124.jpg)
Chess Rating
Arpad Elo (1903-1992)An avid Chess Player
Created an efficient method to rate and rank chess playersHis system was approved byUSCF (United States Chess Federation)FIDE (Federaton Internationale des Eches) - The World ChessFederationBecame popular outside chess world and adapted to rate othersports and competitive situations
![Page 125: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/125.jpg)
Chess Rating
Arpad Elo (1903-1992)An avid Chess PlayerCreated an efficient method to rate and rank chess players
His system was approved byUSCF (United States Chess Federation)FIDE (Federaton Internationale des Eches) - The World ChessFederationBecame popular outside chess world and adapted to rate othersports and competitive situations
![Page 126: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/126.jpg)
Chess Rating
Arpad Elo (1903-1992)An avid Chess PlayerCreated an efficient method to rate and rank chess playersHis system was approved by
USCF (United States Chess Federation)FIDE (Federaton Internationale des Eches) - The World ChessFederationBecame popular outside chess world and adapted to rate othersports and competitive situations
![Page 127: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/127.jpg)
Chess Rating
Arpad Elo (1903-1992)An avid Chess PlayerCreated an efficient method to rate and rank chess playersHis system was approved byUSCF (United States Chess Federation)
FIDE (Federaton Internationale des Eches) - The World ChessFederationBecame popular outside chess world and adapted to rate othersports and competitive situations
![Page 128: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/128.jpg)
Chess Rating
Arpad Elo (1903-1992)An avid Chess PlayerCreated an efficient method to rate and rank chess playersHis system was approved byUSCF (United States Chess Federation)FIDE (Federaton Internationale des Eches) - The World ChessFederation
Became popular outside chess world and adapted to rate othersports and competitive situations
![Page 129: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/129.jpg)
Chess Rating
Arpad Elo (1903-1992)An avid Chess PlayerCreated an efficient method to rate and rank chess playersHis system was approved byUSCF (United States Chess Federation)FIDE (Federaton Internationale des Eches) - The World ChessFederationBecame popular outside chess world and adapted to rate othersports and competitive situations
![Page 130: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/130.jpg)
The Basic Formulation
Based on the premise that“the performance of a player is a normally distributed randomvariable”Keep Updating the rating after each game(ri )old is the rating of Player Pi before he plays a game(ri )new is the rating of Player Pi after he plays the gameHow are (ri )old and (ri )new related?
![Page 131: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/131.jpg)
The Basic Formulation
Based on the premise that“the performance of a player is a normally distributed randomvariable”
Keep Updating the rating after each game(ri )old is the rating of Player Pi before he plays a game(ri )new is the rating of Player Pi after he plays the gameHow are (ri )old and (ri )new related?
![Page 132: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/132.jpg)
The Basic Formulation
Based on the premise that“the performance of a player is a normally distributed randomvariable”Keep Updating the rating after each game
(ri )old is the rating of Player Pi before he plays a game(ri )new is the rating of Player Pi after he plays the gameHow are (ri )old and (ri )new related?
![Page 133: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/133.jpg)
The Basic Formulation
Based on the premise that“the performance of a player is a normally distributed randomvariable”Keep Updating the rating after each game(ri )old is the rating of Player Pi before he plays a game
(ri )new is the rating of Player Pi after he plays the gameHow are (ri )old and (ri )new related?
![Page 134: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/134.jpg)
The Basic Formulation
Based on the premise that“the performance of a player is a normally distributed randomvariable”Keep Updating the rating after each game(ri )old is the rating of Player Pi before he plays a game(ri )new is the rating of Player Pi after he plays the game
How are (ri )old and (ri )new related?
![Page 135: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/135.jpg)
The Basic Formulation
Based on the premise that“the performance of a player is a normally distributed randomvariable”Keep Updating the rating after each game(ri )old is the rating of Player Pi before he plays a game(ri )new is the rating of Player Pi after he plays the gameHow are (ri )old and (ri )new related?
![Page 136: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/136.jpg)
Elo’s Hypothesis
µ is the mean score of Pi till that timeS is the score in the new gameS − µ is the variation (could be positive or negative or zero)The correction factor to the old ratng of Pi is proportional to thevariation S − µ, that is,
(ri )new = (ri )old + K (S − µ)
where K is the constant of proportion.Elo originally set K = 10For chess games,
S =
1 if Pi wins12 if Pi draws0 if Pi loses
![Page 137: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/137.jpg)
Elo’s Hypothesis
µ is the mean score of Pi till that time
S is the score in the new gameS − µ is the variation (could be positive or negative or zero)The correction factor to the old ratng of Pi is proportional to thevariation S − µ, that is,
(ri )new = (ri )old + K (S − µ)
where K is the constant of proportion.Elo originally set K = 10For chess games,
S =
1 if Pi wins12 if Pi draws0 if Pi loses
![Page 138: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/138.jpg)
Elo’s Hypothesis
µ is the mean score of Pi till that timeS is the score in the new game
S − µ is the variation (could be positive or negative or zero)The correction factor to the old ratng of Pi is proportional to thevariation S − µ, that is,
(ri )new = (ri )old + K (S − µ)
where K is the constant of proportion.Elo originally set K = 10For chess games,
S =
1 if Pi wins12 if Pi draws0 if Pi loses
![Page 139: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/139.jpg)
Elo’s Hypothesis
µ is the mean score of Pi till that timeS is the score in the new gameS − µ is the variation (could be positive or negative or zero)
The correction factor to the old ratng of Pi is proportional to thevariation S − µ, that is,
(ri )new = (ri )old + K (S − µ)
where K is the constant of proportion.Elo originally set K = 10For chess games,
S =
1 if Pi wins12 if Pi draws0 if Pi loses
![Page 140: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/140.jpg)
Elo’s Hypothesis
µ is the mean score of Pi till that timeS is the score in the new gameS − µ is the variation (could be positive or negative or zero)The correction factor to the old ratng of Pi is proportional to thevariation S − µ, that is,
(ri )new = (ri )old + K (S − µ)
where K is the constant of proportion.Elo originally set K = 10For chess games,
S =
1 if Pi wins12 if Pi draws0 if Pi loses
![Page 141: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/141.jpg)
Elo’s Hypothesis
µ is the mean score of Pi till that timeS is the score in the new gameS − µ is the variation (could be positive or negative or zero)The correction factor to the old ratng of Pi is proportional to thevariation S − µ, that is,
(ri )new = (ri )old + K (S − µ)
where K is the constant of proportion.Elo originally set K = 10For chess games,
S =
1 if Pi wins12 if Pi draws0 if Pi loses
![Page 142: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/142.jpg)
Elo’s Hypothesis
µ is the mean score of Pi till that timeS is the score in the new gameS − µ is the variation (could be positive or negative or zero)The correction factor to the old ratng of Pi is proportional to thevariation S − µ, that is,
(ri )new = (ri )old + K (S − µ)
where K is the constant of proportion.
