faculty of science and engineering

mathematics and applied mathematics

A Comparison Between Poisson Regression And The Bradley-Terry Model To Predict The Rank Order Of The 2019 Eurohockey Championship

Bachelor’s Project Mathematics

July 2019

Student: B.B. Looijen

First supervisor: Dr. W.P. Krijnen

Second assessor: Dr. M. Grzegorczyk

Abstract

Field hockey is a growing sport and even though more than 1 billionpeople play or watch the sport, there is little statistical research on thesport. In this paper we will use two statistical models to predict the Eu-rohockey Championship that will take place in Antwerp in August 2019.The first model that is used is the Bradley-Terry model which is a knownmodel used for predicting sports outcomes. The second model is a Gen-eralized Linear Model where more variables are taken into account suchas the shape of the teams and home advantage. These models can beextended for predicting future field hockey events.

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Contents

1 Introduction 5

2 The tournament 62.1 The Group Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 The Knock-Out Stage . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Competition for places 5 to 8 . . . . . . . . . . . . . . . . . . . . 72.4 The final rank order . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Theory 83.1 Bradley-Terry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.1.1 The original model . . . . . . . . . . . . . . . . . . . . . . 83.1.2 Bradley-Terry with draws . . . . . . . . . . . . . . . . . . 9

3.2 Generalized Linear Models . . . . . . . . . . . . . . . . . . . . . . 103.2.1 Linear Models . . . . . . . . . . . . . . . . . . . . . . . . 103.2.2 Generalized Linear Models . . . . . . . . . . . . . . . . . 11

3.3 The Poisson distribution . . . . . . . . . . . . . . . . . . . . . . . 113.3.1 Skellam distribution . . . . . . . . . . . . . . . . . . . . . 12

4 Model Selection 134.1 Ranking Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2 Test of equal preference in Bradley-Terry . . . . . . . . . . . . . 134.3 Parameter testing in Generalized Linear Model . . . . . . . . . . 144.4 Collinearity in Generalized Linear Model . . . . . . . . . . . . . . 154.5 R2 and Pseudo R2 in Generalized Linear Model . . . . . . . . . . 154.6 Akaike’s Information Criterion . . . . . . . . . . . . . . . . . . . 16

5 Data 175.1 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.2 Preparing data for Generalized Linear Model . . . . . . . . . . . 19

6 Benchmark model 216.1 Bradley-Terry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216.2 Generalized Linear Model . . . . . . . . . . . . . . . . . . . . . . 23

7 Results 277.1 Bradley-Terry model . . . . . . . . . . . . . . . . . . . . . . . . . 277.2 Generalized Linear Model most likely outcome . . . . . . . . . . 287.3 Generalized Linear Model Predictions . . . . . . . . . . . . . . . 29

8 Concluding remarks 30

9 Discussion 31

A Data set 33

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B Bradley-Terry Estimates 48B.1 Values of qi in the 3 different models . . . . . . . . . . . . . . . . 48B.2 Final rank matrix for the Bradley-Terry Models . . . . . . . . . . 49

C Estimates for the Generalized Linear Models 50C.1 All possible linear combinations for η . . . . . . . . . . . . . . . . 50C.2 Most likely outcomes for the 2019 Eurohockey Championship . . 53

D R code 54

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1 Introduction

In this paper the goal is to predict the 2019 Eurohockey Championship. Whilemultiple models are used to predict soccer outcomes, there is no prior researchon predicting field hockey games, and the goal of this paper is to fill that void.In the first part of the paper the format of the tournament is explained, afterwhich we introduce the rank order which we want to predict in this thesis. Af-terwards we introduce the reader to the theoretical knowledge required for thesepredictions. Then the model selection criteria are chosen after which we startthe model testing by predicting the 2017 Eurohockey Championship. When thebest models are chosen we will try to predict the Eurohockey Championship inChapter 7.

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2 The tournament

The Eurohockey Championship is a biennial event where the 8 best Europeanfield hockey nations play for the title of European Champion alongside a ticketfor the 2020 Olympic Games. This year the tournament will take place inAntwerp, Belgium from August 16 until August 24, when the new EurohockeyChampions are crowned. The qualification for this tournament is based on per-formance in the previous edition of the Eurohockey Championship. The worstperforming teams are demoted to the Eurohockey Championship II and the bestfrom the Eurohockey Championship II are promoted to the main tournament.

Team Way of qualifyingBelgium Host country

Netherlands Reigning championEngland 3rd place EHCGermany 4th place EHC

Spain 5th place EHCIreland 6th place EHC

Scotland Champion EHC IIWales Runner-up EHC II

Table 1: The eight teams that participate in the 2019 Eurohockey Championship

2.1 The Group Stage

On August 28, 2018 the two groups A and B were drawn by the EuropeanHockey Federation (EHF). [4] In each group all participants will play a gameagainst the 3 other teams once, resulting in 6 games in the group stage. Atthe end of the game the teams are rewarded points for the final scoreline. Awin results in 3 points for the winning team, a draw results in 1 point for bothteams, and a loss results in 0 points. After these 6 games are played, both groupA and B will be ordered based on the following criteria:

• total points

• goal difference

• goals scored

• head-to-head result

In each group there are 4! = 4 · 3 · 2 · 1 = 24 unique orderings of the teams, eachresulting in a different post-group stage. Unlike in a traditional Group Stagetournament, where only the top 2 of each group proceed, all 8 participants moveon to the next stage of the tournament.

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2.2 The Knock-Out Stage

For both groups the number 1 and 2 qualify for the knock-out stage of thetournament. In the knock-out stage these four teams compete in a traditionalsingle elimination bracket. In a single elimination bracket ties are not allowed,and hence if after 60 minutes of play the score is tied, the teams face off inshootouts to determine the winner.

Champion

Winner SF1

Group A 1st

Group B 2nd

Winner SF2

Group A 1st

Group B 2nd

3rd place

Loser SF1

Loser SF2

Figure 1: Bracket for the knock-out stage of the Eurohockey Championship

2.3 Competition for places 5 to 8

As mentioned earlier in the paper there is a post-group stage for all participants.The teams that end in 3rd or 4th place in their respective group will form a newgroup C. While the other teams play in the knock-out stage these teams willplay another group stage, where all teams face each other one time to determinethe ranking. This second group stage is very important to the teams because 2of these teams will be relegated by the end of the tournament.

2.4 The final rank order

On the final day of the tournament there will be a unique rank order of the 8teams. The best team will be crowned European Champion, and automaticallyqualifies for the 2020 Olympic Games. The teams that en in number 7 and 8will be demoted to the 2021 Eurohockey Championship II. There are a totalof 8! = 40320 possible orders of teams, and since there are 22 games in total,which can result in a win, draw or loss there are 322 = 31381059609 possiblegame results. The goal of this thesis is to predict the order of the 8 teams inthe 2019 Eurohockey Championship.

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3 Theory

3.1 Bradley-Terry

In 1952 Bradley and Terry [2] presented a model to compare two different treat-ments. This model assigns a strength q to each team and based on the relativestrengths qi and qj assigns a probability of preference of treatment i over j. In2006, Huang, Weng and Lin extended the Bradley-Terry model and allowedequal preference between treatments, making it better suited for predictingsports outcomes.

3.1.1 The original model

In the original model there are m possible treatments, m ≥ 2. Each of the mteams is assigned a preference value qi, giving us the preference vector q ∈ Rm

Then for each i, j ∈ m the probabilities for preference of treatment i or j overthe other are given by

P ( i preferred over j ) =qi

qi + qj

P ( j preferred over i ) =qj

qi + qj

(1)

In this case the possibility of equal preference is equal to 0 since

P ( equal preference ) = 1− (qi

qi + qj+

qjqi + qj

) = 0 (2)

In this model the assumption is made that P( equal preference ) = 0. Howeverwhen predicting field hockey outcomes this is not the case. Besides team i orteam j winning there is a third option which is a draw. In order to allow drawsin the Bradley-Terry model there is the extended Bradley-Terry model.

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3.1.2 Bradley-Terry with draws

For a more realistic Bradley-Terry model we use the modification made byHuang, Weng and Lin. [8] In this model we have the following probabilities forthe three different treatments

P ( i preferred over j ) =qi

qi + θqj

P ( j preferred over i ) =qj

θqi + qj

P ( equal preference ) =(θ2 − 1)qiqj

(θqi + qj)(qi + θqj)

Where 1 ≤ θ <∞ is the draw-parameter to be estimated. Let m be the numberof teams, tij be the number of times that team i ties team j, rij is the numberof times i beats team j, we then need to minimize the following negative log-likelihood function:

minq,θ l(q, θ) =

= −m∑

j=i+1

m∑i=1

(rij logqi

qi + θqj+ rjilog

qjθqi + qj

+ tij log(θ2 − 1)qiqj

(θqi + qj)(qi + θqj))

= −m∑

j=i+1

m∑i=1

(rij logqi

qi + θqj+ rj,ilog

qjθqi + qj

+ tij logqi

θqi + qj+ tij log

qjqi + θqj

)

−m∑

j=i+1

m∑i=1

tij logθ2 − 1

θ2

(3)

Under the constraints

(1)

m∑i=1

qi = 1

(2) qi ≥ 0 for all i = 1, . . . ,m

The terms of l(q, θ) related to θ are

= −m∑

j=i+1

m∑i=1

(tij log(θ2 − 1)− (rij + tij)log(qi + θqj)− (rj,i + tij)log(θqi + qj))

≤ −m∑

j=i+1

m∑i=1

(tij log(θ2 − 1)− (rij + tij)(1 + log(qi + θtqj) +qi + θqjqi + θtqj

− (rji + tij)(1− log(θqi + qj) +θqi + qjθqi + qj

≡ Q(θ)

(4)

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Then Q′(θ) = 0 implies

m∑j=i+1

m∑i=1

(2θtijθ2 − 1

− (rij + tijqjqi + θqj

− (rji + tijqiθtqi + qj

)= 0 (5)

This gives us the following algorithm to update θ:

Algorithm 1Given a vector q which has the relative strengths qi where qi > 0 for each teami ∈ 1, . . . ,m, and θ1 = θ0 where θ0 is an arbitrary number between 1 and ∞Then for t = 1, 2, . . . until convergence θ is updated according to:

θt+1 =1

2Ct+

√1 +

1

4C2t

where

Ct =1

2∑mj=i+1

∑mi=1 tij

m∑j=i+1

m∑i=1

(rij + tijqj)

qi + θtqj+

m∑j=i+1

m∑i=1

(rji + tijqi)

θtqi + qj

Note that in this Algorithm qi > 0 instead of qi ≥ 0 so that Ct is not equal to∞

3.2 Generalized Linear Models

3.2.1 Linear Models

Given a response variable Yi and p different explanatory variables Xi1, . . . , Xip

for i = 1, . . . , n in a dataset. A linear model is used to define how responsevariable Yi depends on the explanatory variables. In a linear regression it isassumed that the response variable Yi is normally distributed. We then havethe following linear model:

yi = β0 + β1xi1 + β2xi2 + · · ·+ βpxip + εi = xTi β + εi

for i = 1, . . . , n and εi ∼ N(0, σ2)(6)

In this formula εi is the error term. εi is considered to be normally distributedwith mean µ = 0 and variance equal to σ2. The formula for a Linear Model isoften written in the following vectorized form

y = Xβ + ε

Where the respective vectors are given by

y =

y1y2...yn

, X =

xT1xT2...xTn

, β =

β1β2...βn

, ε =

ε1ε2...εn

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To estimate the parameter β there are two commonly used estimators, the leastsquared estimator and the Maximum Likelihood Estimator. In the book byDobson [1] on page 85 the Maximum Likelihood Estimator is derived, and inchapter 6 the least squared estimator is derived. For a Generalized Linear Modelthese are equal and given by:

βMLS = βLSE = (XTX)−1XTY

3.2.2 Generalized Linear Models

The biggest limitation of the traditional Linear Model is that the response vari-able Yi has to be normally distributed. However in many cases this is not acorrect assumption. The Generalized Linear Model extends the Linear Modelin a way to allow the response variable to be any member of the exponentialfamily. This allows us to use non-negative and discrete distributions as well,while retaining the properties of a Linear Model. For a model to classify as aGeneralized Linear Model it needs to have the following three properties:

• The response variable Yi a member of the exponential family, that is theprobability function of Yi can be written in the standard exponential form.

f(y; θ) = e(a(y)b(θ)+c(θ)+d(y))

• There is a linear predictor η which is of the form of the regular linearmodel in the previous subsection, hence ηi = xTi β

• There is a link function g which links the expected value of Yi to the linearpredictor ηi

g(E[Yi]) = ηi

3.3 The Poisson distribution

The Poisson distribution is a non-negative discrete distribution. It is discoveredby the French mathematician Simeon Denis Poisson[13]. It expresses the prob-ability of a certain number of events k occuring in a fixed interval of time. Inthis model it is assumed that these events happen at a constant rate indepen-dent of the last time an event occured. The distribution function of the Poissondistribution is given by

P (k events in given time interval) = e−λλk

k!

Here λ is the expected number of events in the time interval. The expectedvalue and variance of a Poisson distributed variable P are given by:

E[Y ] = V ar[Y ] = λ

The distribution can be rewritten as:

e−λ · 1

k!· λk = elogλ

k−λ+log 1k!

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Therefore the Poisson distribution belongs to the exponential family, whichallows it to be used for Generalized Linear Models. When a response variableYi is considered to be Poisson distributed, the natural link function is commonlyused to link Yi to ηi, that is:

g(E[Y ]) = logE[Y ] = log(λ)

3.3.1 Skellam distribution

Given two random variables Y1 and Y2 that are both independently Poissondistributed with mean λ1, λ2 respectively, the difference Z between these twovalues, Z = Y1−Y2 follows a Skellam distribution. That is Z∼ Skellam(λ1, λ2)The distribution is given by:

f(z;λ1, λ2) = e−(λ1+λ2)

(λ1λ2

)z/2Iz(2

√λ1λ2) (7)

where Iz is the modified Bessel-function which is defined by:

Iz(x) =

∞∑m=0

1

m!Γ(m+ z + 1)

(x2

)2m+z

Karlis and Ntouzfras [9] proved that when Y1 and Y2 are dependent as is the casewhen predicting sports outcome with a Generalized Linear Model, the Skellamdistribution still can be used to predict Z = Y1 − Y2 For the random variable Zwe have:

E[Z] = λ1 − λ2, and V ar[Z] = λ1 + λ2

Using the Skellam distribution the probabilities P (Y1 > Y2), P (Y1 = Y2) andP (Y1 < Y2) can be calculated.

P (Y1 > Y2) = P (Z > 0) =

∞∑z=1

e−(λ1+λ2)

(λ1λ2

)z/2Iz(2

√λ1λ2)

P (Y1 > Y2) = P (Z = 0) = e−(λ1+λ2)I0(2√λ1λ2)

P (Y1 < Y2) = P (Z < 0) =

−1∑z=−∞

e−(λ1+λ2)

(λ1λ2

)z/2Iz(2

√λ1λ2)

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4 Model Selection

4.1 Ranking Coefficient

As was stated in the introduction of this paper the goal is to predict the rankorder at the Eurohockey Championship. To do so we define the Ranking Coef-ficient as:

RC ≡∏8i=1 Pi18

8 (8)

Where Pi is the probability of correctly predicting the team that ends in the ith

place. The completely random model where all teams have a probability of 18

of ending in each of the 8 places has an RC value of 1, and the maximum valueof RC is equal to 1

188 = 88 = 1.68 ∗ 107.

