Game,

Set,

Maths

Cath Moore MEI Conference 2016

Starter Activity - which sports?

Uses a ball

Uses a ‘stick’ Team sport

• Gives you a hook to get students interested

– does the sport matter?

• Use the situation as a reason to develop the

maths

• Is based in real life

– Is messy

– Needs estimation and approximation

– Needs modelling

Using sports

• Most students familiar with the basics

• Most students have the opportunity to play

• Scoring system is not a straightforward as

football

• Tournaments tend to be over a concentrated

time period

• Lots of maths involved

• Get a cool title for the session…

• How about rugby?

Tennis – why?

• Tennis scores: 0, 15, 30, 40, win

• Players need to win by two points, so if get to

40-40 (deuce) winner gets A then win.

• How can a player win? What are the possible

scoring lines?

• Develops: listing, systematic listing, logical

thinking

• Extend to: if all outcomes are equally likely, what

is the average number of points per game

How can you win a game?

• Possible outcomes: 0-w, 15-w, 30-w, 40-w;

• Points per game: 4, 5, 6, 8….

10...or 12…or 18…

• We need some real data…

Average points score per game

• Men’s singles:

– 28 805 points in 127 matches = 226.8 ppm

• Women’s singles:

– 17 978 points in 127 matches = 141.6 ppm

So it seems reasonable that men are paid more than women

as they play more points…

– unless you calculate it by game…

• Men’s singles: 28 805 ÷4759 = 6.05 ppg

• Women’s singles: 17 978 ÷ 2787 = 6.45 ppg

Which must make women’s games more exciting to watch…

Average points

• To win a set you have to score two more games

than your opposition, unless you get to 6-6 when

you have a tiebreak unless it is the final set. The

winner is the first to three sets for men.

• How may different ways of winning a set are

there?

• Develops: problem solving skills, reasoning,

systematic listing

• Extend to: ways of winning matches

Ways to win a set

• How do we know how the set was won…

6-0, 6-1, 6-2, 6-3, 6-4, 7-5, 7-6 (which brings in tie breaks)…

or some other score up to 70-68 (Isner bt Mahut 2010)

• We could use real data…

Average points score per set

What else could we investigate?

• Assuming that each player (Alan or Bob) is equally likely

to win a game, what is the probability of a five set

match?

• Probability of winning in exactly 5 sets is 12/32

• How did you do this?

• How would you expect your students to do this?

• Historically the probability of a 5 set match (looking at

data since 1968) is about 32%...

Probability of winning

• Average length of match is approx 150min M (90min F)

• Playing time per day is 1130 to approx 2100 (1300 start

on Centre and No1 court)

• How many matches can you fit on a court in one day?

• 19 grass courts – how many matches in a day

altogether? (need to fit in 662 over the fortnight)

• Develops logical thinking, reasoning processes – leads

to maths covered in A level decision units

Scheduling matches

• Can we calculate/estimate the reaction time for a

successful return of serve?

• Time = distance ÷ speed

• Distance: 60’ to 78’

• Speed (as recorded on speed camera) eg

127mph

• Reaction time…

= 60'(to 78')/127mph

= 18m (to 23.4m)/55mps

= 0.3 to 0.4 seconds

Reaction times

It was considered wrong that men were paid more than women and

since 2007, the men’s singles and women’s singles winners have been

paid the same amount… but is this fair?

Let’s take 2015 as an example…

• Both winners won 7 matches including the final to win £1.88m, but…

• Djokovic played a max 35 sets (actually 24 sets)

• Williams played a max 21 sets (actually 16 sets)

• So Djokovic averaged £54,000 (£78,000) per set

• And Williams averaged £90,000 (£118,000) per set

Is this fair? Should we plan to pay women £36,000 extra per set?

Paying winners…

However, some people say that as each game lasts longer in women’s

singles it is fairer to think about the time spent playing…

• Djokovic played for 16 hours exactly

• Williams played for 10 hours and 32 minutes

• Djokovic was paid £118,000 per hour

• Williams was paid £179,000 per hour

Could we have an hourly rate for winners depending on length of

match?

• The longest match was in 2010 when in the first round Isner beat

Mahout after playing 138 games and taking 11hours and 5 minutes

Paying winners…

• Closing the angle on the serve - where is best to

stand - using geogebra?

• returner off base line.ggb

Closing the angle

• Scoring – which score lines are possible?

• What’s the force acting on the centre in the

pack?

• Where’s the best place to stand to take the

conversion? • rugby angles.ggb

– Do you have to do the ‘bottom out’ pose to

kick well?

Rugby questions

The Further Mathematics

Support Programme

Our aim is to increase the uptake of AS

and A level Further Mathematics to

ensure that more students reach their

potential in mathematics.

To find out more please visit

www.furthermaths.org.uk

The FMSP works closely with school/college

maths departments to provide professional

development opportunities for teachers and

maths promotion events for students.

About MEI

• Registered charity committed to improving

mathematics education

• Independent UK curriculum development body

• We offer continuing professional development

courses, provide specialist tuition for students

and work with industry to enhance mathematical

skills in the workplace

• We also pioneer the development of innovative

teaching and learning resources