Elo originally set K = 10For chess games,
S =
1 if Pi wins12 if Pi draws0 if Pi loses
![Page 143: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/143.jpg)
Elo’s Hypothesis
µ is the mean score of Pi till that timeS is the score in the new gameS − µ is the variation (could be positive or negative or zero)The correction factor to the old ratng of Pi is proportional to thevariation S − µ, that is,
(ri )new = (ri )old + K (S − µ)
where K is the constant of proportion.Elo originally set K = 10
For chess games,
S =
1 if Pi wins12 if Pi draws0 if Pi loses
![Page 144: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/144.jpg)
Elo’s Hypothesis
µ is the mean score of Pi till that timeS is the score in the new gameS − µ is the variation (could be positive or negative or zero)The correction factor to the old ratng of Pi is proportional to thevariation S − µ, that is,
(ri )new = (ri )old + K (S − µ)
where K is the constant of proportion.Elo originally set K = 10For chess games,
S =
1 if Pi wins12 if Pi draws0 if Pi loses
![Page 145: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/145.jpg)
Modifications
As more data became available it was found thatnormal distribution assumption is not a good assumptionA more suitable assuption is the Logistic DistributionThis changes the formula aboveIn 1917 Bob Runyan adapted for International FootballJeff Segarin (USA Today) adapted for American Football
![Page 146: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/146.jpg)
Modifications
As more data became available it was found that
normal distribution assumption is not a good assumptionA more suitable assuption is the Logistic DistributionThis changes the formula aboveIn 1917 Bob Runyan adapted for International FootballJeff Segarin (USA Today) adapted for American Football
![Page 147: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/147.jpg)
Modifications
As more data became available it was found thatnormal distribution assumption is not a good assumption
A more suitable assuption is the Logistic DistributionThis changes the formula aboveIn 1917 Bob Runyan adapted for International FootballJeff Segarin (USA Today) adapted for American Football
![Page 148: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/148.jpg)
Modifications
As more data became available it was found thatnormal distribution assumption is not a good assumptionA more suitable assuption is the Logistic Distribution
This changes the formula aboveIn 1917 Bob Runyan adapted for International FootballJeff Segarin (USA Today) adapted for American Football
![Page 149: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/149.jpg)
Modifications
As more data became available it was found thatnormal distribution assumption is not a good assumptionA more suitable assuption is the Logistic DistributionThis changes the formula above
In 1917 Bob Runyan adapted for International FootballJeff Segarin (USA Today) adapted for American Football
![Page 150: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/150.jpg)
Modifications
As more data became available it was found thatnormal distribution assumption is not a good assumptionA more suitable assuption is the Logistic DistributionThis changes the formula aboveIn 1917 Bob Runyan adapted for International Football
Jeff Segarin (USA Today) adapted for American Football
![Page 151: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/151.jpg)
Modifications
As more data became available it was found thatnormal distribution assumption is not a good assumptionA more suitable assuption is the Logistic DistributionThis changes the formula aboveIn 1917 Bob Runyan adapted for International FootballJeff Segarin (USA Today) adapted for American Football
![Page 152: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/152.jpg)
Current Version
Suppose Pi plays against Pj
Sij =
1 if Pi beats Pj12 if game is a draw0 if Pi loses
µij = The Score Pi is expected to score against Pj
dij = (ri )old − (rj)old
( the difference in rating at the start of the game)
µij = L
(dij
400
)where
L(x) =1
1 + 10−x
µij =1
1 + 10−((ri )old−(rj )old)
400
![Page 153: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/153.jpg)
Current Version
Suppose Pi plays against Pj
Sij =
1 if Pi beats Pj12 if game is a draw0 if Pi loses
µij = The Score Pi is expected to score against Pj
dij = (ri )old − (rj)old
( the difference in rating at the start of the game)
µij = L
(dij
400
)where
L(x) =1
1 + 10−x
µij =1
1 + 10−((ri )old−(rj )old)
400
![Page 154: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/154.jpg)
Current Version
Suppose Pi plays against Pj
Sij =
1 if Pi beats Pj12 if game is a draw0 if Pi loses
µij = The Score Pi is expected to score against Pj
dij = (ri )old − (rj)old
( the difference in rating at the start of the game)
µij = L
(dij
400
)where
L(x) =1
1 + 10−x
µij =1
1 + 10−((ri )old−(rj )old)
400
![Page 155: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/155.jpg)
Current Version
Suppose Pi plays against Pj
Sij =
1 if Pi beats Pj12 if game is a draw0 if Pi loses
µij = The Score Pi is expected to score against Pj
dij = (ri )old − (rj)old
( the difference in rating at the start of the game)
µij = L
(dij
400
)where
L(x) =1
1 + 10−x
µij =1
1 + 10−((ri )old−(rj )old)
400
![Page 156: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/156.jpg)
Current Version
Suppose Pi plays against Pj
Sij =
1 if Pi beats Pj12 if game is a draw0 if Pi loses
µij = The Score Pi is expected to score against Pj
dij = (ri )old − (rj)old
( the difference in rating at the start of the game)
µij = L
(dij
400
)where
L(x) =1
1 + 10−x
µij =1
1 + 10−((ri )old−(rj )old)
400
![Page 157: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/157.jpg)
Current Version
Suppose Pi plays against Pj
Sij =
1 if Pi beats Pj12 if game is a draw0 if Pi loses
µij = The Score Pi is expected to score against Pj
dij = (ri )old − (rj)old
( the difference in rating at the start of the game)
µij = L
(dij
400
)where
L(x) =1
1 + 10−x
µij =1
1 + 10−((ri )old−(rj )old)
400
![Page 158: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/158.jpg)
Current Version
Suppose Pi plays against Pj
Sij =
1 if Pi beats Pj12 if game is a draw0 if Pi loses
µij = The Score Pi is expected to score against Pj
dij = (ri )old − (rj)old
( the difference in rating at the start of the game)
µij = L
(dij
400
)where
L(x) =1
1 + 10−x
µij =1
1 + 10−((ri )old−(rj )old)
400
![Page 159: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/159.jpg)
Current Version
Suppose Pi plays against Pj
Sij =
1 if Pi beats Pj12 if game is a draw0 if Pi loses
µij = The Score Pi is expected to score against Pj
dij = (ri )old − (rj)old
( the difference in rating at the start of the game)
µij = L
(dij
400
)where
L(x) =1
1 + 10−x
µij =1
1 + 10−((ri )old−(rj )old)
400
![Page 160: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/160.jpg)
Current Version
Suppose Pi plays against Pj
Sij =
1 if Pi beats Pj12 if game is a draw0 if Pi loses
µij = The Score Pi is expected to score against Pj
dij = (ri )old − (rj)old
( the difference in rating at the start of the game)
µij = L
(dij
400
)where
L(x) =1
1 + 10−x
µij =1
1 + 10−((ri )old−(rj )old)
400
![Page 161: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/161.jpg)
The Logistic Curve L(x)
![Page 162: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/162.jpg)
Current Version
(ri )new = (ri )old + K (Sij − µij)
The K Factor Used For Chess:K = 25 for new players (upto 30 recognized games)K = 15 for those with more than 30 gamesK = 10 for those who have recahed 2400 points at some point oftime
![Page 163: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/163.jpg)
Current Version
(ri )new = (ri )old + K (Sij − µij)
The K Factor Used For Chess:K = 25 for new players (upto 30 recognized games)K = 15 for those with more than 30 gamesK = 10 for those who have recahed 2400 points at some point oftime
![Page 164: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/164.jpg)
Current Version
(ri )new = (ri )old + K (Sij − µij)
The K Factor Used For Chess:
K = 25 for new players (upto 30 recognized games)K = 15 for those with more than 30 gamesK = 10 for those who have recahed 2400 points at some point oftime
![Page 165: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/165.jpg)
Current Version
(ri )new = (ri )old + K (Sij − µij)
The K Factor Used For Chess:K = 25 for new players (upto 30 recognized games)
K = 15 for those with more than 30 gamesK = 10 for those who have recahed 2400 points at some point oftime
![Page 166: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/166.jpg)
Current Version
(ri )new = (ri )old + K (Sij − µij)
The K Factor Used For Chess:K = 25 for new players (upto 30 recognized games)K = 15 for those with more than 30 games
K = 10 for those who have recahed 2400 points at some point oftime
![Page 167: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/167.jpg)
Current Version
(ri )new = (ri )old + K (Sij − µij)
The K Factor Used For Chess:K = 25 for new players (upto 30 recognized games)K = 15 for those with more than 30 gamesK = 10 for those who have recahed 2400 points at some point oftime
![Page 168: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/168.jpg)
Better Reward For beating stronger Team
Consider a game in which a weaker player Ti plays against astronger player Tj . This means at the time the game starts
ri < rj
In the Elo system of rating,the reward that the weaker player Ti gets if he beats Tj is,greater than the reward that stronger player Tj gets if he beats Ti
![Page 169: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/169.jpg)
Better Reward For beating stronger Team
Consider a game in which a weaker player Ti plays against astronger player Tj .