Since we do not know the result of the 2019 Eurohockey Championship, allmodels will be tested on the 2017 Eurohockey Championship.

4.2 Test of equal preference in Bradley-Terry

In order to assure that in the Bradley-Terry model the parameters q are not allequal we use the following test of equal preferences

H0 : qi =1

mfor all i ∈ 1, . . . ,m

H1 : qi 6=1

mfor some i ∈ 1, . . . ,m

Under the null hypothesis we have T ties in N games. In order to maximize thiswe can calculate our value of θ

P (tie) =(θ2 − 1) 1

m2

( θ+1m )2

while P (win) =2 ∗ 1

mθ+1m

This can be simplified to:

P (tie) =θ2 − 1

(θ + 1)2and P (win) =

2

θ + 1

Solving P (win) ∗N = N − T yields

2

θ + 1∗N = N − T

2N = (N − T )(θ + 1)

2N = (N − T )θ +N − TN + T = (N − T )θ

θ0 =N + T

N − T

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Given our θ0 and q under the null hypothesis we can use the likelihood ratiotest statistic Λ to obtain the statistic S for testing the null hypothesis againstthe alternative:

S = −2log Λ

= 2

(l(q, θ)− (N − T )log

N − TN

− T logT

N

)= 2

(l(q, θ)− (N − T )log(N − T )− T logT +N logN

)d−→ χ2(m− 1)

We can then calculate the P-value of this statistic as:

p = P (X ≥ S), X ∼ χ2(m− 1)

We will reject the test of equal preference if p < 0.05

4.3 Parameter testing in Generalized Linear Model

When using a Generalized Linear Model the goal is to estimate the vector β.In this paper we will use the Maximum Likelihood Estimator βMLE . As can beseen in [1] the maximum likelihood estimates convergence in distribution to anormal distribution, that is

βMLEd−→ N(β, I−1)

Where I−1 is the inverse of the information matrix I which is given by

[I(β)]i,j = E

[(δ

δβilogf(Y ;β)

)(δ

δβjlogf(Y ;β)

) ∣∣∣β]In the Generalized Linear Model we want to check if the variable xi affects theresponse variable Yi that is if the coefficient βi is non-zero. To test this weformulate the null hypothesis H0 and the alternative hypothesis H1 as follows:

H0 : βi = 0

H1 : βi 6= 0

Under H0 we have that βid−→ N(0, σ2

βi) ⇔ βi

σ2βi

d−→ N(0, 1) where σ2βi∼ N(0, 1)

is the ith element along the diagonal of the inverse of the information matrixI. We can now follow the standard procedure for hypothesis testing from [1] tocalculate the p-value for the null hypothesis.

pj = P

(|Z| ≥

∣∣∣ βiσ2βi

∣∣∣) Z ∼ N(0, 1)

We reject H0 if pj < 0.05

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4.4 Collinearity in Generalized Linear Model

When modelling a Generalized Linear Model it is important to look at thecollinearity between the predictors Xi in the model. A measure of the collinear-ity is the Variance Inflation Factor (VIF) which can be calculated in the followingmanner:

For each i ∈ 1, . . . , m we run an ordinary least square regression where Xi is afunction of the other explanatory variables X, for i = 1 that yields:

X1 = α0 + α2X2 + α3X3 + · · ·+ αkXk + ε

Then for each βi we can calculate the Variance Inflation Factor by:

VIFi =1

1−R2i

Where R2i is obtained from the regression in step one with Xi on the left hand

side and all the other predictors Xj with j 6= i, j = 1, . . . ,m on the right handside. We then obtain a vector VIF which consists of all the different values ofV IFi. According to the article by Mansfield and Helms [11] we should removea parameter in a predictive model if for a given i we have VIF(βi) > 5. For thenew model we have to redo the ordinary least squares regression to find the newVariance Inflation Factors. If for all i we have VIF(βi) < 5 the model does nothave high multicollinearity and can be used as a prediction model.

4.5 R2 and Pseudo R2 in Generalized Linear Model

In an ordinary least squares regression (OLS) R2 is the ratio of explained vari-ance in the model. Therefore a higher R2 implies a better model. In OLS theR2 can be computed by:

R2 = 1−∑Ni=1(yi − yi)2∑Ni=1(yi − yi)2

Where N is the number of observations, y is the dependent variable, y is equalto the mean of the of y y is the value predicted by the model. However for aGeneralized Linear Model it is not possible to compute the R2. An alternativeto R2 for generalized linear models is McFadden’s pseudo R2 [6]. It is definedas:

R2 = 1− logL(Mfull)

logL(Mint)

where Mfull is the model with all predictors, and Mint is the model where only

the intercept term is used. L is the estimated likelihood under each of themodels.

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4.6 Akaike’s Information Criterion

In the book by Koneshi and Kitagawa [10] the different criteria for model se-lection are discussed. Akaike’s Information Criterion (AIC) is an evaluationcriterion for the badness of the model whose parameters are estimated by themaximum likelihood, and it indicates that the bias of the log-likelihood approx-imately becomes the number of free parameters contained in the model.

AIC = 2k − 2log(L)

Where k is the number of parameters to be estimated, and L is the maximumlikelihood under the model that is tested. An alternative Information Criterionthat can be considered is the Bayesian Information Criterion. (BIC)

BIC = log(n) · k − 2log(L)

Here k and L are the same as in the previous model, and n is the number ofobservations in the data set. A complex model is more heavily punished by BICthan AIC, and therefore for predictive model the AIC is the best statistic to testaccording to Koneshi and Kitagawa [10]. The goal of the AIC comparison is tominimize it. A lower AIC means that the model is a better predictive model.That also means that complex models are punished and hence simpler modelsare better for predicting. When comparing models there are cutoff values, whenthey have a difference in AIC of less than 2 they are considered equally favored.While a model with a difference of between 2 and 5 is slightly favored over theother model. When the difference in AIC is more than 5, the model with thelower AIC is strongly favored. Therefore we will consider models that have adifference of at most 5 with the best model.

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5 Data

For the data set all the games of the top 20 countries according to the FederationInternational Hockey (FIH) since the 2014 World Cup are taken. These teamsare ranked based on the ELO of a team. The ELO is determined by the resultson all official tournaments by a team. When a team finishes in first place theyreceive the maximum amount of points for the given tournament, and everyteam after that receives less points than the team above. In Table 2 the pointsawarded for the top 4 teams at the major tournaments are listed, a full listof points can be found on [7]. All tournaments that were played over the lastfour years count towards the current ELO, however the number of points arereduced by 25% each year. Tournaments played more than four years ago donot contribute to the ELO. [7] Based on this ELO system, the 20 teams arechosen for each year. This results in a total of 712 games played between 27unique countries. For each of these games the following data is recorded. Thefull data list can be found in Appendix A.

• Teami: Team 1 and respectively Team 2, the participants of the game.

• Scorei: Goals scored by Team i

• Home: Which team played at home: 1 if Team1 played at home, -1 ifTeam2 played at home and 0 if the game was played on neutral grounds

• Date & Year: The exact date and time when the game was played

• ELOi: The ELO of Team i at the time of the game

• WorldRankingi: The world ranking of Team i at the time of the game.

Tournament 1st Place 2nd Place 3rd Place 4th PlaceOlympic Games 750 650 550 450

World Cup 750 650 550 450Pro League 700 650 625 575Euro Cup 750 700 650 600

Table 2: Points counting towards ELO a European team can earn every fouryear period

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5.1 Data analysis

In Table 4 the total data for the 27 different teams is presented. Since the gamesfrom the top 20 teams are only recorded, the number of games in the data setvaries from country to country. The number of drawn games is equal to 120out of 712, therefore on average a game has a 120

712 ∗ 100% = 16.85% chance ofdrawing, when two teams are randomly chosen. Clearly this probability variesdepending on which teams are chosen. The average number of goals a teamscores is equal to 2.32, and clearly the average number of goals conceded isequal to that since all games are in the data set. Since our goal is to fit thenumber of goals scored with a Generalized Linear Model, it is required to findwhich distribution fits this data.

In Table 3 the number of goals scored in each game is recorded. Since thereare two teams participating in each game, there is a total of 1424 observationsfor our variable Y . According to the literature [12] , goals scored in a team basedsport follow a Poisson distribution. Hence the data was fitted with a Poissondistribution with λ = average number of goals. The result for the total data setand the result for the number of goals scored by Belgium are in Figure 2

Goals scored 0 1 2 3 4 5 6 7Frequency 202 354 335 228 141 66 45 29

Goals scored 8 9 10 11 12 13 ≥14 TotalFrequency 9 6 5 2 1 1 0 1424

Table 3: Frequencies of number of goals scored in all games played by the 27teams

Figure 2: Goals scored versus best Poisson approximation for all games played(left) and specifically for Belgium (right)

18

Team Games Goals Conceded W D L GA GCAArgentina 90 220 178 51 12 27 2.44 1.98Australia 109 366 131 84 13 12 3.36 1.2Austria 14 19 33 3 5 6 1.36 2.36Belgium 98 332 169 61 19 18 3.39 1.72Brazil 5 1 46 0 0 5 0.2 9.2

Canada 70 115 225 13 10 47 1.64 3.21China 19 24 89 2 2 15 1.26 4.68Egypt 12 9 46 1 1 10 0.75 3.83

England 106 262 221 40 25 41 2.47 2.08France 47 84 126 16 7 24 1.79 2.68

Germany 97 294 182 55 21 21 3.03 1.88India 101 240 200 44 19 38 2.38 1.98

Ireland 74 145 179 23 13 38 1.96 2.42Italy 2 5 11 0 1 1 2.5 5.5

Japan 36 59 102 5 3 28 1.64 2.83Korea 36 69 99 10 7 19 1.92 2.75

Malaysia 63 129 188 23 7 33 2.05 2.98Netherlands 97 293 150 60 16 21 3.02 1.55New Zealand 76 175 172 26 17 33 2.3 2.26

Pakistan 45 68 124 11 8 26 1.51 2.76Poland 30 37 92 7 3 20 1.23 3.07Russia 5 7 42 0 0 5 1.4 8.4

Scotland 30 53 80 8 4 18 1.77 2.67South Africa 32 53 109 8 3 21 1.66 3.41

Spain 89 187 197 33 20 36 2.1 2.21USA 12 14 34 2 1 9 1.17 2.83Wales 29 38 73 6 3 20 1.31 2.52Total 1424 3298 3298 592 240 592 2.32 2.32

Table 4: Statistics of the 27 countries in the data set

5.2 Preparing data for Generalized Linear Model

When predicting the number of goals scored Yi by a given team there are manyfactors to consider. First off it is to be expected that a team that is higherranked than their opponent will score more goals, since in order to be rankedhigher they have to win more games. Therefore in our model we will use thetwo statistics from our dataset ELO and WorldRanking for both teams, anduse their difference in our predictive model. Also as was shown in [5] andvarious other statistical models predicting sport outcomes playing at home alsoinfluences the performance of a team, therefore we will also use the predictorHome. The most important predictor for how many goals a team will score isthe amount of goals that they have scored in the previous games, similarly theamount of goals that the opposing team has conceded in the previous games are

19

also important. Therefore the factors average goals scored and average goalsconceded in the games before could be added as predictors in the model. It ishowever not a reasonable assumption that the number of goals scored in a game3 years ago have the same impact as the number of goals in the previous game.Therefore the attacking and defending qualities of each team are divided intothree subgroups:

• ATTf The average over the 3 most recent games is called the form, thisaccounts for teams that are currently on a roll

• ATTlfThe average over the next 7 games, the long-term form, this dataallows us to look at a steady increase or decline in strength of a team

• ATTb The average over the rest of the games is considered as the baseattacking strength of a team.

When a game has less games preceding it than required for any of the givensubgroups, it is set equal to the statistic of the game after it, ensuring that allstatistics are smooth everywhere in the data set. The same subscripts are usedfor the defensive stats where instead of goals scored we look at the number ofgoals conceded. After each game a team has played these different forms will beupdated, to illustrate how this works the three most recent games Germany hasplayed are in Table 5.2. The average number of goals scored by Germany in thesegames is 5

3 = 1.67 and the average number of goals conceded is 83 = 2.33 which

is in accordance with Table 6. In this table all statistics for the Eurohockeychampionship participants are shown.

Team 1 Team 2 Score 1 Score 2 DateGermany England 0 1 28.04.2019Germany Netherlands 2 4 26.04.2019

Spain Germany 4 4 15.03.2019

Table 5: Germany’s three most recent games in the data set

Team Rank ELO ATTb DEFb ATTf ATTfl DEFf DEFflBelgium 1 2246 3.33 1.77 5.00 3.29 1.33 1.29England 7 1551 2.51 1.95 1.00 2.71 2.67 3.43

Spain 9 1133 2.06 2.05 1.67 2.86 4.67 3.14Wales 24 433 1.33 2.67 0.33 1.43 2.33 2.29

Netherlands 3 2079 3.03 1.50 2.33 3.00 1.67 2.00Germany 6 1681 3.13 1.85 2.00 2.29 3.00 1.57Ireland 11 1030 2.10 2.24 1.00 1.14 3.33 3.43

Scotland 23 484 2.00 2.84 1.33 1.57 1.67 2.86

Table 6: The coefficients for each of the linear predictors for the 8 Eurohockeyparticipants

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6 Benchmark model

As mentioned earlier in the paper we will now test our various models to predictthe Eurohockey Championship 2017 results, which are known. However in ourpredictions we will only use explanatory variables which were availabe prior tothe start of the 2017 Eurohockey championship, which means that the conditionsare similar to our prediction for the 2019 Eurohockey Championship.

6.1 Bradley-Terry

For the Bradley-Terry model we look at three different models. The first twomodels are commonly used, where the teams are awarded points for every winand drawn game in the data set. The third model bases the strength purely onthe ELO of each of the teams.

(1) : qi =2 ∗ ri + ti

Ni

(2) : qi =3 ∗ ri + ti

Nifor i = 1, . . . ,m

(3) : qi = ELOi

Note that in order for Algorithm 1 to be applied, it is necessary that giveni ∈ 1, . . . ,m qi > 0. In model (1) and (2) we therefore add 1

Nito each team’s

qi to allow us to compute the draw parameter θ. Before calculating θ for eachof the models we first have to normalize qi, such that

∑mi=1 qi = 1. For all 3

models the values of qi are computed after which they are used in Algorithm1 to find the draw parameter θ. We can then calculate the probability a givengame will end in a win, draw or loss using the extended Bradley-Terry model.In Table 7 the game results in group A for model 3 are shown. The differentvalues of qi in each of the models are in Appendix B Combining these results wecan predict in which order the teams are finishing the group stage, these resultscan be found in Table 8

After the group stage the teams either advance to the Knock-Out stage orare moved in to the new group C where they battle in a new group stage in orderto remain in the Eurohockey Championship. In the knock-out stage draws are

game Team 1 Team 2 P(win) P(Draw) P(Loss)1 Netherlands Belgium 0.31 0.39 0.302 Netherlands Spain 0.39 0.38 0.233 Netherlands Austria 0.59 0.29 0.124 Belgium Spain 0.38 0.38 0.245 Belgium Austria 0.58 0.30 0.126 Spain Austria 0.50 0.34 0.16

Table 7: Game results at the 2017 Eurohockey Championship in group A ac-cording to the third Bradley-Terry model

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Group A P(1st place) P(2nd place) P(3rd place) P(4th place)Netherlands 0.37 0.30 0.22 0.11

Belgium 0.36 0.30 0.23 0.11Spain 0.22 0.27 0.31 0.20

Austria 0.05 0.13 0.24 0.58

Table 8: Final standings in Group A of the 2017 Eurohockey Championshipaccording to the third Bradley-Terry model

Rank Team P(1st) P(2nd) P(3rd) P(4th) P(5th) P(6th) P(7th) P(8th)1 Netherlands 0.202 0.162 0.166 0.120 0.154 0.111 0.074 0.0402 Belgium 0.194 0.161 0.163 0.122 0.154 0.114 0.077 0.0423 England 0.145 0.151 0.153 0.141 0.144 0.132 0.102 0.0644 Germany 0.206 0.163 0.177 0.126 0.142 0.106 0.070 0.0375 Spain 0.112 0.136 0.125 0.136 0.148 0.148 0.127 0.0886 Ireland 0.107 0.134 0.130 0.146 0.137 0.146 0.129 0.0917 Poland 0.018 0.048 0.046 0.111 0.061 0.122 0.210 0.3088 Austria 0.016 0.044 0.040 0.098 0.060 0.121 0.212 0.330

Total 1 1 1 1 1 1 1 1

Table 9: Probabilities for each team to attain a given rank at the 2017 Euro-hockey Championship according to Bradley-Terry model 3

no longer allowed, and therefore we use the traditional Bradley-Terry model tocalculate the probability that Team i beats Team j. After this stage of the tour-nament we have an 8x8 matrix with all possible outcomes. Along the diagonalof this matrix are the probabilities that a certain country is correctly assignedthe rank that it achieved on the 2017 Eurohockey Championship. In AppendixB.2 these matrices are also available for the other Bradley-Terry models. Wecan now compute for each of the Models the value of θ, the p value for the testof equal preferences and the value of our Ranking Coefficient.

Model 1 Model 2 Model 3θ 2.35 2.33 2.26p < 2e−16 < 2e−16 < 2e−16

RC 8.67 7.84 14.91

Table 10: Results for the 3 different Bradley-Terry Models at the 2017 Euro-hockey Championship

In Table 10 the results for the different models are presented. As was expectedfor all 3 models the test of equal preferences is rejected. The best model is the3rd model which only using the data available prior to the 2017 EurohockeyChampionship was 15 times more likely to correctly predict the outcome thana random model. Therefore we will use this model as our best Bradley-Terrymodel for predicting the 2019 Eurohockey Championship.

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6.2 Generalized Linear Model

In the previous chapter we defined 9 explanatory variables for the amount ofgoals scored by a given team. Because each of these explanatory variablescan be in- or excluded in the predictor this yields a total of 29 = 512 modelsto be compared. However before we can compare these models we first haveto check if there is multicollinearity in the data set. As explained in section4.4, We do this by computing the Variance Inflation Factor for each of the 9explanatory variables and obtain the results in Table 11. As was to be expectedthe ELO difference (∆ELO)and rank difference (∆rank) are heavily collinearand therefore one of the predictors has to be removed from the full model. Sincethe Variance Inflation Factor is higher for the ELO difference we remove thisfrom the model, we now obtain the results in Table 12. The results are betterthan before, however, the Variance Inflation Factor of the long-term defensiveform is still above our threshold value of 5. This leads to the removal of thispredictive variable from the model as well. The Variance Inflation Factor forour final model is in Table 13. Given the 7 remaining predictive variables Xi

we have a total of 27 = 128 different possibilities for the linear predictor η.For each of these models we will compute the AIC and will choose the 10

best models based on their AIC. A table with the coefficients and AIC of all128 models is added in the Appendix C

Home ∆Rank ∆ELO ATTb DEFb ATTf ATTfl DEFf DEFfl1.04 8.86 9.57 2.19 4.35 1.28 1.69 2.30 5.16

Table 11: VIF for the full Generalized Linear Model with all 9 predictors forthe 2017 Eurohockey Championship

Home ∆Rank ATTb DEFb ATTf ATTfl DEFf DEFfl1.03 1.90 1.98 4.44 1.28 2.35 1.67 5.27

Table 12: VIF after removing the ELO difference from the model yielding 8remaining predictors

Home ∆Rank ATTb DEFb ATTf ATTfl DEFf1.03 1.89 1.96 2.90 1.28 1.66 2.26

Table 13: VIF after removing the predictors which were over the threshold.Model we will use for testing the 2017 Euorohockey Championship

According to the AIC the first model is the best model, although the 3 followingmodels have no significant difference in AIC, because the difference in AIC isless than the cutoff value of 2 introduced by Konishi and Kitagawa [3]. The 6remaining models are slightly unfavored over the best model and we will takethat into account when comparing these models. For these 10 models we willcompute the pseudo R2 as well as the final rank matrix and Ranking Coefficient.

23

(Int) ATTf ATTfl ATTb DEFf DEFb Home ∆Rank df AIC127 -0.057 0 0.091 0.109 0.035 0.111 0.089 -0.028 7 2592.917128 -0.094 0.023 0.088 0.099 0.036 0.115 0.091 -0.027 8 2593.65119 -0.047 0 0.094 0.105 0 0.143 0.089 -0.028 6 2593.966120 -0.082 0.022 0.091 0.096 0 0.147 0.091 -0.027 7 2594.84395 0.005 0 0.082 0.109 0.035 0.108 0 -0.028 6 2595.31996 -0.029 0.022 0.079 0.099 0.036 0.112 0 -0.027 7 2596.23987 0.014 0 0.086 0.105 0 0.14 0 -0.028 5 2596.40288 -0.016 0.02 0.083 0.096 0 0.144 0 -0.027 6 2597.472124 0.025 0.035 0.129 0 0.034 0.109 0.092 -0.03 7 2598.083125 0.049 0 0 0.168 0.039 0.1 0.074 -0.028 6 2598.872

Table 14: The 10 best models ordered by their AIC value for predicting the2017 Eurohockey Championship

In Table 15 the outcomes for the group stage in group B are presentedwhen using Generalized Linear Model 6 from Table 14. These probabilities areobtained by calculating the expected number of goals scored by each of theteams using the Generalized Linear Model, and then using these as values λ1and λ2 for the Skellam distribution discussed in section 3.3.1. We then usethese to simulate the group stage in R to obtain the predicted results in groupB. Combining this with the predicted results of group A yields the final rankmatrix in Table 16

Group B P(1st place) P(2nd place) P(3rd place) P(4th place)Germany 0.504 0.329 0.154 0.012England 0.360 0.389 0.226 0.024Ireland 0.133 0.265 0.502 0.101Poland 0.003 0.017 0.118 0.863

Table 15: Results in group B at the 2017 Eurohockey Championship accordingto Generalized Linear Model 6

Rank Team P(1st) P(2nd) P(3rd) P(4th) P(5th) P(6th) P(7th) P(8th)1 Netherlands 0.4 0.211 0.178 0.06 0.091 0.024 0.002 02 Belgium 0.339 0.242 0.187 0.076 0.109 0.033 0.003 03 England 0.084 0.184 0.219 0.256 0.157 0.106 0.02 0.0034 Germany 0.147 0.224 0.275 0.201 0.116 0.059 0.008 0.0015 Spain 0.015 0.069 0.05 0.122 0.283 0.353 0.109 0.0276 Ireland 0.015 0.069 0.09 0.258 0.214 0.269 0.092 0.0247 Austria 0 0 0 0.007 0.015 0.078 0.381 0.4898 Poland 0 0 0.001 0.02 0.014 0.076 0.385 0.455

Total 1 1 1 1 1 1 1 1

Table 16: Final rank matrix at the 2017 Eurohockey Championship for Gener-alized Linear Model 6

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Table 16 is ordered such that the teams are in the order they finished at the2017 Eurohockey Championship. Therefore we can multiply the elements in the

diagonal of the matrix and divide by 18

8to obtain the Ranking Coefficient. In

the case of Model 6 the ranking coefficient is therefore calculated by:

RC6 =0.400 ∗ 0.242 ∗ 0.219 ∗ 0.201 ∗ 0.283 ∗ 0.269 ∗ 0.381 ∗ 0.455

(0.125)8= 944

Model AIC Pseudo R2 RC1 2592.92 0.106 16112 2593.65 0.107 17473 2593.97 0.105 18834 2594.84 0.106 20315 2595.32 0.105 8796 2596.24 0.105 9447 2596.40 0.104 10628 2597.47 0.104 11419 2598.08 0.105 250510 2598.87 0.104 523

Table 17: AIC, pseudo R2 and RC for the 10 different Generalized Linear Modelswhen predicting the 2017 Eurohockey Championship

For all 10 models we have calculated the ranking coefficient, the AIC and pseudoR2 and summarized these in Table 17

Based on the results in Table 17 we see that the pseudo R2 for all modelsis approximately the same. Therefore we choose our model based on the AICand the Ranking Coefficient. As described in section 4.6, when a model has adifference of less than 2 with the best model they are considered equally goodfor predicting. Therefore we will examine Model 3 and 4. The model with thebest ranking coefficient, Model 9 has an AIC which is less than 5 above the AICas our best model, and therefore we will also look at that model. In Table 6.2the β are estimated for the models. As mentioned in section 4.3, if pj > 0.05 weassume that the estimated parameter β is equal to 0. This results in the factthat all models have the same explanatory variables, because ATTf and DEFfare not significant in model 4 and 9. Therefore our best Generalized LinearModel is Model 3 and our linear predictor is:

ηi =− 0.047 + 0.094 ·ATTfl(i) + 0.105 ·ATTb(i) + 0.143·DEFb(j) + 0.089 ·Home(i)− 0.028 · (Rank(i)−Rank(j))

E[Yi] =eηi

The explanatory variables in our model are in line with our expectations. Theform of a team is significant, and therefore hot streaks appear to be a thingin field hockey. Also the home advantage that is discussed in [5] is present in

25

our model. The reason why the coefficient for the rank difference is negative isbecause a lower rank means a higher ELO, and therefore a better team.

Dependent variable:

Score1

(Model 3) (Model 4) (Model 9)

ATTf 0.022 0.035∗

(0.020) (0.020)

ATTfl 0.094∗∗∗ 0.091∗∗∗ 0.129∗∗∗

(0.032) (0.032) (0.027)

ATTb 0.105∗∗∗ 0.096∗∗

(0.038) (0.039)

DEFf 0.034∗

(0.020)

DEFb 0.143∗∗∗ 0.147∗∗∗ 0.109∗∗∗

(0.021) (0.021) (0.028)

Home 0.089∗∗ 0.091∗∗ 0.092∗∗

(0.042) (0.042) (0.042)

∆ Rank −0.028∗∗∗ −0.027∗∗∗ −0.030∗∗∗

(0.004) (0.004) (0.004)

Intercept −0.047 −0.082 0.025(0.114) (0.118) (0.108)

Observations 712 712 712Log Likelihood −1,290.924 −1,290.342 −1,291.962Akaike Inf. Crit. 2,593.847 2,594.684 2,597.924

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Table 18: The 3 best Poisson Regression models to predict the 2017 EurohockeyChampionship

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7 Results

In this section we will predict the 2019 Eurohockey Championship using thebest Bradley-Terry and General Linearized Model which were found in the pre-vious section. For the Bradley-Terry model the estimated results in the groupstage and the final rank matrix is shown. For the Generalized Linear Modelwe will also add the most likely results of all games on the 2019 EurohockeyChampionship.

7.1 Bradley-Terry model

In this section we first look at the probabilities in the group stage of the Eu-rohockey Championship according to the Bradley-Terry model. These proba-bilities are calculated using the estimates qi from model 3. These probabilitiesresult in the final rank matrix in Table 21, as is to be expected Belgium has thebiggest probability to win the tournament because they have the highest ELOcurrently.

Group A Team 1 Team 2 P(win) P(Draw) P(Loss)1 Belgium England 0.492 0.192 0.3162 Belgium Spain 0.570 0.178 0.2523 Belgium Wales 0.776 0.110 0.1144 England Spain 0.478 0.194 0.3285 England Wales 0.706 0.137 0.1576 Spain Wales 0.636 0.160 0.204

Table 19: game outcomes according to the Bradley-Terry model

Group B Team 1 Team 2 P(win) P(Draw) P(Loss)1 Netherlands Germany 0.453 0.196 0.3512 Netherlands Ireland 0.574 0.177 0.2493 Netherlands Scotland 0.742 0.123 0.1354 Germany Ireland 0.522 0.187 0.2915 Germany Scotland 0.699 0.139 0.1616 Ireland Scotland 0.587 0.173 0.239

Table 20: game outcomes according to the Bradley-Terry model

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Rank Team P(1st) P(2nd) P(3rd) P(4th) P(5th) P(6th) P(7th) P(8th)1 Belgium 0.260 0.176 0.191 0.112 0.138 0.083 0.041 0.0172 Netherlands 0.235 0.177 0.190 0.121 0.143 0.093 0.049 0.0213 Germany 0.175 0.171 0.171 0.139 0.156 0.121 0.074 0.0364 England 0.155 0.166 0.160 0.143 0.160 0.131 0.084 0.0445 Spain 0.087 0.131 0.120 0.151 0.153 0.165 0.134 0.0856 Ireland 0.071 0.117 0.109 0.152 0.143 0.170 0.15 0.1017 Scotland 0.010 0.034 0.033 0.097 0.058 0.125 0.237 0.3228 Wales 0.007 0.028 0.027 0.086 0.048 0.112 0.231 0.374

Total 1 1 1 1 1 1 1 1

Table 21: The final rank matrix according to the Bradley-Terry model

7.2 Generalized Linear Model most likely outcome

Besides calculating the probability that one team beats the other we can also cal-culate the most likely number of goals that each team scores. Using this methodwe will predict the outcome of all games in the 2019 Eurohockey Championship.Given a random Poisson distributed variable Yi with mean λ the most likely out-come, the mode is given bybλc, the first integer equal to or less than λ. Given

Team1 Team2 Score 1 Score 2Belgium England 5 1Belgium Spain 5 1Belgium Wales 7 0England Spain 3 3England Wales 5 1

Spain Wales 4 1

Team1 Team2 Score 1 Score 2Netherlands Germany 3 2Netherlands Ireland 4 1Netherlands Scotland 6 1

Germany Ireland 4 1Germany Scotland 5 1Ireland Scotland 4 2

Table 22: Most probable outcomes in the group stage according to GLM 3

these game results the group winners will be Belgium and the Netherlands, whileGermany and England complete the top 4 for the knock out stage. In group AEngland and Spain both have 4 points, and England goes to the knock-out stagebased on goal difference. The remaining four teams will be moved to group Cwhere they will play a new group stage, the results of the games in this groupare in Table 7.2. In group C Wales and Scotland will both only receive one point

Team1 Team2 Score 1 Score 2Spain Ireland 3 2Spain Wales 4 1Spain Scotland 5 1

Ireland Wales 3 1Ireland Scotland 4 2Wales Scotland 2 2

Table 23: Most probable outcomes in group C

and therefore will be demoted to the Eurohockey Championship II according tothis model.