This means at the time the game starts
ri < rj
In the Elo system of rating,the reward that the weaker player Ti gets if he beats Tj is,greater than the reward that stronger player Tj gets if he beats Ti
![Page 170: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/170.jpg)
Better Reward For beating stronger Team
Consider a game in which a weaker player Ti plays against astronger player Tj . This means at the time the game starts
ri < rj
In the Elo system of rating,
the reward that the weaker player Ti gets if he beats Tj is,greater than the reward that stronger player Tj gets if he beats Ti
![Page 171: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/171.jpg)
Better Reward For beating stronger Team
Consider a game in which a weaker player Ti plays against astronger player Tj . This means at the time the game starts
ri < rj
In the Elo system of rating,the reward that the weaker player Ti gets if he beats Tj is,
greater than the reward that stronger player Tj gets if he beats Ti
![Page 172: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/172.jpg)
Better Reward For beating stronger Team
Consider a game in which a weaker player Ti plays against astronger player Tj . This means at the time the game starts
ri < rj
In the Elo system of rating,the reward that the weaker player Ti gets if he beats Tj is,greater than the reward that stronger player Tj gets if he beats Ti
![Page 173: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/173.jpg)
Better Reward For beating stronger Team
Consider a game in which a weaker player Ti plays against astronger player Tj . This means at the time the game starts
ri < rj
In the Elo system of rating,the reward that the weaker player Ti gets if he beats Tj is,greater than the reward that stronger player Tj gets if he beats Ti
![Page 174: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/174.jpg)
The Rewards
Reward for Ti if he beats Tj = K (Sij − µij)
= K
{1− 1
1 + 10−αij
}where
αij =(ri )old − (rj)old
400
Similarly
Reward for Tj if he beats Ti = K (Sji − µji )
= K
{1− 1
1 + 10−αji
}where
αji =(rj)old − (ri )old
400
![Page 175: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/175.jpg)
The Rewards
Reward for Ti if he beats Tj = K (Sij − µij)
= K
{1− 1
1 + 10−αij
}where
αij =(ri )old − (rj)old
400
Similarly
Reward for Tj if he beats Ti = K (Sji − µji )
= K
{1− 1
1 + 10−αji
}where
αji =(rj)old − (ri )old
400
![Page 176: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/176.jpg)
The Rewards
Reward for Ti if he beats Tj = K (Sij − µij)
= K
{1− 1
1 + 10−αij
}where
αij =(ri )old − (rj)old
400
Similarly
Reward for Tj if he beats Ti = K (Sji − µji )
= K
{1− 1
1 + 10−αji
}where
αji =(rj)old − (ri )old
400
![Page 177: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/177.jpg)
The Rewards
Reward for Ti if he beats Tj = K (Sij − µij)
= K
{1− 1
1 + 10−αij
}where
αij =(ri )old − (rj)old
400
Similarly
Reward for Tj if he beats Ti = K (Sji − µji )
= K
{1− 1
1 + 10−αji
}where
αji =(rj)old − (ri )old
400
![Page 178: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/178.jpg)
The Rewards
Reward for Ti if he beats Tj = K (Sij − µij)
= K
{1− 1
1 + 10−αij
}where
αij =(ri )old − (rj)old
400
Similarly
Reward for Tj if he beats Ti = K (Sji − µji )
= K
{1− 1
1 + 10−αji
}where
αji =(rj)old − (ri )old
400
![Page 179: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/179.jpg)
An Example
Ti has rating 1700, Tj has rating 2100Suppose Ti beats Tj :
Reward for Ti = K
(1− 1
1 + 10−1700−2100
400
)= K
(1− 1
1 + 101
)≈ K (1− 0.09)
= (0.91)K
![Page 180: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/180.jpg)
An Example
Ti has rating 1700, Tj has rating 2100
Suppose Ti beats Tj :
Reward for Ti = K
(1− 1
1 + 10−1700−2100
400
)= K
(1− 1
1 + 101
)≈ K (1− 0.09)
= (0.91)K
![Page 181: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/181.jpg)
An Example
Ti has rating 1700, Tj has rating 2100Suppose Ti beats Tj :
Reward for Ti = K
(1− 1
1 + 10−1700−2100
400
)= K
(1− 1
1 + 101
)≈ K (1− 0.09)
= (0.91)K
![Page 182: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/182.jpg)
An Example
Ti has rating 1700, Tj has rating 2100Suppose Ti beats Tj :
Reward for Ti =
K
(1− 1
1 + 10−1700−2100
400
)= K
(1− 1
1 + 101
)≈ K (1− 0.09)
= (0.91)K
![Page 183: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/183.jpg)
An Example
Ti has rating 1700, Tj has rating 2100Suppose Ti beats Tj :
Reward for Ti = K
(1− 1
1 + 10−1700−2100
400
)
= K
(1− 1
1 + 101
)≈ K (1− 0.09)
= (0.91)K
![Page 184: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/184.jpg)
An Example
Ti has rating 1700, Tj has rating 2100Suppose Ti beats Tj :
Reward for Ti = K
(1− 1
1 + 10−1700−2100
400
)= K
(1− 1
1 + 101
)
≈ K (1− 0.09)
= (0.91)K
![Page 185: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/185.jpg)
An Example
Ti has rating 1700, Tj has rating 2100Suppose Ti beats Tj :
Reward for Ti = K
(1− 1
1 + 10−1700−2100
400
)= K
(1− 1
1 + 101
)≈ K (1− 0.09)
= (0.91)K
![Page 186: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/186.jpg)
An Example
Ti has rating 1700, Tj has rating 2100Suppose Ti beats Tj :
Reward for Ti = K
(1− 1
1 + 10−1700−2100
400
)= K
(1− 1
1 + 101
)≈ K (1− 0.09)
= (0.91)K
![Page 187: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/187.jpg)
An Example (Continued)
Similarly, interchanging the roles of i and j , we get if Tj beats Ti
then
Reward for Tj = K
(1− 1
1 + 10−2100−1700
400
)= K
(1− 1
1 + 10−1
)≈ K (1− 0.91)
= (0.09)K
![Page 188: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/188.jpg)
An Example (Continued)
Similarly, interchanging the roles of i and j , we get if Tj beats Ti
then
Reward for Tj = K
(1− 1
1 + 10−2100−1700
400
)= K
(1− 1
1 + 10−1
)≈ K (1− 0.91)
= (0.09)K
![Page 189: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/189.jpg)
Total expected Score is One
µij =1
1 + 10−αij(where, recall, αij = ((ri )old − (rj)old)
µji =1
1 + 10αij(since αji = −αij)
=⇒µij + µji =
1
1 + 10−αij+
1
1 + 10αij
= 1
![Page 190: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/190.jpg)
Total expected Score is One
µij =1
1 + 10−αij
(where, recall, αij = ((ri )old − (rj)old)
µji =1
1 + 10αij(since αji = −αij)
=⇒µij + µji =
1
1 + 10−αij+
1
1 + 10αij
= 1
![Page 191: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/191.jpg)
Total expected Score is One
µij =1
1 + 10−αij(where, recall, αij = ((ri )old − (rj)old)
µji =1
1 + 10αij
(since αji = −αij)
=⇒µij + µji =
1
1 + 10−αij+
1
1 + 10αij
= 1
![Page 192: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/192.jpg)
Total expected Score is One
µij =1
1 + 10−αij(where, recall, αij = ((ri )old − (rj)old)
µji =1
1 + 10αij(since αji = −αij)
=⇒
µij + µji =1
1 + 10−αij+
1
1 + 10αij
= 1
![Page 193: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/193.jpg)
Total expected Score is One
µij =1
1 + 10−αij(where, recall, αij = ((ri )old − (rj)old)
µji =1
1 + 10αij(since αji = −αij)
=⇒µij + µji =
1
1 + 10−αij+
1
1 + 10αij
= 1
![Page 194: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/194.jpg)
The Total score is One
Clearly we have
Sij + Sji = 1
![Page 195: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/195.jpg)
The Total score is One
Clearly we have
Sij + Sji = 1
![Page 196: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/196.jpg)
The Total Rating is Invariant
If Ti and Tj play then only the ratings of Ti and Tj change afterthe game depending on the reward they get. Hence
![Page 197: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/197.jpg)
The Total Rating is Invariant
If Ti and Tj play then only the ratings of Ti and Tj change afterthe game depending on the reward they get. Hence
![Page 198: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/198.jpg)
n∑k=1
(rk)new =
∑k 6=i ,j
(rk)new + (ri )new + (rj)new
=∑k 6=i ,j
(rk)old
+ {(ri )old + K (Sij − µij)}+ {(rj)old + K (Sji − µji )}
=n∑
k=1
(rk)old + K {(Sij + Sji )− (µij + µji )}
=n∑
k=1
(rk)old + K (1− 1)
=n∑
k=1
(rk)old
![Page 199: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/199.jpg)
n∑k=1
(rk)new =∑k 6=i ,j
(rk)new +
(ri )new + (rj)new
=∑k 6=i ,j
(rk)old
+ {(ri )old + K (Sij − µij)}+ {(rj)old + K (Sji − µji )}
=n∑
k=1
(rk)old + K {(Sij + Sji )− (µij + µji )}
=n∑
k=1
(rk)old + K (1− 1)
=n∑
k=1
(rk)old
![Page 200: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/200.jpg)
n∑k=1
(rk)new =∑k 6=i ,j
(rk)new + (ri )new +
(rj)new
=∑k 6=i ,j
(rk)old
+ {(ri )old + K (Sij − µij)}+ {(rj)old + K (Sji − µji )}
=n∑
k=1
(rk)old + K {(Sij + Sji )− (µij + µji )}
=n∑
k=1
(rk)old + K (1− 1)
=n∑
k=1
(rk)old
![Page 201: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/201.jpg)
n∑k=1
(rk)new =∑k 6=i ,j
(rk)new + (ri )new + (rj)new
=∑k 6=i ,j
(rk)old
+ {(ri )old + K (Sij − µij)}+ {(rj)old + K (Sji − µji )}
=n∑
k=1
(rk)old + K {(Sij + Sji )− (µij + µji )}
=n∑
k=1
(rk)old + K (1− 1)
=n∑
k=1
(rk)old
![Page 202: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/202.jpg)
n∑k=1
(rk)new =∑k 6=i ,j
(rk)new + (ri )new + (rj)new
=∑k 6=i ,j
(rk)old
+ {(ri )old + K (Sij − µij)}
+ {(rj)old + K (Sji − µji )}
=n∑
k=1
(rk)old + K {(Sij + Sji )− (µij + µji )}
=n∑
k=1
(rk)old + K (1− 1)
=n∑
k=1
(rk)old
![Page 203: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/203.jpg)
n∑k=1
(rk)new =∑k 6=i ,j
(rk)new + (ri )new + (rj)new
=∑k 6=i ,j
(rk)old
+ {(ri )old + K (Sij − µij)}+ {(rj)old + K (Sji − µji )}
=n∑
k=1
(rk)old + K {(Sij + Sji )− (µij + µji )}
=n∑
k=1
(rk)old + K (1− 1)
=n∑
k=1
(rk)old
![Page 204: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/204.jpg)
n∑k=1
(rk)new =∑k 6=i ,j
(rk)new + (ri )new + (rj)new
=∑k 6=i ,j
(rk)old
+ {(ri )old + K (Sij − µij)}+ {(rj)old + K (Sji − µji )}
=n∑
k=1
(rk)old
+ K {(Sij + Sji )− (µij + µji )}
=n∑
k=1
(rk)old + K (1− 1)
=n∑
k=1
(rk)old
![Page 205: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/205.jpg)
n∑k=1
(rk)new =∑k 6=i ,j
(rk)new + (ri )new + (rj)new
=∑k 6=i ,j
(rk)old
+ {(ri )old + K (Sij − µij)}+ {(rj)old + K (Sji − µji )}
=n∑
k=1
(rk)old + K {(Sij + Sji )− (µij + µji )}
=n∑
k=1
(rk)old + K (1− 1)
=n∑
k=1
(rk)old
![Page 206: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/206.jpg)
n∑k=1
(rk)new =∑k 6=i ,j
(rk)new + (ri )new + (rj)new
=∑k 6=i ,j
(rk)old
+ {(ri )old + K (Sij − µij)}+ {(rj)old + K (Sji − µji )}
=n∑
k=1
(rk)old + K {(Sij + Sji )− (µij + µji )}
=n∑
k=1
(rk)old + K (1− 1)
=n∑
k=1
(rk)old
![Page 207: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/207.jpg)
n∑k=1
(rk)new =∑k 6=i ,j
(rk)new + (ri )new + (rj)new
=∑k 6=i ,j
(rk)old
+ {(ri )old + K (Sij − µij)}+ {(rj)old + K (Sji − µji )}
=n∑
k=1
(rk)old + K {(Sij + Sji )− (µij + µji )}
=n∑
k=1
(rk)old + K (1− 1)
=n∑
k=1
(rk)old
![Page 208: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/208.jpg)
SPREAD BETTING
![Page 209: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/209.jpg)
Charles K. McNeil (16 August 1903 - April 1981)
Inventor of the point spread in sports gamblingMcNeil earned a Master’s Degree from the University of Chicago.He then taught Mathematics at the Riverdale Country School inNew York and in Connecticut.His students included John F. Kennedy.He was also a securities analyst in ChicagoWhile gambling on the side, he developed the point spread,betting not on the probability of the final outcome,but on the expected difference in score.He eventually opened his own bookmaking operation in the 1940sCharles McNeil method is used today in different areas: anythingfrom basketball to poker.He started the new method of trading and changed the way peoplebet
![Page 210: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/210.jpg)
Charles K. McNeil (16 August 1903 - April 1981)
Inventor of the point spread in sports gambling
McNeil earned a Master’s Degree from the University of Chicago.He then taught Mathematics at the Riverdale Country School inNew York and in Connecticut.His students included John F. Kennedy.He was also a securities analyst in ChicagoWhile gambling on the side, he developed the point spread,betting not on the probability of the final outcome,but on the expected difference in score.He eventually opened his own bookmaking operation in the 1940sCharles McNeil method is used today in different areas: anythingfrom basketball to poker.He started the new method of trading and changed the way peoplebet
![Page 211: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/211.jpg)
Charles K. McNeil (16 August 1903 - April 1981)
Inventor of the point spread in sports gamblingMcNeil earned a Master’s Degree from the University of Chicago.
He then taught Mathematics at the Riverdale Country School inNew York and in Connecticut.His students included John F. Kennedy.He was also a securities analyst in ChicagoWhile gambling on the side, he developed the point spread,betting not on the probability of the final outcome,but on the expected difference in score.He eventually opened his own bookmaking operation in the 1940sCharles McNeil method is used today in different areas: anythingfrom basketball to poker.He started the new method of trading and changed the way peoplebet
![Page 212: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/212.jpg)
Charles K. McNeil (16 August 1903 - April 1981)
Inventor of the point spread in sports gamblingMcNeil earned a Master’s Degree from the University of Chicago.He then taught Mathematics at the Riverdale Country School inNew York and in Connecticut.
His students included John F. Kennedy.He was also a securities analyst in ChicagoWhile gambling on the side, he developed the point spread,betting not on the probability of the final outcome,but on the expected difference in score.He eventually opened his own bookmaking operation in the 1940sCharles McNeil method is used today in different areas: anythingfrom basketball to poker.He started the new method of trading and changed the way peoplebet
![Page 213: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/213.jpg)
Charles K. McNeil (16 August 1903 - April 1981)
Inventor of the point spread in sports gamblingMcNeil earned a Master’s Degree from the University of Chicago.He then taught Mathematics at the Riverdale Country School inNew York and in Connecticut.His students included John F. Kennedy.