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For the knock out stage we take the bracket in Figure 1 and using the winnersand runner-ups of the two groups according to the Generalized Linear Modeland for these games also predict the expected scoreline.

Belgium

Belgium 3

Belgium 3

Germany 2

Netherlands 2

Netherlands 4

England 2

Germany

Germany 3

England 2

Figure 3: Knock-out stage Eurohockey Championship

According to the most probable outcome of the Generalized Linear Model Bel-gium will become European Champion. This model however does not take intoaccount any randomness and therefore we will also use the Generalized LinearModel to determine a rank matrix.

7.3 Generalized Linear Model Predictions

For the Generalized Linear Model we will predict the tournament in the sameway we did for the Bradley-Terry model. To determine the probability of acertain game resulting in a win, draw or loss, we again use the Skellam distribu-tion. The probabilities for each of the groups and games are in Appendix C.2The final rank matrix is given in Table 24

Rank Team P(1st) P(2nd) P(3rd) P(4th) P(5th) P(6th) P(7th) P(8th)1 Belgium 0.618 0.162 0.188 0.026 0.024 0.002 0.000 0.0002 Netherlands 0.220 0.323 0.248 0.095 0.065 0.018 0.002 0.0003 Germany 0.119 0.254 0.285 0.168 0.113 0.048 0.008 0.0014 England 0.027 0.145 0.140 0.284 0.269 0.152 0.038 0.0075 Spain 0.014 0.096 0.100 0.256 0.295 0.205 0.062 0.0156 Ireland 0.002 0.018 0.037 0.130 0.191 0.365 0.180 0.0697 Wales 0.000 0.001 0.001 0.024 0.021 0.102 0.347 0.4598 Scotland 0.000 0.000 0.001 0.017 0.022 0.107 0.363 0.447

Total 1 1 1 1 1 1 1 1

Table 24: The final rank matrix according to the Bradley-Terry model

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8 Concluding remarks

The goal of this thesis was to obtain the best prediction of the rank order of the2019 Eurohockey Championship. All models that were tested in this thesis werebetter at predicting the outcome of the benchmark tournament in 2017 thanrandomly assigning each team a rank, however there were major differences.Due to the ability to add more variables in the Generalized Linear Model it isconsidered to be much better at predicting the outcome of a tournament thanthe commonly used Bradley-Terry model. The most likely outcome of the bestmodel for the 2017 Eurohockey Championship is given in Table 25

Rank Team Predicted team1 Netherlands Netherlands2 Belgium Belgium3 England Germany4 Germany England5 Spain Spain6 Ireland Ireland7 Austria Poland8 Poland Austria

Table 25: Most likely outcome according to our best Generalized Linear Modelcompared with real results for the 2017 Eurohockey Championship

As can be seen in the table the model and real outcomes only differ by2 permutations. Our ranking coefficient for the Generalized Linear Model weended up using was 1883, meaning that it is 1883 times as likely to predict thecorrect outcomes compared to randomly assigning each team a rank. Howeverin reality it is not the case that all teams have an equal chance of winning theEurohockey Championship and therefore this statistic by itself is not enough tosay that this model does a good job at predicting the Eurohockey Championship.In the case that the model is indeed correct then the probability of this exactordering is still only the multiplication of the diagonal, 2.869 ∗ 10−4, and sportindeed remains unpredictable. On the other hand this is the best field hockeyprediction model that is currently out there, and definitely can be extended andimproved on for further research.

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9 Discussion

Sport events and especially team sports are very unpredictable. Therefore itis very likely that there is pure error when predicting sports events, and themaximum pseudo R2 that a predictive model can have in this case is less than1. However as we have seen the pseudo R2 is not higher than 0.107 in anyof the Generalized Linearized Models that we have considered in this paper.There definitely is room for improvement there. Because of this randomnessit is perhaps better to add a random effect to the games in the form of aGeneralized Linear Mixed Model (GLMM) to better predict the variance in theoutcomes. Another point of discussion in the final model is that it does not useall the available data to predict the outcome of a game. The variables ATTf ,DEFfl and DEFf are omitted in the final model selection, which means that inthe prediction the 3 most recent games of the attacking team, and the 10 mostrecent games of the defending team are omitted. To better account for the shapeof the teams perhaps these variables need to be chosen differently to make surethat all available data is used. Due to the pseudo-R2 that is 0.104 it is likelythat variables that influence the outcome of a field hockey game have not beentested in this thesis. Perhaps individual skill of the players can be incorporated,the strength of the manager and the training regime. Different cultural aspectspossibly can also make an impact on the game, where for example Europeancountries have a playstyle which is favoured against Asian and South-Americancountries. Another improvement is testing these models on more tournaments.For certain teams the number of recorded games is small yielding outliers inthe average goals scored and conceded. In order to solve this problem the dataset would have to be enlarged to include more teams so that for each teamon the tournament we wish to predict at least 50 games are recorded, howeverin order for this to be possible the interest in the statistics for field hockeyneeds to increase since these games are not available to the public. Lastly thismodel is now tested only on the prediction of a single tournament, the 2017Eurohockey Championship. The Ranking Coefficient therefore is a predictivevariable which allows for a model to luckily predict the right outcome. In orderto better assess the Ranking Coefficient the model should be tested on moretournaments, however due to the limited data set this was not yet possible.

31

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[3] Kenneth P. Burnham and David R. Anderson. Multimodel inference: Un-derstanding aic and bic in model selection. Sociological Methods & Re-search, 33(2):261–304, 2004.

[4] European Hockey Federation. Regulations for eurohockey championships2019, 2019.

[5] Miguel A. Gomez, Richard Pollard, and Juan-Carlos Luis-Pascual. Com-parison of the home advantage in nine different professional team sports inspain. Perceptual and Motor Skills, 113(1):150–156, 2011. PMID: 21987916.

[6] Giselmar A. J. Hemmert, Laura M. Schons, Jan Wieseke, and Heiko Schim-melpfennig. Log-likelihood-based pseudo-r2 in logistic regression: Derivingsample-sensitive benchmarks. Sociological Methods & Research, 47(3):507–531, 2018.

[7] Federation International Hockey. http://www.fih.ch/rankings/outdoor/.

[8] Tzu-kuo Huang, Ruby C Weng, and Chih-jen Lin. Generalized bradley-terry models and multi-class probability estimates. Journal of MachineLearning Research, 7:85–115, 2006.

[9] Dimitris Karlis and Ioannis Ntzoufras. Bayesian modelling of football out-comes: Using the skellam’s distribution for the goal difference. Ima Journalof Management Mathematics - IMA J MANAG MATH, 20, 08 2008.

[10] Sadanori Konishi and Genshiro Kitagawa. Information Criteria and Sta-tistical Modeling. Springer, 2008.

[11] Edward R. Mansfield and Billy P. Helms. Detecting multicollinearity. TheAmerican Statistician, 36(3a):158–160, 1982.

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[13] Dennis Simeon Poisson. Connaiss. des temps. 1827.

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A Data set

The data set consists of all games from the 2014 World Cup until June 1st 2019

Game Team1 Team2 Score1 Score2 Home Event Date Year Rank1 Rank2 ELO1 ELO2

1 Belgium England 4 2 1 PL 30.05. 13:30 2019 1 7 2246 15512 Germany Argentina 3 3 1 PL 22.05 21:00 2019 6 4 1681 19083 England Belgium 0 4 1 PL 19.05. 16:00 2019 7 1 1551 22464 England Argentina 2 3 1 PL 18.05. 16:00 2019 7 4 1551 190839 Poland Scotland 1 0 1 FM 18.05. 17:00 2019 21 23 552 48440 Poland Scotland 1 2 1 FM 17.05. 19:00 2019 21 23 552 4845 Argentina Australia 1 2 1 PL 04.05. 23:30 2019 4 2 1908 22316 England Spain 1 1 1 PL 04.05 13:00 2019 7 9 1551 11337 China Wales 2 3 1 PL 02.05 14:05 2019 14 24 843 4338 Malaysia Wales 2 1 1 PL 01.05 14:05 2019 13 24 953 4339 Wales Austria 0 2 1 PL 29.04 10:05 2019 24 19 433 63810 Germany England 0 1 1 PL 28.04. 14:30 2019 6 7 1681 155111 Germany Netherlands 2 4 1 PL 26.04. 20:45 2019 6 3 1681 207912 New Zealand Australia 3 4 1 PL 25.04. 06:30 2019 8 2 1228 223113 Argentina New Zealand 4 3 1 PL 13.04. 23:00 2019 4 8 1908 122814 Netherlands Spain 4 0 1 PL 13.04. 18:00 2019 3 9 2079 113315 Belgium Spain 7 3 1 PL 10.04. 20:30 2019 1 9 2246 113316 Argentina England 1 5 1 PL 06.04. 20:30 2019 4 7 1908 155117 Argentina Spain 3 2 1 PL 31.03. 23:00 2019 4 9 1908 113341 India Korea 1 1 1 FM 30.03. 13:35 2019 5 17 1765 74042 Malaysia Canada 4 2 1 FM 30.03. 11:05 2019 13 10 953 106743 Japan Poland 6 1 1 FM 30.03. 08:40 2019 18 21 675 55244 Malaysia Canada 3 2 1 FM 29.03. 13:35 2019 13 10 953 106745 Korea Japan 4 2 1 FM 29.03. 11:05 2019 17 18 740 67546 India Poland 10 0 1 FM 29.03. 09:05 2019 5 21 1765 55247 Korea Malaysia 2 1 1 FM 27.03. 13:35 2019 17 13 740 95348 Canada India 3 7 1 FM 27.03. 11:05 2019 10 5 1067 176549 Poland Japan 0 3 1 FM 27.03. 09:05 2019 21 18 552 67550 Malaysia India 2 4 1 FM 26.03. 13:35 2019 13 5 953 176551 Poland Korea 2 3 1 FM 26.03. 11:05 2019 21 17 552 74052 Japan Canada 1 2 1 FM 26.03. 09:05 2019 18 10 675 106753 Japan Malaysia 3 4 1 FM 24.03. 13:35 2019 18 13 675 95354 Canada Poland 0 4 1 FM 24.03. 11:05 2019 10 21 1067 55255 India Korea 1 1 1 FM 24.03. 09:05 2019 5 17 1765 74056 Malaysia Poland 5 1 1 FM 23.03. 13:35 2019 13 21 953 55257 Canada Korea 3 6 1 FM 23.03. 11:05 2019 10 17 1067 74058 India Japan 2 0 1 FM 23.03. 09:05 2019 5 18 1765 67518 Australia New Zealand 5 1 1 PL 17.03. 05:00 2019 2 8 2231 122819 Australia Argentina 3 2 1 PL 16.03. 05:00 2019 2 4 2231 190820 Spain Germany 4 4 1 PL 15.03 11:00 2019 9 6 1133 168121 New Zealand Argentina 1 2 1 PL 10.03. 02:30 2019 8 4 1228 190822 New Zealand Spain 3 3 1 PL 08.03. 07:00 2019 8 9 1228 113323 Netherlands Germany 0 1 1 PL 05.03. 18:45 2019 3 6 2079 168124 Australia Spain 2 1 1 PL 02.03. 05:00 2019 2 9 2231 113325 Argentina Netherlands 4 3 1 PL 24.02. 20:00 2019 4 3 1908 2079

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26 Argentina Germany 0 0 1 PL 23.02. 01:00 2019 4 6 1908 168127 Australia England 2 0 1 PL 16.02. 08:30 2019 2 7 2231 155128 Spain Netherlands 3 3 1 PL 15.02 11:00 2019 9 3 1133 207929 New Zealand Germany 1 3 1 PL 15.02. 07:00 2019 8 6 1228 168130 Australia Germany 4 2 1 PL 10.02. 05:00 2019 2 6 2231 168131 New Zealand England 2 6 1 PL 08.02. 05:00 2019 8 7 1228 155132 Australia Belgium 1 4 1 PL 03.02. 05:00 2019 2 1 2231 224633 Australia Netherlands 5 5 1 PL 02.02 05:00 2019 2 3 2231 207934 New Zealand Belgium 4 4 1 PL 01.02 07:00 2019 8 1 1228 224635 New Zealand Netherlands 3 4 1 PL 27.01. 02:30 2019 8 3 1228 207936 Argentina Belgium 2 4 1 PL 26.01. 22:15 2019 4 1 1908 224637 Spain England 5 6 1 PL 25.01. 11:00 2019 9 7 1133 155138 Spain Belgium 2 2 1 PL 19.01. 13:00 2019 9 1 1133 224659 Belgium Netherlands 0 0 0 WC 43815 2018 3 4 1709 165460 England Australia 1 8 0 WC 43815 2018 7 1 1220 190661 Australia Netherlands 2 2 0 WC 43814 2018 1 4 1906 165462 England Belgium 0 6 0 WC 43814 2018 7 3 1220 170963 India Netherlands 1 2 1 WC 43812 2018 5 4 1484 165464 Germany Belgium 1 2 0 WC 43812 2018 6 3 1456 170965 Australia France 3 0 0 WC 43811 2018 1 20 1906 53966 Argentina England 2 3 0 WC 43811 2018 2 7 1883 122067 Netherlands Canada 5 0 0 WC 43810 2018 4 11 1654 88268 Belgium Pakistan 5 0 0 WC 43810 2018 3 13 1709 81869 France China 1 0 0 WC 43809 2018 20 17 539 59370 England New Zealand 2 0 0 WC 43809 2018 7 9 1220 110371 Netherlands Pakistan 5 1 0 WC 43808 2018 4 13 1654 81872 Malaysia Germany 3 5 0 WC 43808 2018 12 6 843 145673 Canada India 1 5 -1 WC 43807 2018 11 5 882 148474 Belgium South Africa 5 1 0 WC 43807 2018 3 15 1709 68075 Ireland England 2 4 0 WC 43806 2018 10 7 910 122076 Australia China 11 0 0 WC 43806 2018 1 17 1906 59377 Argentina France 3 5 0 WC 43805 2018 2 20 1883 53978 Spain New Zealand 2 2 0 WC 43805 2018 8 9 1105 110379 Malaysia Pakistan 1 1 0 WC 43804 2018 12 13 843 81880 Germany Netherlands 4 1 0 WC 43804 2018 6 4 1456 165481 Ireland China 1 1 0 WC 43803 2018 10 17 910 59382 England Australia 0 3 0 WC 43803 2018 7 1 1220 190683 New Zealand Argentina 0 3 0 WC 43802 2018 9 2 1103 188384 Spain France 1 1 0 WC 43802 2018 8 20 1105 53985 India Belgium 2 2 1 WC 43801 2018 5 3 1484 170986 Canada South Africa 1 1 0 WC 43801 2018 11 15 882 68087 Germany Pakistan 1 0 0 WC 43800 2018 6 13 1456 81888 Netherlands Malaysia 7 0 0 WC 43800 2018 4 12 1654 84389 England China 2 2 0 WC 43799 2018 7 17 1220 59390 Australia Ireland 2 1 0 WC 43799 2018 1 10 1906 91091 New Zealand France 2 1 0 WC 43798 2018 9 20 1103 53992 Argentina Spain 4 3 0 WC 43798 2018 2 8 1883 110593 India South Africa 5 0 1 WC 43797 2018 5 15 1484 68094 Belgium Canada 2 1 0 WC 43797 2018 3 11 1709 882113 Malaysia New Zealand 4 2 1 FM 22.11. 11:00 2018 12 9 843 1103