He was also a securities analyst in ChicagoWhile gambling on the side, he developed the point spread,betting not on the probability of the final outcome,but on the expected difference in score.He eventually opened his own bookmaking operation in the 1940sCharles McNeil method is used today in different areas: anythingfrom basketball to poker.He started the new method of trading and changed the way peoplebet
![Page 214: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/214.jpg)
Charles K. McNeil (16 August 1903 - April 1981)
Inventor of the point spread in sports gamblingMcNeil earned a Master’s Degree from the University of Chicago.He then taught Mathematics at the Riverdale Country School inNew York and in Connecticut.His students included John F. Kennedy.He was also a securities analyst in Chicago
While gambling on the side, he developed the point spread,betting not on the probability of the final outcome,but on the expected difference in score.He eventually opened his own bookmaking operation in the 1940sCharles McNeil method is used today in different areas: anythingfrom basketball to poker.He started the new method of trading and changed the way peoplebet
![Page 215: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/215.jpg)
Charles K. McNeil (16 August 1903 - April 1981)
Inventor of the point spread in sports gamblingMcNeil earned a Master’s Degree from the University of Chicago.He then taught Mathematics at the Riverdale Country School inNew York and in Connecticut.His students included John F. Kennedy.He was also a securities analyst in ChicagoWhile gambling on the side, he developed the point spread,
betting not on the probability of the final outcome,but on the expected difference in score.He eventually opened his own bookmaking operation in the 1940sCharles McNeil method is used today in different areas: anythingfrom basketball to poker.He started the new method of trading and changed the way peoplebet
![Page 216: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/216.jpg)
Charles K. McNeil (16 August 1903 - April 1981)
Inventor of the point spread in sports gamblingMcNeil earned a Master’s Degree from the University of Chicago.He then taught Mathematics at the Riverdale Country School inNew York and in Connecticut.His students included John F. Kennedy.He was also a securities analyst in ChicagoWhile gambling on the side, he developed the point spread,betting not on the probability of the final outcome,
but on the expected difference in score.He eventually opened his own bookmaking operation in the 1940sCharles McNeil method is used today in different areas: anythingfrom basketball to poker.He started the new method of trading and changed the way peoplebet
![Page 217: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/217.jpg)
Charles K. McNeil (16 August 1903 - April 1981)
Inventor of the point spread in sports gamblingMcNeil earned a Master’s Degree from the University of Chicago.He then taught Mathematics at the Riverdale Country School inNew York and in Connecticut.His students included John F. Kennedy.He was also a securities analyst in ChicagoWhile gambling on the side, he developed the point spread,betting not on the probability of the final outcome,but on the expected difference in score.
He eventually opened his own bookmaking operation in the 1940sCharles McNeil method is used today in different areas: anythingfrom basketball to poker.He started the new method of trading and changed the way peoplebet
![Page 218: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/218.jpg)
Charles K. McNeil (16 August 1903 - April 1981)
Inventor of the point spread in sports gamblingMcNeil earned a Master’s Degree from the University of Chicago.He then taught Mathematics at the Riverdale Country School inNew York and in Connecticut.His students included John F. Kennedy.He was also a securities analyst in ChicagoWhile gambling on the side, he developed the point spread,betting not on the probability of the final outcome,but on the expected difference in score.He eventually opened his own bookmaking operation in the 1940s
Charles McNeil method is used today in different areas: anythingfrom basketball to poker.He started the new method of trading and changed the way peoplebet
![Page 219: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/219.jpg)
Charles K. McNeil (16 August 1903 - April 1981)
Inventor of the point spread in sports gamblingMcNeil earned a Master’s Degree from the University of Chicago.He then taught Mathematics at the Riverdale Country School inNew York and in Connecticut.His students included John F. Kennedy.He was also a securities analyst in ChicagoWhile gambling on the side, he developed the point spread,betting not on the probability of the final outcome,but on the expected difference in score.He eventually opened his own bookmaking operation in the 1940sCharles McNeil method is used today in different areas: anythingfrom basketball to poker.
He started the new method of trading and changed the way peoplebet
![Page 220: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/220.jpg)
Charles K. McNeil (16 August 1903 - April 1981)
Inventor of the point spread in sports gamblingMcNeil earned a Master’s Degree from the University of Chicago.He then taught Mathematics at the Riverdale Country School inNew York and in Connecticut.His students included John F. Kennedy.He was also a securities analyst in ChicagoWhile gambling on the side, he developed the point spread,betting not on the probability of the final outcome,but on the expected difference in score.He eventually opened his own bookmaking operation in the 1940sCharles McNeil method is used today in different areas: anythingfrom basketball to poker.He started the new method of trading and changed the way peoplebet
![Page 221: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/221.jpg)
Beat The Spread
Since the time of McNeil,“BEATING THE SPREADis the HOLY GRAIL of the betting world
![Page 222: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/222.jpg)
Beat The Spread
Since the time of McNeil,
“BEATING THE SPREADis the HOLY GRAIL of the betting world
![Page 223: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/223.jpg)
Beat The Spread
Since the time of McNeil,“BEATING THE SPREAD
is the HOLY GRAIL of the betting world
![Page 224: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/224.jpg)
Beat The Spread
Since the time of McNeil,“BEATING THE SPREADis the HOLY GRAIL of the betting world
![Page 225: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/225.jpg)
What does “Beating the spread mean?
Suppose two Teams A and B are playing a basketball game. Thebookmaker announces the betting as follows:A will beat B by 10 PointsSuppose the match score is as follows:
I CASE 1: A beats B with score line 58− 47
I CASE 2: A beats B with score line 61− 54
I CASE 3: A loses to B
![Page 226: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/226.jpg)
What does “Beating the spread mean?
Suppose two Teams A and B are playing a basketball game.
Thebookmaker announces the betting as follows:A will beat B by 10 PointsSuppose the match score is as follows:
I CASE 1: A beats B with score line 58− 47
I CASE 2: A beats B with score line 61− 54
I CASE 3: A loses to B
![Page 227: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/227.jpg)
What does “Beating the spread mean?
Suppose two Teams A and B are playing a basketball game. Thebookmaker announces the betting as follows:
A will beat B by 10 PointsSuppose the match score is as follows:
I CASE 1: A beats B with score line 58− 47
I CASE 2: A beats B with score line 61− 54
I CASE 3: A loses to B
![Page 228: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/228.jpg)
What does “Beating the spread mean?
Suppose two Teams A and B are playing a basketball game. Thebookmaker announces the betting as follows:A will beat B by 10 Points
Suppose the match score is as follows:
I CASE 1: A beats B with score line 58− 47
I CASE 2: A beats B with score line 61− 54
I CASE 3: A loses to B
![Page 229: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/229.jpg)
What does “Beating the spread mean?
Suppose two Teams A and B are playing a basketball game. Thebookmaker announces the betting as follows:A will beat B by 10 PointsSuppose the match score is as follows:
I CASE 1: A beats B with score line 58− 47
I CASE 2: A beats B with score line 61− 54
I CASE 3: A loses to B
![Page 230: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/230.jpg)
What does “Beating the spread mean?
Suppose two Teams A and B are playing a basketball game. Thebookmaker announces the betting as follows:A will beat B by 10 PointsSuppose the match score is as follows:
I CASE 1: A beats B with score line 58− 47
I CASE 2: A beats B with score line 61− 54
I CASE 3: A loses to B
![Page 231: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/231.jpg)
What does “Beating the spread mean?
Suppose two Teams A and B are playing a basketball game. Thebookmaker announces the betting as follows:A will beat B by 10 PointsSuppose the match score is as follows:
I CASE 1: A beats B with score line 58− 47
I CASE 2: A beats B with score line 61− 54
I CASE 3: A loses to B
![Page 232: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/232.jpg)
What does “Beating the spread mean?
Suppose two Teams A and B are playing a basketball game. Thebookmaker announces the betting as follows:A will beat B by 10 PointsSuppose the match score is as follows:
I CASE 1: A beats B with score line 58− 47
I CASE 2: A beats B with score line 61− 54
I CASE 3: A loses to B
![Page 233: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/233.jpg)
What does “Beating the spread mean?
Suppose two Teams A and B are playing a basketball game. Thebookmaker announces the betting as follows:A will beat B by 10 PointsSuppose the match score is as follows:
I CASE 1: A beats B with score line 58− 47
I CASE 2: A beats B with score line 61− 54
I CASE 3: A loses to B
![Page 234: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/234.jpg)
My Bet on A
Suppose I bet on AIn Case 1, I win the bet because A beats B by more than 10 PointsIn Case 2, I lose the bet because even though A beats B it is notby more than 10 PointsIn Case 3, I lose the bet because A loses to B
![Page 235: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/235.jpg)
My Bet on A
Suppose I bet on A
In Case 1, I win the bet because A beats B by more than 10 PointsIn Case 2, I lose the bet because even though A beats B it is notby more than 10 PointsIn Case 3, I lose the bet because A loses to B
![Page 236: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/236.jpg)
My Bet on A
Suppose I bet on AIn Case 1, I win the bet because A beats B by more than 10 Points
In Case 2, I lose the bet because even though A beats B it is notby more than 10 PointsIn Case 3, I lose the bet because A loses to B
![Page 237: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/237.jpg)
My Bet on A
Suppose I bet on AIn Case 1, I win the bet because A beats B by more than 10 PointsIn Case 2, I lose the bet because even though A beats B it is notby more than 10 Points
In Case 3, I lose the bet because A loses to B
![Page 238: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/238.jpg)
My Bet on A
Suppose I bet on AIn Case 1, I win the bet because A beats B by more than 10 PointsIn Case 2, I lose the bet because even though A beats B it is notby more than 10 PointsIn Case 3, I lose the bet because A loses to B
![Page 239: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/239.jpg)
My Bet on B
Suppose I bet on BIn Case 1 I lose because A has beaten B by more than 10 pointsIn Case 2 I win because even though B lost he has lost it by lessthan 10 pointsIn Case 3 I win because anyway B has won
![Page 240: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/240.jpg)
My Bet on B
Suppose I bet on B
In Case 1 I lose because A has beaten B by more than 10 pointsIn Case 2 I win because even though B lost he has lost it by lessthan 10 pointsIn Case 3 I win because anyway B has won
![Page 241: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/241.jpg)
My Bet on B
Suppose I bet on BIn Case 1 I lose because A has beaten B by more than 10 points
In Case 2 I win because even though B lost he has lost it by lessthan 10 pointsIn Case 3 I win because anyway B has won
![Page 242: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/242.jpg)
My Bet on B
Suppose I bet on BIn Case 1 I lose because A has beaten B by more than 10 pointsIn Case 2 I win because even though B lost he has lost it by lessthan 10 points
In Case 3 I win because anyway B has won
![Page 243: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/243.jpg)
My Bet on B
Suppose I bet on BIn Case 1 I lose because A has beaten B by more than 10 pointsIn Case 2 I win because even though B lost he has lost it by lessthan 10 pointsIn Case 3 I win because anyway B has won
![Page 244: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/244.jpg)
Handling Ties
To handle ties the book makers usually give the spread as 7.5 or8.5 etc.
![Page 245: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/245.jpg)
Handling Ties
To handle ties the book makers usually give the spread as 7.5 or8.5 etc.
![Page 246: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/246.jpg)
Using the Spread For Rating
![Page 247: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/247.jpg)
The Spread matrix
Consider a tournament with n Teams T1, T2,· · · ,Tn,For simplicity assume each plays the other onceLet sij be the score of Ti against Tj
(Obvioulsiy sji denotes the score of Tj against Ti )Sij = sij − sjiNote that Sij = −SjiThe Spread Matrix S:S = (Sij)n×n (diagonal entries are defined to be zero)S is a SKEW SYMMETRIC MATRIX
![Page 248: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/248.jpg)
The Spread matrix
Consider a tournament with n Teams T1, T2,· · · ,Tn,
For simplicity assume each plays the other onceLet sij be the score of Ti against Tj
(Obvioulsiy sji denotes the score of Tj against Ti )Sij = sij − sjiNote that Sij = −SjiThe Spread Matrix S:S = (Sij)n×n (diagonal entries are defined to be zero)S is a SKEW SYMMETRIC MATRIX
![Page 249: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/249.jpg)
The Spread matrix
Consider a tournament with n Teams T1, T2,· · · ,Tn,For simplicity assume each plays the other once
Let sij be the score of Ti against Tj
(Obvioulsiy sji denotes the score of Tj against Ti )Sij = sij − sjiNote that Sij = −SjiThe Spread Matrix S:S = (Sij)n×n (diagonal entries are defined to be zero)S is a SKEW SYMMETRIC MATRIX
![Page 250: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/250.jpg)
The Spread matrix
Consider a tournament with n Teams T1, T2,· · · ,Tn,For simplicity assume each plays the other onceLet sij be the score of Ti against Tj
(Obvioulsiy sji denotes the score of Tj against Ti )Sij = sij − sjiNote that Sij = −SjiThe Spread Matrix S:S = (Sij)n×n (diagonal entries are defined to be zero)S is a SKEW SYMMETRIC MATRIX
![Page 251: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/251.jpg)
The Spread matrix
Consider a tournament with n Teams T1, T2,· · · ,Tn,For simplicity assume each plays the other onceLet sij be the score of Ti against Tj
(Obvioulsiy sji denotes the score of Tj against Ti )
Sij = sij − sjiNote that Sij = −SjiThe Spread Matrix S:S = (Sij)n×n (diagonal entries are defined to be zero)S is a SKEW SYMMETRIC MATRIX
![Page 252: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/252.jpg)
The Spread matrix
Consider a tournament with n Teams T1, T2,· · · ,Tn,For simplicity assume each plays the other onceLet sij be the score of Ti against Tj
(Obvioulsiy sji denotes the score of Tj against Ti )Sij = sij − sji
Note that Sij = −SjiThe Spread Matrix S:S = (Sij)n×n (diagonal entries are defined to be zero)S is a SKEW SYMMETRIC MATRIX
![Page 253: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/253.jpg)
The Spread matrix
Consider a tournament with n Teams T1, T2,· · · ,Tn,For simplicity assume each plays the other onceLet sij be the score of Ti against Tj
(Obvioulsiy sji denotes the score of Tj against Ti )Sij = sij − sjiNote that Sij = −Sji
The Spread Matrix S:S = (Sij)n×n (diagonal entries are defined to be zero)S is a SKEW SYMMETRIC MATRIX
![Page 254: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/254.jpg)
The Spread matrix
Consider a tournament with n Teams T1, T2,· · · ,Tn,For simplicity assume each plays the other onceLet sij be the score of Ti against Tj
(Obvioulsiy sji denotes the score of Tj against Ti )Sij = sij − sjiNote that Sij = −SjiThe Spread Matrix S:
S = (Sij)n×n (diagonal entries are defined to be zero)S is a SKEW SYMMETRIC MATRIX
![Page 255: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/255.jpg)
The Spread matrix
Consider a tournament with n Teams T1, T2,· · · ,Tn,For simplicity assume each plays the other onceLet sij be the score of Ti against Tj
(Obvioulsiy sji denotes the score of Tj against Ti )Sij = sij − sjiNote that Sij = −SjiThe Spread Matrix S:S = (Sij)n×n
(diagonal entries are defined to be zero)S is a SKEW SYMMETRIC MATRIX
![Page 256: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/256.jpg)
The Spread matrix
Consider a tournament with n Teams T1, T2,· · · ,Tn,For simplicity assume each plays the other onceLet sij be the score of Ti against Tj
(Obvioulsiy sji denotes the score of Tj against Ti )Sij = sij − sjiNote that Sij = −SjiThe Spread Matrix S:S = (Sij)n×n (diagonal entries are defined to be zero)S is a SKEW SYMMETRIC MATRIX
![Page 257: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/257.jpg)
The Rating Spread matrix
Suppose
x =
x1x2...xn
be any rating of the teams.The Rating Spread Matrix:X = (xij)n×n where xij = xi − xj
![Page 258: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/258.jpg)
The Rating Spread matrix
Suppose
x =
x1x2...xn
be any rating of the teams.