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114 Malaysia New Zealand 3 4 1 FM 20.11. 11:00 2018 12 9 843 1103115 Netherlands Ireland 7 1 1 FM 19.11. 19:00 2018 4 10 1654 910116 Malaysia New Zealand 1 2 1 FM 16.11. 10:00 2018 12 9 843 1103117 Belgium France 2 0 1 FM 14.11. 20:00 2018 3 20 1709 539118 Spain Germany 2 5 1 FM 14.11. 12:30 2018 8 6 1105 1456119 Spain Germany 1 2 1 FM 12.11. 12:30 2018 8 6 1105 1456120 Belgium Netherlands 3 4 -1 FM 11.11. 15:00 2018 3 4 1709 1654121 Spain Germany 0 7 1 FM 10.11. 15:00 2018 8 6 1105 1456122 South Africa France 1 2 1 FM 10.11. 15:00 2018 15 20 680 539123 Belgium Ireland 4 1 1 FM 10.11. 14:00 2018 3 10 1709 910124 South Africa France 1 3 1 FM 09.11. 17:30 2018 15 20 680 539125 Spain Netherlands 2 3 -1 FM 04.11. 12:30 2018 8 4 1105 1654126 South Africa France 1 4 1 FM 04.11. 11:00 2018 15 20 680 539127 England Ireland 2 2 1 FM 04.11. 10:00 2018 7 10 1220 910128 Netherlands Ireland 5 2 1 FM 03.11. 12:30 2018 4 10 1654 910129 South Africa France 2 2 1 FM 03.11. 11:00 2018 15 20 680 539130 Spain England 3 0 1 FM 03.11. 10:00 2018 8 7 1105 1220131 Spain England 2 1 1 FM 01.11. 18:30 2018 8 7 1105 1220132 Netherlands Ireland 7 1 1 FM 01.11. 16:30 2018 4 10 1654 910133 Spain Ireland 1 0 1 FM 30.10. 18:30 2018 8 10 1105 910134 England Netherlands 1 2 1 FM 30.10. 16:30 2018 7 4 1220 1654135 Netherlands Spain 1 2 1 FM 29.10. 17:30 2018 4 8 1654 1105136 England Ireland 1 2 1 FM 29.10. 15:30 2018 7 10 1220 910137 England Belgium 2 3 1 FM 02.10. 13:00 2018 7 3 1220 1709138 Australia Japan 3 0 1 FM 21.09. 11:30 2018 1 16 1906 625139 Malaysia Argentina 2 3 1 FM 21.09. 09:45 2018 12 2 843 1883140 Argentina Australia 2 0 1 FM 19.09. 11:30 2018 2 1 1883 1906141 Malaysia Japan 3 3 1 FM 19.09. 09:45 2018 12 16 843 625142 Australia Malaysia 5 2 1 FM 18.09. 11:30 2018 1 12 1906 843143 Argentina Japan 2 1 1 FM 18.09. 09:45 2018 2 16 1883 625144 Australia Argentina 1 0 1 FM 16.09. 11:30 2018 1 2 1906 1883145 Canada France 2 0 1 FM 11.08. 22:00 2018 11 20 882 539146 Canada France 13 0 1 FM 10.08. 22:00 2018 11 20 882 539147 Canada France 2 2 1 FM 08.08. 21:00 2018 11 20 882 539148 Canada France 0 2 1 FM 07.08. 21:00 2018 11 20 882 539149 Germany Ireland 4 0 1 FM 27.07. 19:15 2018 6 10 1456 910150 Argentina France 2 1 1 FM 27.07. 17:00 2018 2 20 1883 539151 Germany France 6 1 1 FM 26.07. 19:15 2018 6 20 1456 539152 Ireland Argentina 1 3 1 FM 26.07. 17:00 2018 10 2 910 1883153 India New Zealand 4 0 1 FM 22.07. 12:30 2018 5 9 1484 1103154 India New Zealand 3 1 1 FM 21.07. 12:30 2018 5 9 1484 1103155 India New Zealand 4 2 1 FM 19.07. 12:30 2018 5 9 1484 1103156 Japan Germany 1 5 1 FM 18.07. 10:00 2018 16 6 625 1456157 Germany New Zealand 7 4 1 FM 14.07. 11:00 2018 6 9 1456 1103158 Ireland USA 1 2 1 FM 13.07. 20:00 2018 10 27 910 329159 Japan New Zealand 1 0 1 FM 13.07. 11:00 2018 16 9 625 1103160 Ireland USA 5 1 1 FM 12.07. 21:00 2018 10 27 910 329161 Japan Germany 1 6 1 FM 12.07. 10:00 2018 16 6 625 1456162 Scotland USA 1 1 1 FM 11.07. 15:00 2018 22 27 434 329163 Japan New Zealand 2 3 1 FM 11.07. 12:00 2018 16 9 625 1103

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164 Scotland USA 1 3 1 FM 09.07. 19:00 2018 22 27 434 329165 Scotland USA 3 1 1 FM 08.07. 13:00 2018 22 27 434 329166 Japan New Zealand 3 3 1 FM 08.07. 09:00 2018 16 9 625 1103167 Canada China 3 4 1 FM 08.07. 04:00 2018 11 17 882 593168 Spain USA 2 0 1 FM 06.07. 11:00 2018 8 27 1105 329169 Canada China 5 0 1 FM 05.07. 04:00 2018 11 17 882 593170 Spain USA 3 1 1 FM 04.07. 19:00 2018 8 27 1105 329171 Spain USA 6 1 1 FM 03.07. 19:00 2018 8 27 1105 329172 France Ireland 0 3 1 FM 01.07. 15:00 2018 18 10 645 1043173 Ireland France 6 1 1 FM 30.06. 15:00 2018 10 18 1043 645174 Ireland France 1 1 1 FM 28.06. 20:00 2018 10 18 1043 645175 Austria Wales 3 0 1 FM 26.06. 16:00 2018 19 24 623 41095 Australia India 1 1 0 CT 1.7.16:00 2018 1 6 2005 156696 Netherlands Argentina 2 0 0 CT 1.7.13:45 2018 4 2 1703 197597 Belgium Pakistan 2 2 0 CT 1.7.11:30 2018 3 13 1850 89598 Netherlands India 1 1 0 CT 30.06.16:00 2018 4 6 1703 156699 Argentina Australia 3 2 0 CT 30.06.14:00 2018 2 1 1975 2005100 Belgium Pakistan 4 2 0 CT 29.06.15:00 2018 3 13 1850 895101 Netherlands Australia 1 3 0 CT 28.06.19:30 2018 4 1 1703 2005102 India Belgium 1 1 0 CT 28.06.17:00 2018 6 3 1566 1850103 Argentina Pakistan 1 4 0 CT 28.06.15:00 2018 2 13 1975 895104 India Australia 2 3 0 CT 27.06.15:00 2018 6 1 1566 2005105 Netherlands Pakistan 4 0 0 CT 26.06.20:00 2018 4 13 1703 895106 Argentina Belgium 1 1 0 CT 26.06.18:00 2018 2 3 1975 1850107 Australia Pakistan 2 1 0 CT 24.06.16:00 2018 1 13 2005 895108 Netherlands Belgium 6 1 0 CT 24.06.14:00 2018 4 3 1703 1850109 India Argentina 2 1 0 CT 24.06.12:00 2018 6 2 1566 1975110 Australia Belgium 3 3 0 CT 23.06.18:00 2018 1 3 2005 1850111 Netherlands Argentina 1 2 0 CT 23.06.16:00 2018 4 2 1703 1975112 India Pakistan 4 0 0 CT 23.06.14:00 2018 6 13 1566 895176 Germany England 5 5 1 FM 22.06. 11:00 2018 5 7 1680 1407177 Germany England 1 1 1 FM 20.06. 19:30 2018 5 7 1680 1407178 Germany Australia 2 2 1 FM 17.06. 14:30 2018 5 1 1680 2005179 Germany Australia 0 2 1 FM 16.06. 16:00 2018 5 1 1680 2005180 Belgium England 3 2 1 FM 16.06. 15:00 2018 3 7 1850 1407181 Netherlands France 3 1 1 FM 15.06. 19:00 2018 4 18 1703 645182 Netherlands France 3 1 1 FM 14.06. 19:00 2018 4 18 1703 645183 Belgium Spain 5 2 1 FM 12.06. 15:00 2018 3 8 1850 1218184 Netherlands Spain 2 0 1 FM 10.06. 16:00 2018 4 8 1703 1218185 Belgium France 4 0 1 FM 10.06. 15:00 2018 3 18 1850 645186 Poland Wales 0 1 1 FM 10.06. 12:00 2018 21 24 542 410187 Poland Wales 3 1 1 FM 09.06. 18:00 2018 21 24 542 410215 Netherlands Spain 2 0 1 FM 09.06. 17:00 2018 4 8 1703 1218216 Poland Wales 1 0 1 FM 08.06. 19:00 2018 21 24 542 410217 Argentina Malaysia 1 2 1 FM 01.06. 23:00 2018 2 12 1975 975218 Argentina Malaysia 1 1 1 FM 31.05. 23:00 2018 2 12 1975 975219 Poland Austria 1 3 1 FM 22.05. 11:00 2018 21 19 542 623188 Australia New Zealand 2 0 1 CG 14.04. 13:15 2018 1 9 2005 1214189 England India 2 1 0 CG 14.04. 11:00 2018 7 6 1407 1566190 Australia England 2 1 1 CG 13.04. 13:45 2018 1 7 2005 1407

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191 India New Zealand 2 3 0 CG 13.04. 11:30 2018 6 9 1566 1214192 Scotland Malaysia 1 2 0 CG 13.04. 08:15 2018 23 12 462 975193 Canada Pakistan 1 3 0 CG 13.04. 02:45 2018 11 13 1015 895194 South Africa Wales 2 3 0 CG 13.04. 00:30 2018 15 24 733 410195 Canada South Africa 0 2 0 CG 11.04. 13:30 2018 11 15 1015 733196 India England 4 3 0 CG 11.04. 11:30 2018 6 7 1566 1407197 Australia New Zealand 2 1 1 CG 11.04. 08:30 2018 1 9 2005 1214198 Malaysia Pakistan 1 1 0 CG 11.04. 06:30 2018 12 13 975 895199 Australia Canada 4 0 1 CG 10.04. 08:30 2018 1 11 2005 1015200 England Wales 3 2 0 CG 10.04. 06:30 2018 7 24 1407 410201 New Zealand Scotland 5 2 0 CG 10.04. 03:30 2018 9 23 1214 462202 India Malaysia 2 1 0 CG 10.04. 01:30 2018 6 12 1566 975203 Australia Scotland 6 1 1 CG 08.04. 13:30 2018 1 23 2005 462204 India Wales 4 3 0 CG 08.04. 11:30 2018 6 24 1566 410205 New Zealand South Africa 6 0 0 CG 08.04. 08:30 2018 9 15 1214 733206 England Pakistan 2 2 0 CG 08.04. 06:30 2018 7 13 1407 895207 Australia South Africa 4 0 1 CG 07.04. 08:30 2018 1 15 2005 733208 India Pakistan 2 2 0 CG 07.04. 06:30 2018 6 13 1566 895209 Canada Scotland 1 0 0 CG 07.04. 03:30 2018 11 23 1015 462210 Malaysia Wales 3 0 0 CG 07.04. 01:30 2018 12 24 975 410211 New Zealand Canada 6 2 0 CG 06.04. 03:30 2018 9 11 1214 1015212 England Malaysia 7 0 0 CG 06.04. 01:30 2018 7 12 1407 975213 South Africa Scotland 2 4 0 CG 05.04. 13:30 2018 15 23 733 462214 Pakistan Wales 0 1 0 CG 05.04 11:30 2018 13 24 895 410220 England Australia 1 2 1 FM 10.03. 13:30 2018 7 1 1407 2005221 Malaysia Argentina 2 3 1 FM 10.03. 11:00 2018 12 2 975 1975222 India Ireland 4 1 1 FM 10.03. 08:30 2018 6 10 1566 1043223 England Malaysia 7 2 1 FM 09.03. 13:35 2018 7 12 1407 975224 Ireland India 3 2 1 FM 09.03. 11:05 2018 10 6 1043 1566225 Argentina Australia 1 3 1 FM 09.03. 09:05 2018 2 1 1975 2005226 India Malaysia 5 1 1 FM 07.03. 13:35 2018 6 12 1566 975227 Argentina England 1 1 1 FM 07.03. 11:05 2018 2 7 1975 1407228 Australia Ireland 4 1 1 FM 07.03. 09:05 2018 1 10 2005 1043229 Malaysia Argentina 2 1 1 FM 06.03. 13:30 2018 12 2 975 1975230 India Australia 2 4 1 FM 06.03. 11:00 2018 6 1 1566 2005231 England Ireland 4 1 1 FM 06.03. 09:00 2018 7 10 1407 1043232 Malaysia Australia 1 3 1 FM 04.03. 13:30 2018 12 1 975 2005233 Ireland Argentina 3 5 1 FM 04.03. 11:00 2018 10 2 1043 1975234 India England 1 1 1 FM 04.03. 09:00 2018 6 7 1566 1407235 Malaysia Ireland 4 1 1 FM 03.03. 13:30 2018 12 10 975 1043236 Australia England 4 1 1 FM 03.03. 11:00 2018 1 7 2005 1407237 Argentina India 3 2 1 FM 03.03. 09:00 2018 2 6 1975 1566238 Pakistan Japan 2 3 1 FM 20.02. 16:30 2018 13 16 895 711239 Japan Pakistan 1 2 1 FM 18.02. 15:00 2018 16 13 711 895240 Japan Pakistan 2 2 1 FM 15.02. 15:00 2018 16 13 711 895241 Spain Canada 4 1 1 FM 04.02. 11:00 2018 8 11 1218 1015242 USA Ireland 2 4 1 FM 03.02. 14:00 2018 26 10 375 1043243 Australia Netherlands 6 1 1 FM 03.02. 12:00 2018 1 4 2005 1703244 Scotland Spain 0 3 1 FM 03.02. 12:00 2018 23 8 462 1218245 Canada USA 3 1 1 FM 02.02. 17:00 2018 11 26 1015 375

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246 Scotland Ireland 1 5 1 FM 01.02. 17:00 2018 23 10 462 1043247 Australia Netherlands 3 3 1 FM 01.02. 12:00 2018 1 4 2005 1703248 Spain USA 2 0 1 FM 31.01. 17:00 2018 8 26 1218 375249 Spain Ireland 3 2 1 FM 30.01. 17:00 2018 8 10 1218 1043250 Scotland Canada 1 2 1 FM 30.01. 15:00 2018 23 11 462 1015251 USA Scotland 1 3 1 FM 29.01. 16:30 2018 26 23 375 462252 Canada Ireland 1 4 1 FM 29.01. 14:30 2018 11 10 1015 1043253 France Wales 2 0 1 FM 28.01. 11:00 2018 18 24 645 410254 Australia Netherlands 2 3 1 FM 28.01. 09:30 2018 1 4 2005 1703255 France Wales 1 0 1 FM 27.01. 14:30 2018 18 24 645 410256 Australia Netherlands 3 3 1 FM 27.01. 09:30 2018 1 4 2005 1703257 France Wales 4 0 1 FM 26.01. 14:30 2018 18 24 645 410258 New Zealand India 2 3 1 FM 24.01. 07:30 2018 9 6 1214 1566259 Belgium Japan 3 2 1 FM 24.01. 05:45 2018 3 16 1850 711260 Spain Wales 4 1 1 FM 21.01. 12:00 2018 8 24 1218 410261 Spain Wales 2 2 1 FM 20.01. 15:30 2018 8 24 1218 410267 Argentina Australia 1 2 0 WL 10.12. 15:00 2017 1 2 1845 1825268 India Germany 2 1 0 WL 10.12. 12:45 2017 6 3 1461 1700269 Australia Germany 3 0 0 WL 09.12. 15:00 2017 2 3 1825 1700270 Belgium Spain 1 0 0 WL 09.12. 12:45 2017 5 9 1640 1178271 India Argentina 0 1 0 WL 08.12. 15:00 2017 6 1 1461 1845272 England Netherlands 0 1 0 WL 08.12. 12:45 2017 7 4 1357 1683273 Germany Netherlands 3 3 0 WL 7.12. 15:00 2017 3 4 1700 1683274 England Argentina 2 3 0 WL 07.12. 12:45 2017 7 1 1357 1845275 Belgium India 3 3 -1 WL 6.12. 15:00 2017 5 6 1640 1461276 Spain Australia 1 4 0 WL 06.12. 12:45 2017 9 2 1178 1825277 Belgium Netherlands 3 0 0 WL 05.12. 15:00 2017 5 4 1640 1683278 Argentina Spain 1 2 0 WL 05.12. 13:00 2017 1 9 1845 1178279 India Germany 0 2 1 WL 04.12. 15:00 2017 6 3 1461 1700280 Australia England 2 2 0 WL 04.12. 13:00 2017 2 7 1825 1357281 Netherlands Argentina 3 3 0 WL 03.12. 15:00 2017 4 1 1683 1845282 Belgium Spain 5 0 0 WL 03.12. 13:00 2017 5 9 1640 1178283 India England 2 3 1 WL 02.12. 15:00 2017 6 7 1461 1357284 Germany Australia 2 2 0 WL 02.12. 13:00 2017 3 2 1700 1825285 Netherlands Spain 2 3 0 WL 02.12. 09:30 2017 4 9 1683 1178286 Argentina Belgium 2 3 0 WL 02.12. 07:30 2017 1 5 1845 1640287 Australia India 1 1 -1 WL 01.12. 15:00 2017 2 6 1825 1461288 Germany England 2 0 0 WL 01.12. 12:15 2017 3 7 1700 1357362 Belgium Netherlands 2 4 0 EC 27.08.16:00 2017 5 4 1640 1683363 Germany England 2 4 0 EC 27.08.13:30 2017 3 7 1700 1357364 Ireland Austria 2 2 0 EC 27.08.11:00 2017 10 22 1143 523365 Spain Poland 2 1 0 EC 27.08.09:00 2017 9 20 1178 542366 Netherlands England 3 1 0 EC 25.08.20:00 2017 4 7 1683 1357367 Germany Belgium 2 2 0 EC 25.08.17:00 2017 3 5 1700 1640368 Spain Ireland 1 0 0 EC 25.08.14:45 2017 9 10 1178 1143369 Austria Poland 1 1 0 EC 25.08.12:30 2017 22 20 523 542370 Ireland England 1 2 0 EC 23.08.14:45 2017 10 7 1143 1357371 Germany Poland 7 3 0 EC 23.08.12:30 2017 3 20 1700 542372 Belgium Netherlands 5 0 0 EC 21.08.20:00 2017 5 4 1640 1683373 England Germany 3 4 0 EC 21.08.17:00 2017 7 3 1357 1700

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374 Ireland Poland 7 1 0 EC 21.08.14:45 2017 10 20 1143 542375 Spain Austria 2 2 0 EC 21.08.12:30 2017 9 22 1178 523376 Germany Ireland 1 1 0 EC 20.08.15:30 2017 3 10 1700 1143377 England Poland 6 0 0 EC 20.08.09:00 2017 7 20 1357 542378 Netherlands Spain 7 1 0 EC 19.08.20:00 2017 4 9 1683 1178379 Belgium Austria 4 1 0 EC 19.08.17:00 2017 5 22 1640 523262 Germany England 5 2 1 FM 16.11. 11:00 2017 3 7 1700 1357263 Poland Austria 1 1 1 FM 12.08. 11:00 2017 20 22 542 523264 Belgium India 3 1 1 FM 10.08. 19:00 2017 5 6 1640 1461265 Germany Netherlands 1 7 1 FM 09.08. 15:00 2017 3 4 1700 1683266 Spain England 2 2 1 FM 09.08. 13:00 2017 9 7 1178 1357289 Germany Belgium 1 6 0 WL 23.07. 18:00 2017 3 5 1700 1640290 Australia Spain 8 1 0 WL 23.07. 13:15 2017 2 9 1825 1178291 New Zealand Ireland 0 1 0 WL 22.07. 18:00 2017 8 10 1214 1143292 Egypt France 0 3 0 WL 22.07. 15:45 2017 19 16 613 720293 Australia Belgium 1 2 0 WL 21.07. 19:00 2017 2 5 1825 1640294 Spain Germany 1 1 0 WL 21.07. 16:45 2017 9 3 1178 1700295 Ireland France 1 1 0 WL 21.07. 14:30 2017 10 16 1143 720296 Egypt New Zealand 0 2 0 WL 21.07. 12:15 2017 19 8 613 1214297 Japan South Africa 2 4 -1 WL 21.07. 10:00 2017 17 15 711 733298 Belgium New Zealand 2 0 0 WL 19.07. 18:00 2017 5 8 1640 1214299 Germany France 4 1 0 WL 19.07. 15:45 2017 3 16 1700 720300 Spain Ireland 2 1 0 WL 19.07. 13:30 2017 9 10 1178 1143301 Australia Egypt 4 0 0 WL 19.07. 11:15 2017 2 19 1825 613302 South Africa Belgium 1 9 1 WL 17.07. 18:00 2017 15 5 733 1640303 Germany Ireland 2 0 0 WL 17.07. 16:00 2017 3 10 1700 1143304 Spain New Zealand 4 3 0 WL 17.07. 14:00 2017 9 8 1178 1214305 Australia Japan 7 2 0 WL 17.07. 12:00 2017 2 17 1825 711306 Belgium Germany 2 3 0 WL 15.07. 18:00 2017 5 3 1640 1700307 Egypt South Africa 2 1 0 WL 15.07. 16:00 2017 19 15 613 733308 New Zealand Australia 1 2 0 WL 15.07. 14:00 2017 8 2 1214 1825309 France Spain 0 2 0 WL 15.07. 12:00 2017 16 9 720 1178310 South Africa Germany 3 4 0 WL 13.07. 18:00 2017 15 3 733 1700311 Spain Australia 0 2 0 WL 13.07. 16:00 2017 9 2 1178 1825312 Japan France 1 4 0 WL 13.07. 14:00 2017 17 16 711 720313 Ireland Egypt 2 1 0 WL 13.07. 12:00 2017 10 19 1143 613314 Belgium Ireland 6 2 0 WL 11.07. 18:00 2017 5 10 1640 1143315 New Zealand Japan 3 1 0 WL 11.07. 16:00 2017 8 17 1214 711316 Australia France 3 2 0 WL 11.07. 14:00 2017 2 16 1825 720317 Germany Egypt 5 0 0 WL 11.07. 12:00 2017 3 19 1700 613318 South Africa Ireland 0 2 0 WL 09.07. 18:00 2017 15 10 733 1143319 Belgium Egypt 10 0 0 WL 09.07. 16:00 2017 5 19 1640 613320 Spain Japan 2 1 0 WL 09.07. 14:00 2017 9 17 1178 711321 New Zealand France 3 3 0 WL 09.07. 12:00 2017 8 16 1214 720322 Argentina Netherlands 1 6 0 WL 25.06. 17:15 2017 2 3 2152 1967323 Malaysia England 1 4 -1 WL 25.06. 15:00 2017 13 7 908 1560324 Canada India 3 2 0 WL 25.06. 12:45 2017 11 6 1025 1628325 China Pakistan 1 3 0 WL 25.06. 10:30 2017 18 14 618 907326 England Netherlands 0 2 1 WL 24.06. 17:15 2017 7 3 1560 1967327 Argentina Malaysia 2 1 0 WL 24.06. 15:00 2017 2 13 2152 908

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328 Pakistan India 1 6 0 WL 24.06. 12:45 2017 14 6 907 1628329 Canada China 7 3 0 WL 24.06. 10:30 2017 11 18 1025 618330 England Canada 4 2 1 WL 22.06. 21:00 2017 7 11 1560 1025331 Netherlands China 7 0 0 WL 22.06. 18:45 2017 3 18 1967 618332 India Malaysia 2 3 0 WL 22.06. 16:30 2017 6 13 1628 908333 Argentina Pakistan 3 1 0 WL 22.06. 14:15 2017 2 14 2152 907334 Korea Scotland 6 3 0 WL 22.06. 12:00 2017 12 27 1002 367335 England Korea 7 2 1 WL 20.06. 21:00 2017 7 12 1560 1002336 China Malaysia 1 5 0 WL 20.06. 19:00 2017 18 13 618 908337 India Netherlands 1 3 0 WL 20.06. 15:00 2017 6 3 1628 1967338 Scotland Canada 1 1 0 WL 20.06. 13:00 2017 27 11 367 1025339 Argentina China 10 0 0 WL 19.06. 21:00 2017 2 18 2152 618340 Korea Malaysia 0 1 0 WL 19.06. 19:00 2017 12 13 1002 908341 Netherlands Canada 3 1 0 WL 19.06. 15:00 2017 3 11 1967 1025342 Scotland Pakistan 1 3 0 WL 19.06. 13:00 2017 27 14 367 907343 England Argentina 3 3 0 WL 18.06. 17:00 2017 7 2 1560 2152344 Pakistan India 1 7 0 WL 18.06. 15:00 2017 14 6 907 1628345 Scotland Netherlands 0 3 -1 WL 17.06. 19:00 2017 27 3 367 1967346 England Malaysia 7 3 0 WL 17.06. 17:00 2017 7 13 1560 908347 Canada India 0 3 0 WL 17.06. 15:00 2017 11 6 1025 1628348 China Korea 5 2 0 WL 17.06. 13:00 2017 18 12 618 1002349 Argentina Malaysia 5 2 0 WL 16.06. 21:00 2017 2 13 2152 908350 Pakistan Canada 0 6 0 WL 16.06. 19:00 2017 14 11 907 1025351 England China 2 0 0 WL 15.06. 21:00 2017 7 18 1560 618352 Netherlands Pakistan 4 0 1 WL 15.06. 19:00 2017 3 14 1967 907353 India Scotland 4 1 0 WL 15.06. 15:00 2017 6 27 1628 367354 Korea Argentina 1 2 0 WL 15.06. 13:00 2017 12 2 1002 2152355 Wales Scotland 0 4 0 WL 19.03. 18:00 2017 34 27 274 367356 Ireland Wales 3 1 0 WL 18.03. 15:00 2017 10 34 1148 274357 France Wales 1 0 0 WL 14.03. 18:00 2017 17 34 701 274358 Scotland Poland 2 1 0 WL 14:03 15:00 2017 27 19 367 590359 Scotland Wales 2 2 0 WL 12.03 11:00 2017 27 34 367 274360 Poland Wales 1 3 0 WL 11.03 14:00 2017 19 34 590 274361 France Scotland 3 1 0 WL 11.03 11:00 2017 17 27 701 367380 Spain Poland 6 0 1 FM 04.12. 12:00 2016 9 19 1215 584381 Spain Poland 5 0 1 FM 03.12. 13:15 2016 9 19 1215 584382 Spain Ireland 2 1 1 FM 01.12. 12:00 2016 9 10 1215 1106383 Spain Ireland 4 0 1 FM 29.11. 16:30 2016 9 10 1215 1106384 Australia India 2 3 1 FM 29.11. 08:30 2016 1 6 2154 1661385 Austria Wales 1 5 1 FM 28.08. 11:00 2016 22 36 508 206386 Scotland Italy 8 2 1 FM 21.08. 11:30 2016 27 33 325 246387 Scotland Italy 3 3 1 FM 20.08. 16:00 2016 27 33 325 246465 Belgium Argentina 2 4 0 OG 18.08. 22:00 2016 6 7 1475 1436466 Netherlands Germany 1 1 0 OG 18.08. 17:00 2016 2 3 1838 1701467 Belgium Netherlands 3 1 0 OG 16.08. 22:00 2016 6 2 1475 1838468 Argentina Germany 5 2 0 OG 16.08. 17:00 2016 7 3 1436 1701469 Germany New Zealand 3 2 0 OG 15.08. 01:30 2016 3 8 1701 1308470 Netherlands Australia 4 0 0 OG 14.08. 23:00 2016 2 1 1838 2179471 Belgium India 3 1 0 OG 14.08. 17:30 2016 6 5 1475 1543472 Spain Argentina 1 2 0 OG 14.08. 15:00 2016 11 7 1028 1436