The Rating Spread Matrix:X = (xij)n×n where xij = xi − xj
![Page 259: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/259.jpg)
The Rating Spread matrix
Suppose
x =
x1x2...xn
be any rating of the teams.The Rating Spread Matrix:X = (xij)n×n where xij = xi − xj
![Page 260: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/260.jpg)
Ideal Situation
The ideal situation is to get a rating system X such that
S = X
The best way is to find the error S − X and find “the” x thatminimzes this error
![Page 261: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/261.jpg)
Ideal Situation
The ideal situation is to get a rating system X such that
S = X
The best way is to find the error S − X and find “the” x thatminimzes this error
![Page 262: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/262.jpg)
Ideal Situation
The ideal situation is to get a rating system X such that
S = X
The best way is to find the error S − X and find “the” x thatminimzes this error
![Page 263: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/263.jpg)
Ideal Situation
The ideal situation is to get a rating system X such that
S = X
The best way is to find the error S − X and find “the” x thatminimzes this error
![Page 264: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/264.jpg)
How do we Quantify the Error?
For A an n× n real matrix we define the “FROBENIUS NORM”,
‖A‖F =
√√√√ n∑i=1
n∑j=1
(aij)2
So get a rating r such that
‖S −R‖ < ‖S − X‖for any other rating x 6= r
![Page 265: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/265.jpg)
How do we Quantify the Error?
For A an n× n real matrix we define the “FROBENIUS NORM”,
‖A‖F =
√√√√ n∑i=1
n∑j=1
(aij)2
So get a rating r such that
‖S −R‖ < ‖S − X‖for any other rating x 6= r
![Page 266: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/266.jpg)
How do we Quantify the Error?
For A an n× n real matrix we define the “FROBENIUS NORM”,
‖A‖F =
√√√√ n∑i=1
n∑j=1
(aij)2
So get a rating r such that
‖S −R‖ < ‖S − X‖for any other rating x 6= r
![Page 267: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/267.jpg)
How do we Quantify the Error?
For A an n× n real matrix we define the “FROBENIUS NORM”,
‖A‖F =
√√√√ n∑i=1
n∑j=1
(aij)2
So get a rating r such that
‖S −R‖ < ‖S − X‖for any other rating x 6= r
![Page 268: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/268.jpg)
How do we Quantify the Error?
For A an n× n real matrix we define the “FROBENIUS NORM”,
‖A‖F =
√√√√ n∑i=1
n∑j=1
(aij)2
So get a rating r such that
‖S −R‖ < ‖S − X‖for any other rating x 6= r
![Page 269: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/269.jpg)
Can we find such an r?
A little bit of simple Linear Algebra and calculus shows that suchan r exists and is given bythe “centroid” of the columns of S
r =1
n{S1 + S2 + · · ·+ Sn}
where Sj denotes the j-th column of the Spread matrix SIn simple language,(The Rating of Team Ti namely ri )=(Total Scores of Ti in all games) -(Total opponents’ score against Ti )
n
![Page 270: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/270.jpg)
Can we find such an r?
A little bit of simple Linear Algebra and calculus shows that suchan r exists and is given by
the “centroid” of the columns of S
r =1
n{S1 + S2 + · · ·+ Sn}
where Sj denotes the j-th column of the Spread matrix SIn simple language,(The Rating of Team Ti namely ri )=(Total Scores of Ti in all games) -(Total opponents’ score against Ti )
n
![Page 271: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/271.jpg)
Can we find such an r?
A little bit of simple Linear Algebra and calculus shows that suchan r exists and is given bythe “centroid” of the columns of S
r =1
n{S1 + S2 + · · ·+ Sn}
where Sj denotes the j-th column of the Spread matrix SIn simple language,(The Rating of Team Ti namely ri )=(Total Scores of Ti in all games) -(Total opponents’ score against Ti )
n
![Page 272: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/272.jpg)
Can we find such an r?
A little bit of simple Linear Algebra and calculus shows that suchan r exists and is given bythe “centroid” of the columns of S
r =1
n{S1 + S2 + · · ·+ Sn}
where Sj denotes the j-th column of the Spread matrix SIn simple language,(The Rating of Team Ti namely ri )=(Total Scores of Ti in all games) -(Total opponents’ score against Ti )
n
![Page 273: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/273.jpg)
Can we find such an r?
A little bit of simple Linear Algebra and calculus shows that suchan r exists and is given bythe “centroid” of the columns of S
r =1
n{S1 + S2 + · · ·+ Sn}
where Sj denotes the j-th column of the Spread matrix S
In simple language,(The Rating of Team Ti namely ri )=(Total Scores of Ti in all games) -(Total opponents’ score against Ti )
n
![Page 274: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/274.jpg)
Can we find such an r?
A little bit of simple Linear Algebra and calculus shows that suchan r exists and is given bythe “centroid” of the columns of S
r =1
n{S1 + S2 + · · ·+ Sn}
where Sj denotes the j-th column of the Spread matrix SIn simple language,
(The Rating of Team Ti namely ri )=(Total Scores of Ti in all games) -(Total opponents’ score against Ti )
n
![Page 275: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/275.jpg)
Can we find such an r?
A little bit of simple Linear Algebra and calculus shows that suchan r exists and is given bythe “centroid” of the columns of S
r =1
n{S1 + S2 + · · ·+ Sn}
where Sj denotes the j-th column of the Spread matrix SIn simple language,(The Rating of Team Ti namely ri )=
(Total Scores of Ti in all games) -(Total opponents’ score against Ti )n
![Page 276: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/276.jpg)
Can we find such an r?
A little bit of simple Linear Algebra and calculus shows that suchan r exists and is given bythe “centroid” of the columns of S
r =1
n{S1 + S2 + · · ·+ Sn}
where Sj denotes the j-th column of the Spread matrix SIn simple language,(The Rating of Team Ti namely ri )=(Total Scores of Ti in all games) -(Total opponents’ score against Ti )
n
![Page 277: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/277.jpg)
Conclusion
![Page 278: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/278.jpg)
Tell Us The Truth Mark
It is not clear if in real life Mark Zuckerberg used Elo’s formula torate girls at Harvard!Only he knows!!
![Page 279: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/279.jpg)
Tell Us The Truth Mark
It is not clear if in real life Mark Zuckerberg used Elo’s formula torate girls at Harvard!
Only he knows!!
![Page 280: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/280.jpg)
Tell Us The Truth Mark
It is not clear if in real life Mark Zuckerberg used Elo’s formula torate girls at Harvard!Only he knows!!
![Page 281: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/281.jpg)
Shakespeare
“Good Lord Boyet, my beauty, though but mean,Needs not the painted flourish of your praise:Beauty is bought by judgement of the eye,Not utter’d by base sale of chapmen’s tongues”(Love ′s Labours Lost, 1588)(Nor rated by heartless mathematicians’ formulae!!)
![Page 282: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/282.jpg)
Shakespeare
“Good Lord Boyet, my beauty, though but mean,
Needs not the painted flourish of your praise:Beauty is bought by judgement of the eye,Not utter’d by base sale of chapmen’s tongues”(Love ′s Labours Lost, 1588)(Nor rated by heartless mathematicians’ formulae!!)