40

473 Australia Brazil 9 0 0 OG 13.08. 01:30 2016 1 30 2179 273474 Ireland Argentina 2 3 0 OG 13.08. 00:30 2016 12 7 969 1436475 Belgium New Zealand 1 3 0 OG 12.08. 23:00 2016 6 8 1475 1308476 England Spain 1 1 0 OG 12.08. 22:00 2016 4 11 1550 1028477 Germany Netherlands 2 1 0 OG 12.08. 18:30 2016 3 2 1701 1838478 India Canada 2 2 0 OG 12.08. 17:30 2016 5 15 1543 847479 Spain Belgium 1 3 0 OG 11.08. 18:30 2016 11 6 1028 1475480 Argentina Germany 4 4 0 OG 11.08. 17:30 2016 7 3 1436 1701481 Ireland Canada 4 2 0 OG 11.08. 16:00 2016 12 15 969 847482 Netherlands India 2 1 0 OG 11.08. 15:00 2016 2 5 1838 1543483 England Australia 1 2 0 OG 11.08. 01:30 2016 4 1 1550 2179484 New Zealand Brazil 9 0 0 OG 11.08. 00:30 2016 8 30 1308 273485 Belgium Australia 1 0 0 OG 10.08. 01:30 2016 6 1 1475 2179486 Brazil England 1 9 0 OG 09.08. 23:00 2016 30 4 273 1550487 Netherlands Canada 7 0 0 OG 09.08. 18:30 2016 2 15 1838 847488 Germany Ireland 3 2 0 OG 09.08. 17:30 2016 3 12 1701 969489 Argentina India 1 2 0 OG 09.08. 16:00 2016 7 5 1436 1543490 New Zealand Spain 2 3 0 OG 09.08. 15:00 2016 8 11 1308 1028491 Canada Argentina 1 3 0 OG 08.08. 17:30 2016 15 7 847 1436492 Germany India 2 1 0 OG 08.08. 16:00 2016 3 5 1701 1543493 Australia Spain 0 1 0 OG 08.08. 01:30 2016 1 11 2179 1028494 Brazil Belgium 0 12 0 OG 08.08. 00:30 2016 30 6 273 1475495 Netherlands Ireland 5 0 0 OG 07.08. 23:00 2016 2 12 1838 969496 England New Zealand 2 2 0 OG 07.08. 22:00 2016 4 8 1550 1308497 Spain Brazil 7 0 0 OG 07.08. 00:30 2016 11 30 1028 273498 Canada Germany 2 6 0 OG 06.08. 23:00 2016 15 3 847 1701499 Australia New Zealand 2 1 0 OG 06.08. 18:30 2016 1 8 2179 1308500 Belgium England 4 1 0 OG 06.08. 17:30 2016 6 4 1475 1550501 India Ireland 3 2 0 OG 06.08. 16:00 2016 5 12 1543 969502 Argentina Netherlands 3 3 0 OG 06.08. 15:00 2016 7 2 1436 1838388 Netherlands Germany 2 3 1 FM 17.07. 14:00 2016 2 3 1838 1701389 Belgium England 2 2 1 FM 17.07. 11:30 2016 6 4 1475 1550390 Belgium Germany 2 3 1 FM 16.07. 16:30 2016 6 3 1475 1701391 England Netherlands 3 0 1 FM 16.07. 14:00 2016 4 2 1550 1838392 England Germany 1 1 1 FM 14.07. 18:30 2016 4 3 1550 1701393 Netherlands Belgium 3 2 1 FM 14.07. 13:30 2016 2 6 1838 1475394 Argentina New Zealand 1 4 1 FM 03.07. 14:00 2016 7 8 1436 1308395 Spain India 1 1 1 FM 03.07. 12:00 2016 11 5 1028 1543396 Wales Poland 1 2 1 FM 03.07. 11:00 2016 36 19 206 580397 Germany Ireland 2 0 1 FM 03.07. 10:00 2016 3 12 1701 969398 Wales Poland 2 2 1 FM 02.07. 15:00 2016 36 19 206 580399 India Argentina 3 3 1 FM 02.07. 14:00 2016 5 7 1543 1436400 Spain Germany 3 5 1 FM 02.07. 12:00 2016 11 3 1028 1701401 Ireland New Zealand 1 1 1 FM 02.07. 10:00 2016 12 8 969 1308402 Spain Ireland 2 2 1 FM 30.06. 20:00 2016 11 12 1028 969403 India New Zealand 0 1 1 FM 30.06. 18:00 2016 5 8 1543 1308404 Argentina Germany 4 4 1 FM 30.06. 16:00 2016 7 3 1436 1701405 Spain Argentina 0 4 1 FM 28.06. 20:00 2016 11 7 1028 1436406 Germany New Zealand 6 1 1 FM 28.06. 18:00 2016 3 8 1701 1308407 Ireland India 1 2 1 FM 28.06. 16:00 2016 12 5 969 1543

41

408 Netherlands New Zealand 2 0 1 FM 24.06. 18:30 2016 2 8 1838 1308409 Poland France 3 0 1 FM 19.06. 11:00 2016 19 17 580 721410 Spain Canada 2 2 1 FM 19.06. 11:00 2016 11 15 1028 847503 Australia India 0 0 0 CT 17.06 21:15 2016 1 7 2253 1609504 Germany England 1 0 0 CT 17.06. 19:00 2016 3 4 1783 1658505 Belgium Korea 4 3 0 CT 17.06. 16:45 2016 5 9 1630 1313506 England Belgium 3 3 0 CT 16.06. 21:00 2016 4 5 1658 1630507 Korea Germany 0 7 0 CT 16.06. 19:00 2016 9 3 1313 1783508 Australia India 4 2 0 CT 16.06. 17:00 2016 1 7 2253 1609509 England Germany 1 1 0 CT 14.06. 21:00 2016 4 3 1658 1783510 Australia Belgium 2 0 0 CT 14.06. 19:00 2016 1 5 2253 1630511 India Korea 2 1 0 CT 14.06. 17:00 2016 7 9 1609 1313512 Belgium India 2 1 0 CT 13.06. 17:00 2016 5 7 1630 1609513 Germany Australia 3 4 0 CT 13.06. 15:00 2016 3 1 1783 2253514 Korea England 1 4 0 CT 13.06. 13:00 2016 9 4 1313 1658515 Australia Korea 4 2 0 CT 11.06. 19:00 2016 1 9 2253 1313516 India England 2 1 0 CT 11.06. 17:00 2016 7 4 1609 1658517 Germany Belgium 4 4 0 CT 11.06. 15:00 2016 3 5 1783 1630518 England Australia 0 0 0 CT 10.06. 21:00 2016 4 1 1658 2253519 Belgium Korea 0 2 0 CT 10.06. 19:00 2016 5 9 1630 1313520 Germany India 3 3 0 CT 10.06. 17:00 2016 3 7 1783 1609411 Ireland Canada 2 2 1 FM 14.06. 12:00 2016 12 14 1115 983412 Ireland Canada 2 1 1 FM 10.06. 20:30 2016 12 14 1115 983413 Ireland Korea 3 4 1 FM 05.06. 15:00 2016 12 9 1115 1313414 Ireland Korea 2 1 1 FM 04.06. 15:00 2016 12 9 1115 1313415 Ireland Korea 1 1 1 FM 02.06. 20:00 2016 12 9 1115 1313416 Ireland Korea 5 2 1 FM 31.05. 20:00 2016 12 9 1115 1313417 Australia England 5 1 1 FM 24.05. 12:30 2016 1 4 2253 1658418 Germany Ireland 6 1 1 FM 15.05. 12:00 2016 3 12 1783 1115419 Australia India 4 0 1 FM 16.04. 14:45 2016 1 7 2253 1609420 New Zealand Malaysia 3 3 1 FM 16.04. 12:05 2016 8 13 1496 1096421 Pakistan Canada 3 1 1 FM 16.04. 09:40 2016 10 14 1235 983422 Malaysia India 1 6 1 FM 15.04. 14:35 2016 13 7 1096 1609423 Spain Argentina 3 4 1 FM 15.04. 12:30 2016 11 6 1123 1629424 Australia Canada 3 0 1 FM 15.04. 12:05 2016 1 14 2253 983425 Japan Pakistan 1 4 1 FM 15.04. 10:05 2016 16 10 860 1235426 Spain Argentina 2 3 1 FM 14.04. 16:00 2016 11 6 1123 1629427 Spain Argentina 1 1 1 FM 13.04. 18:00 2016 11 6 1123 1629428 Pakistan Malaysia 0 1 1 FM 13.04. 14:35 2016 10 13 1235 1096429 Australia Japan 3 1 1 FM 13.04. 12:05 2016 1 16 2253 860430 New Zealand India 2 1 1 FM 13.04. 10:05 2016 8 7 1496 1609431 Canada Malaysia 2 2 1 FM 12.04. 14:35 2016 14 13 983 1096432 Pakistan India 1 5 1 FM 12.04. 12:05 2016 10 7 1235 1609433 Australia New Zealand 1 0 1 FM 12.04. 10:05 2016 1 8 2253 1496434 Canada India 1 3 1 FM 10.04. 14:35 2016 14 7 983 1609435 Australia Pakistan 4 0 1 FM 10.04. 12:05 2016 1 10 2253 1235436 Japan New Zealand 2 3 1 FM 10.04. 07:15 2016 16 8 860 1496437 Australia Malaysia 5 1 1 FM 09.04. 14:35 2016 1 13 2253 1096438 New Zealand Pakistan 5 3 1 FM 09.04. 12:05 2016 8 10 1496 1235439 Japan Canada 1 3 1 FM 09.04. 10:05 2016 16 14 860 983

42

440 Japan Malaysia 3 4 1 FM 07.04. 14:35 2016 16 13 860 1096441 New Zealand Canada 1 1 1 FM 07.04. 12:05 2016 8 14 1496 983442 Australia India 5 1 1 FM 07.04. 10:05 2016 1 7 2253 1609443 New Zealand Malaysia 3 3 1 FM 06.04. 14:35 2016 8 13 1496 1096444 Japan India 1 2 1 FM 06.04. 12:05 2016 16 7 860 1609445 Pakistan Canada 3 1 1 FM 06.04. 10:05 2016 10 14 1235 983446 New Zealand Korea 1 1 1 FM 20.03. 03:00 2016 8 9 1496 1313447 Korea Malaysia 1 2 1 FM 12.03. 00:45 2016 9 13 1313 1096448 New Zealand Malaysia 4 2 1 FM 09.03. 06:00 2016 8 13 1496 1096449 New Zealand Malaysia 2 3 1 FM 07.03. 06:00 2016 8 13 1496 1096450 South Africa Germany 2 6 1 FM 29.02. 17:00 2016 15 3 934 1783451 South Africa Germany 1 6 1 FM 27.02. 17:00 2016 15 3 934 1783452 Argentina Netherlands 1 0 1 FM 30.01. 23:30 2016 6 2 1629 2095453 Belgium Canada 5 2 1 FM 30.01. 14:00 2016 5 14 1630 983454 Argentina Netherlands 5 4 1 FM 28.01. 23:30 2016 6 2 1629 2095455 Belgium Canada 8 0 1 FM 28.01. 14:00 2016 5 14 1630 983456 Belgium Canada 7 1 1 FM 27.01. 14:00 2016 5 14 1630 983457 South Africa Canada 2 0 1 FM 24.01. 15:00 2016 15 14 934 983458 Ireland Belgium 3 6 1 FM 24.01. 13:00 2016 12 5 1115 1630459 Ireland Belgium 2 6 1 FM 23.01. 13:00 2016 12 5 1115 1630460 Spain Canada 5 0 1 FM 23.01. 10:00 2016 11 14 1123 983461 Belgium Spain 5 0 1 FM 22.01. 17:00 2016 5 11 1630 1123462 Ireland Canada 0 0 1 FM 21.01. 18:00 2016 12 14 1115 983463 Ireland Canada 4 2 1 FM 20.01. 19:00 2016 12 14 1115 983464 South Africa Spain 2 1 1 FM 20.01. 17:00 2016 15 11 934 1123521 Australia Belgium 2 1 0 WL 06.12. 16:15 2015 1 4 2073 1650522 Netherlands India 5 5 -1 WL 06.12 14:00 2015 2 8 1915 1454523 Germany Canada 8 3 0 WL 05.12. 16:15 2015 3 13 1813 983524 India Belgium 0 1 1 WL 05.12. 14:00 2015 8 4 1454 1650525 England Argentina 2 4 0 WL 04.12. 16:15 2015 5 6 1623 1569526 Australia Netherlands 3 2 0 WL 04.12. 14:00 2015 1 2 2073 1915527 Argentina Belgium 1 2 0 WL 03.12. 16:15 2015 6 4 1569 1650528 England India 1 2 -1 WL 03.12. 14:00 2015 5 8 1623 1454529 Australia Germany 4 1 0 WL 02.12. 16:15 2015 1 3 2073 1813530 Netherlands Canada 2 0 0 WL 02.12. 14:00 2015 2 13 1915 983531 England Belgium 3 3 0 WL 01.12. 17:00 2015 5 4 1623 1650532 Australia Canada 6 0 0 WL 01.12. 14:00 2015 1 13 2073 983533 Argentina Germany 3 1 0 WL 30.11. 16:00 2015 6 3 1569 1813534 Netherlands India 3 1 -1 WL 30.11. 14:00 2015 2 8 1915 1454535 Australia England 2 5 0 WL 29.11. 16:00 2015 1 5 2073 1623536 Belgium Canada 7 2 0 WL 29.11. 14:00 2015 4 13 1650 983537 Netherlands Argentina 3 2 0 WL 28.11. 16:00 2015 2 6 1915 1569538 Germany India 1 1 -1 WL 28.11. 14:00 2015 3 8 1813 1454539 Australia Belgium 1 0 0 WL 28.11. 12:00 2015 1 4 2073 1650540 England Canada 3 1 0 WL 28.11. 10:00 2015 5 13 1623 983541 Germany Netherlands 0 0 0 WL 27.11. 16:00 2015 3 2 1813 1915542 Argentina India 3 0 -1 WL 27.11. 14:00 2015 6 8 1569 1454609 Netherlands Germany 6 1 0 EC 29.08.17:30 2015 2 3 1915 1813610 Ireland England 4 2 0 EC 29.08.15:00 2015 15 5 965 1623611 Spain France 4 3 0 EC 29.08.12:45 2015 10 17 1173 740