![Page 283: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/283.jpg)
Shakespeare
“Good Lord Boyet, my beauty, though but mean,Needs not the painted flourish of your praise:
Beauty is bought by judgement of the eye,Not utter’d by base sale of chapmen’s tongues”(Love ′s Labours Lost, 1588)(Nor rated by heartless mathematicians’ formulae!!)
![Page 284: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/284.jpg)
Shakespeare
“Good Lord Boyet, my beauty, though but mean,Needs not the painted flourish of your praise:Beauty is bought by judgement of the eye,
Not utter’d by base sale of chapmen’s tongues”(Love ′s Labours Lost, 1588)(Nor rated by heartless mathematicians’ formulae!!)
![Page 285: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/285.jpg)
Shakespeare
“Good Lord Boyet, my beauty, though but mean,Needs not the painted flourish of your praise:Beauty is bought by judgement of the eye,Not utter’d by base sale of chapmen’s tongues”
(Love ′s Labours Lost, 1588)(Nor rated by heartless mathematicians’ formulae!!)
![Page 286: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/286.jpg)
Shakespeare
“Good Lord Boyet, my beauty, though but mean,Needs not the painted flourish of your praise:Beauty is bought by judgement of the eye,Not utter’d by base sale of chapmen’s tongues”(Love ′s Labours Lost, 1588)
(Nor rated by heartless mathematicians’ formulae!!)
![Page 287: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/287.jpg)
Shakespeare
“Good Lord Boyet, my beauty, though but mean,Needs not the painted flourish of your praise:Beauty is bought by judgement of the eye,Not utter’d by base sale of chapmen’s tongues”(Love ′s Labours Lost, 1588)(Nor rated by heartless mathematicians’ formulae!!)
![Page 288: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/288.jpg)
Similar Views
Benjamin Franklin, in Poor Richard’s Almanack, 1741, wrote:“Beauty, like supreme dominionIs but supported by opinion”
David Hume’s Essays, Moral and Political, 1742, include:“Beauty in things exists merely in the mind which contemplatesthem.”
The person who is widely credited with coining the saying in itscurrent form is Margaret Wolfe Hungerford (ne Hamilton), whowrote many books, often under the pseudonym of ’The Duchess’.In Molly Bawn, 1878, there’s the line“Beauty is in the eye of the beholder”
![Page 289: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/289.jpg)
Similar Views
Benjamin Franklin, in Poor Richard’s Almanack, 1741, wrote:
“Beauty, like supreme dominionIs but supported by opinion”
David Hume’s Essays, Moral and Political, 1742, include:“Beauty in things exists merely in the mind which contemplatesthem.”
The person who is widely credited with coining the saying in itscurrent form is Margaret Wolfe Hungerford (ne Hamilton), whowrote many books, often under the pseudonym of ’The Duchess’.In Molly Bawn, 1878, there’s the line“Beauty is in the eye of the beholder”
![Page 290: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/290.jpg)
Similar Views
Benjamin Franklin, in Poor Richard’s Almanack, 1741, wrote:“Beauty, like supreme dominion
Is but supported by opinion”
David Hume’s Essays, Moral and Political, 1742, include:“Beauty in things exists merely in the mind which contemplatesthem.”
The person who is widely credited with coining the saying in itscurrent form is Margaret Wolfe Hungerford (ne Hamilton), whowrote many books, often under the pseudonym of ’The Duchess’.In Molly Bawn, 1878, there’s the line“Beauty is in the eye of the beholder”
![Page 291: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/291.jpg)
Similar Views
Benjamin Franklin, in Poor Richard’s Almanack, 1741, wrote:“Beauty, like supreme dominionIs but supported by opinion”
David Hume’s Essays, Moral and Political, 1742, include:“Beauty in things exists merely in the mind which contemplatesthem.”
The person who is widely credited with coining the saying in itscurrent form is Margaret Wolfe Hungerford (ne Hamilton), whowrote many books, often under the pseudonym of ’The Duchess’.In Molly Bawn, 1878, there’s the line“Beauty is in the eye of the beholder”
![Page 292: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/292.jpg)
Similar Views
Benjamin Franklin, in Poor Richard’s Almanack, 1741, wrote:“Beauty, like supreme dominionIs but supported by opinion”
David Hume’s Essays, Moral and Political, 1742, include:
“Beauty in things exists merely in the mind which contemplatesthem.”
The person who is widely credited with coining the saying in itscurrent form is Margaret Wolfe Hungerford (ne Hamilton), whowrote many books, often under the pseudonym of ’The Duchess’.In Molly Bawn, 1878, there’s the line“Beauty is in the eye of the beholder”
![Page 293: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/293.jpg)
Similar Views
Benjamin Franklin, in Poor Richard’s Almanack, 1741, wrote:“Beauty, like supreme dominionIs but supported by opinion”
David Hume’s Essays, Moral and Political, 1742, include:“Beauty in things exists merely in the mind which contemplatesthem.”
The person who is widely credited with coining the saying in itscurrent form is Margaret Wolfe Hungerford (ne Hamilton), whowrote many books, often under the pseudonym of ’The Duchess’.In Molly Bawn, 1878, there’s the line“Beauty is in the eye of the beholder”
![Page 294: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/294.jpg)
Similar Views
Benjamin Franklin, in Poor Richard’s Almanack, 1741, wrote:“Beauty, like supreme dominionIs but supported by opinion”
David Hume’s Essays, Moral and Political, 1742, include:“Beauty in things exists merely in the mind which contemplatesthem.”
The person who is widely credited with coining the saying in itscurrent form is Margaret Wolfe Hungerford (ne Hamilton), whowrote many books, often under the pseudonym of ’The Duchess’.In Molly Bawn, 1878, there’s the line
“Beauty is in the eye of the beholder”
![Page 295: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/295.jpg)
Similar Views
Benjamin Franklin, in Poor Richard’s Almanack, 1741, wrote:“Beauty, like supreme dominionIs but supported by opinion”
David Hume’s Essays, Moral and Political, 1742, include:“Beauty in things exists merely in the mind which contemplatesthem.”
The person who is widely credited with coining the saying in itscurrent form is Margaret Wolfe Hungerford (ne Hamilton), whowrote many books, often under the pseudonym of ’The Duchess’.In Molly Bawn, 1878, there’s the line“Beauty is in the eye of the beholder”
![Page 296: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/296.jpg)
Beauty and the Beast
Poets: “Beauty of a girl cannot be ranked”Arrow: “Beastly politicians cannot be ranked”
![Page 297: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/297.jpg)
Beauty and the Beast
Poets: “Beauty of a girl cannot be ranked”
Arrow: “Beastly politicians cannot be ranked”
![Page 298: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/298.jpg)
Beauty and the Beast
Poets: “Beauty of a girl cannot be ranked”Arrow: “Beastly politicians cannot be ranked”
![Page 299: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/299.jpg)
A Commercial
“There are some things money can’t buy,for everything else there is Mastercard”
“There are some things science can’t rate, rank or bet on,for everything else there is Mathematics”
![Page 300: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/300.jpg)
A Commercial
“There are some things money can’t buy,
for everything else there is Mastercard”
“There are some things science can’t rate, rank or bet on,for everything else there is Mathematics”
![Page 301: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/301.jpg)
A Commercial
“There are some things money can’t buy,for everything else there is Mastercard”
“There are some things science can’t rate, rank or bet on,for everything else there is Mathematics”
![Page 302: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/302.jpg)
A Commercial
“There are some things money can’t buy,for everything else there is Mastercard”
“There are some things science can’t rate, rank or bet on,
for everything else there is Mathematics”
![Page 303: Rating, Ranking, Betting and Mathematics R VITTAL RAO](https://reader031.vdocuments.site/reader031/viewer/2022020704/61fb5c472e268c58cd5d4100/html5/thumbnails/303.jpg)
A Commercial
“There are some things money can’t buy,for everything else there is Mastercard”
“There are some things science can’t rate, rank or bet on,for everything else there is Mathematics”