43

612 Belgium Russia 11 4 1 EC 29.08.10:30 2015 4 19 1650 636613 Germany England 2 2 0 EC 27.08.20:30 2015 3 5 1813 1623614 Spain Belgium 0 3 -1 EC 27.08.18:15 2015 10 4 1173 1650615 Netherlands Ireland 1 0 0 EC 27.08.14:15 2015 2 15 1915 965616 Russia France 2 4 0 EC 27.08.12:00 2015 19 17 636 740617 England Spain 4 0 0 EC 25.08.20:30 2015 5 10 1623 1173618 Russia Netherlands 0 8 0 EC 25.08.18:15 2015 19 2 636 1915619 Belgium Ireland 2 2 1 EC 25.08.14:15 2015 4 15 1650 965620 Germany France 7 2 0 EC 25.08.12:00 2015 3 17 1813 740621 Ireland Germany 0 2 0 EC 23.08.21:30 2015 15 3 965 1813622 Netherlands England 2 0 0 EC 23.08.19:15 2015 2 5 1915 1623623 France Belgium 3 4 -1 EC 23.08.17:00 2015 17 4 740 1650624 Spain Russia 9 0 0 EC 23.08.09:30 2015 10 19 1173 636625 Germany Belgium 4 0 -1 EC 22.08.17:00 2015 3 4 1813 1650626 Ireland France 4 3 0 EC 22.08.09:30 2015 15 17 965 740627 England Russia 10 1 0 EC 21.08.21:00 2015 5 19 1623 636628 Netherlands Spain 2 0 0 EC 21.08.18:15 2015 2 10 1915 1173543 Australia Belgium 1 0 -1 WL 05.07. 18:00 2015 1 4 2073 1650544 England India 5 1 0 WL 05.07. 15:30 2015 5 9 1623 1454545 Ireland Malaysia 4 1 0 WL 05.07. 13:00 2015 15 13 965 1096546 Pakistan France 1 2 0 WL 05.07. 10:30 2015 11 17 1185 740547 Australia England 3 1 0 WL 03.07. 21:00 2015 1 5 2073 1623548 India Belgium 0 4 -1 WL 03.07. 18:30 2015 9 4 1454 1650549 Malaysia France 4 1 0 WL 03.07. 15:30 2015 13 17 1096 740550 Ireland Pakistan 1 0 0 WL 03.07. 13:00 2015 15 11 965 1185551 Belgium France 5 4 1 WL 01.07. 20:30 2015 4 17 1650 740552 India Malaysia 3 2 0 WL 01.07. 18:00 2015 9 13 1454 1096553 England Pakistan 2 1 0 WL 01.07. 15:30 2015 5 11 1623 1185554 Australia Ireland 4 1 0 WL 01.07. 13:00 2015 1 15 2073 965555 Poland China 4 2 0 WL 01.07. 10:30 2015 18 27 718 298556 Belgium Ireland 2 1 0 WL 28.06. 18:00 2015 4 15 1650 965557 India Australia 2 6 0 WL 28.06. 16:00 2015 9 1 1454 2073558 Malaysia England 1 3 0 WL 28.06. 14:00 2015 13 5 1096 1623559 Pakistan France 2 2 0 WL 28.06. 12:00 2015 11 17 1185 740560 Australia Poland 4 0 0 WL 26.06. 20:00 2015 1 18 2073 718561 Malaysia Belgium 0 2 0 WL 26.06. 18:00 2015 13 4 1096 1650562 Pakistan India 2 2 0 WL 26.06. 16:00 2015 11 9 1185 1454563 Ireland China 6 0 0 WL 26.06. 14:00 2015 15 27 965 298564 England China 8 1 0 WL 25.06. 16:00 2015 5 27 1623 298565 Malaysia Ireland 4 2 0 WL 25.06. 14:00 2015 13 15 1096 965566 Pakistan Australia 1 6 0 WL 24.06. 20:00 2015 11 1 1185 2073567 Poland France 1 4 0 WL 24.06. 14:00 2015 18 17 718 740568 Belgium China 6 0 0 WL 23.06. 18:00 2015 4 27 1650 298569 India Poland 3 0 0 WL 23.06. 16:00 2015 9 18 1454 718570 England Ireland 2 2 0 WL 23.06. 12:00 2015 5 15 1623 965571 Australia France 10 0 0 WL 21.06. 18:00 2015 1 17 2073 740572 England Belgium 2 2 0 WL 21.06. 16:00 2015 5 4 1623 1650573 China Malaysia 2 3 0 WL 21.06. 12:00 2015 27 13 298 1096574 Pakistan Poland 2 1 0 WL 20.06. 20:00 2015 11 18 1185 718575 India France 3 2 0 WL 20.06. 18:00 2015 9 17 1454 740

44

576 Germany Argentina 4 1 -1 WL 14.06. 23:00 2015 3 7 1813 1569577 Netherlands Canada 6 0 0 WL 14.06. 20:30 2015 2 16 1915 983578 Spain New Zealand 3 1 0 WL 14.06. 18:00 2015 10 6 1173 1496579 Korea Japan 1 0 0 WL 14.06. 15:30 2015 8 14 1413 860580 Netherlands Germany 1 2 0 WL 13.06. 23:00 2015 2 3 1915 1813581 Canada Argentina 0 3 -1 WL 13.06. 20:30 2015 16 7 983 1569582 New Zealand Japan 4 1 0 WL 13.06. 18:00 2015 6 14 1496 860583 Spain Korea 2 2 0 WL 13.06. 15:30 2015 10 8 1173 1413584 Argentina Japan 2 1 1 WL 12.06. 01:00 2015 7 14 1569 860585 New Zealand Canada 0 0 0 WL 11.06. 22:30 2015 6 16 1496 983586 Netherlands Spain 3 1 0 WL 11.06. 20:00 2015 2 10 1915 1173587 Germany Korea 2 0 0 WL 11.06. 17:30 2015 3 8 1813 1413588 Egypt Austria 2 2 0 WL 11.06. 15:00 2015 21 23 598 540589 Spain Argentina 0 1 0 WL 10.06. 01:00 2015 10 7 1173 1569590 Korea New Zealand 3 3 0 WL 09.06. 23:00 2015 8 6 1413 1496591 Netherlands Japan 3 1 0 WL 09.06. 21:00 2015 2 14 1915 860592 Germany Canada 9 0 0 WL 09.06. 19:00 2015 3 16 1813 983593 Argentina Germany 4 3 0 WL 07.06. 23:00 2015 7 3 1569 1813594 Austria Spain 1 4 0 WL 07.06. 21:00 2015 23 10 540 1173595 New Zealand Netherlands 1 1 0 WL 07.06. 19:00 2015 6 2 1496 1915596 Egypt Korea 3 7 0 WL 07.06. 17:00 2015 21 8 598 1413597 Argentina Canada 2 1 0 WL 06.06. 23:00 2015 7 16 1569 983598 Germany Austria 5 0 0 WL 06.06. 21:00 2015 3 23 1813 540599 Japan Egypt 2 0 0 WL 06.06. 19:00 2015 14 21 860 598600 Korea Netherlands 2 6 0 WL 06.06. 17:00 2015 8 2 1413 1915601 Spain Germany 1 4 0 WL 05.06. 01:00 2015 10 3 1173 1813602 Canada Austria 3 0 0 WL 04.06. 23:00 2015 16 23 983 540603 Netherlands Egypt 4 0 0 WL 04.06. 21:00 2015 2 21 1915 598604 New Zealand Japan 2 1 0 WL 04.06. 19:00 2015 6 14 1496 860605 Argentina Austria 3 0 0 WL 04.06. 01:00 2015 7 23 1569 540606 Spain Canada 2 3 0 WL 03.06. 23:00 2015 10 16 1173 983607 Korea Japan 4 2 0 WL 03.06. 21:00 2015 8 14 1413 860608 New Zealand Egypt 4 1 0 WL 03.06. 19:00 2015 6 21 1496 598629 Germany Pakistan 2 0 0 CT 14.12. 15:00 2014 3 11 1813 1185630 Australia India 2 1 -1 CT 14.12. 12:45 2014 1 9 2073 1454631 Argentina Netherlands 1 4 0 CT 14.12. 09:15 2014 7 2 1569 1915632 England Belgium 3 2 0 CT 14.12. 07:00 2014 5 4 1623 1650633 India Pakistan 3 4 1 CT 13.12. 15:00 2014 9 11 1454 1185634 Germany Australia 3 2 0 CT 13.12. 12:45 2014 3 1 1813 2073635 England Argentina 1 2 0 CT 13.12. 09:15 2014 5 7 1623 1569636 Belgium Netherlands 2 2 0 CT 13.12. 07:00 2014 4 2 1650 1915637 Belgium India 2 4 -1 CT 11.12. 15:00 2014 4 9 1650 1454638 England Germany 0 2 0 CT 11.12. 12:45 2014 5 3 1623 1813639 Argentina Australia 2 4 0 CT 11.12. 09:15 2014 7 1 1569 2073640 Netherlands Pakistan 2 4 0 CT 11.12. 07:00 2014 2 11 1915 1185641 Netherlands India 2 3 -1 CT 09.12. 15:00 2014 2 9 1915 1454642 Australia Pakistan 3 0 0 CT 09.12. 13:00 2014 1 11 2073 1185643 England Belgium 1 1 0 CT 09.12. 09:30 2014 5 4 1623 1650644 Argentina Germany 3 0 0 CT 09.12. 07:30 2014 7 3 1569 1813645 Argentina India 4 2 -1 CT 07.12. 15:00 2014 7 9 1569 1454

45

646 Germany Netherlands 1 4 0 CT 07.12. 13:00 2014 3 2 1813 1915647 England Pakistan 8 2 0 CT 07.12. 09:30 2014 5 11 1623 1185648 Belgium Australia 4 4 0 CT 07.12. 07:30 2014 4 1 1650 2073649 Germany India 1 0 -1 CT 06.12. 15:00 2014 3 9 1813 1454650 Netherlands Argentina 3 0 0 CT 06.12. 13:00 2014 2 7 1915 1569651 Belgium Pakistan 2 1 0 CT 06.12. 09:30 2014 4 11 1650 1185652 Australia England 1 3 0 CT 06.12. 07:30 2014 1 5 2073 1623653 India Australia 0 4 0 CG 03.08 13:15 2014 9 1 1454 2073654 New Zealand England 3 3 -1 CG 03.08 11:00 2014 6 5 1496 1623655 South Africa Canada 7 3 0 CG 02.08. 15:30 2014 12 16 934 983656 New Zealand India 2 3 0 CG 02.08. 13:15 2014 6 9 1496 1454657 Australia England 4 1 -1 CG 02.08. 11:00 2014 1 5 2073 1623658 Scotland Malaysia 1 2 0 CG 01.08. 21:15 2014 25 13 335 1096659 South Africa India 2 5 0 CG 31.07. 17:00 2014 12 9 934 1454660 Australia Scotland 5 0 0 CG 31.07. 15:00 2014 1 25 2073 335661 Malaysia New Zealand 1 6 0 CG 31.07. 12:00 2014 13 6 1096 1496662 England Canada 3 1 1 CG 31.07. 10:00 2014 5 16 1623 983663 Wales South Africa 1 5 0 CG 29.07. 17:00 2014 31 12 249 934664 India Australia 2 4 0 CG 29.07. 15:00 2014 9 1 1454 2073665 New Zealand England 2 1 -1 CG 29.07. 10:00 2014 6 5 1496 1623666 Scotland Wales 4 3 0 CG 28.07. 12:00 2014 25 31 335 249667 South Africa Australia 0 6 0 CG 28.07. 10:00 2014 12 1 934 2073668 Malaysia England 1 8 -1 CG 27.07. 22:00 2014 13 5 1096 1623669 India Scotland 6 2 0 CG 26.07. 17:00 2014 9 25 1454 335670 Australia Wales 7 1 0 CG 26.07. 15:00 2014 1 31 2073 249671 Malaysia Canada 2 0 0 CG 26.07. 12:00 2014 13 16 1096 983672 South Africa Scotland 2 0 0 CG 25.07. 12:00 2014 12 25 934 335673 India Wales 3 1 0 CG 25.07. 10:00 2014 9 31 1454 249674 New Zealand Canada 3 1 0 CG 24.07. 22:00 2014 6 16 1496 983675 Australia Netherlands 6 1 -1 WC 15.06.15:15 2014 1 2 2073 1915676 Argentina England 2 0 0 WC 15.06.12:30 2014 7 5 1569 1623677 Belgium Germany 4 2 0 WC 15.06.10:15 2014 4 3 1650 1813678 Spain New Zealand 1 1 0 WC 15.06.08:00 2014 10 6 1173 1496679 India Korea 3 0 0 WC 14.06.08:00 2014 9 8 1454 1413680 Australia Argentina 5 1 0 WC 13.06.18:00 2014 1 7 2073 1569681 Netherlands England 1 0 1 WC 13.06.15:15 2014 2 5 1915 1623682 Malaysia South Africa 2 6 0 WC 12.06.13:30 2014 13 12 1096 934683 New Zealand Netherlands 1 1 -1 WC 10.06.19:45 2014 6 2 1496 1915684 Germany Korea 6 1 0 WC 10.06.13:00 2014 3 8 1813 1413685 Argentina South Africa 5 1 0 WC 10.06.10:30 2014 7 12 1569 934686 Belgium England 2 3 0 WC 09.06.19:45 2014 4 5 1650 1623687 Spain Malaysia 5 2 0 WC 09.06.14:30 2014 10 13 1173 1096688 Australia India 4 0 0 WC 09.06.13:00 2014 1 9 2073 1454689 South Africa Netherlands 1 7 -1 WC 08.06.19:45 2014 12 2 934 1915690 Korea Argentina 0 5 0 WC 08.06.13:00 2014 8 7 1413 1569691 New Zealand Germany 3 5 0 WC 08.06.10:30 2014 6 3 1496 1813692 England Australia 0 5 0 WC 07.06.16:00 2014 5 1 1623 2073693 India Malaysia 3 2 0 WC 07.06.14:30 2014 9 13 1454 1096694 Spain Belgium 2 5 0 WC 07.06.13:00 2014 10 4 1173 1650695 Germany Netherlands 0 1 -1 WC 06.06.19:45 2014 3 2 1813 1915

46

696 Korea South Africa 0 0 0 WC 06.06.17:30 2014 8 12 1413 934697 New Zealand Argentina 1 3 0 WC 06.06.13:00 2014 6 7 1496 1569698 India Spain 1 1 0 WC 05.06.17:30 2014 9 10 1454 1173699 Belgium Australia 1 3 0 WC 05.06.16:00 2014 4 1 1650 2073700 Malaysia England 0 2 0 WC 05.06.13:00 2014 13 5 1096 1623701 Netherlands Korea 2 1 1 WC 03.06.19:45 2014 2 8 1915 1413702 Germany Argentina 0 1 0 WC 03.06.16:00 2014 3 7 1813 1569703 South Africa New Zealand 0 5 0 WC 03.06.14:30 2014 12 6 934 1496704 Malaysia Belgium 2 6 0 WC 02.06.17:30 2014 13 4 1096 1650705 England India 2 1 0 WC 02.06.16:00 2014 5 9 1623 1454706 Australia Spain 3 0 0 WC 02.06.13:00 2014 1 10 2073 1173707 New Zealand Korea 2 1 0 WC 01.06.17:30 2014 6 8 1496 1413708 Netherlands Argentina 3 1 1 WC 01.06.16:00 2014 2 7 1915 1569709 Germany South Africa 4 0 0 WC 01.06.10:30 2014 3 12 1813 934710 England Spain 1 1 0 WC 31.05.17:30 2014 5 10 1623 1173711 Belgium India 3 2 0 WC 31.05.16:00 2014 4 9 1650 1454712 Australia Malaysia 4 0 0 WC 31.05.10:30 2014 1 13 2073 1096

47

B Bradley-Terry Estimates

B.1 Values of qi in the 3 different models

Country Model 1 Model 2 Model 3Argentina 0.068 0.067 0.068Australia 0.093 0.091 0.08Austria 0.027 0.027 0.023Belgium 0.075 0.074 0.08Brazil 0.004 0.006 0.01

Canada 0.023 0.022 0.038China 0.014 0.014 0.03Egypt 0.012 0.012 0.022

England 0.046 0.045 0.056France 0.041 0.041 0.03

Germany 0.068 0.067 0.06India 0.053 0.052 0.063

Ireland 0.038 0.037 0.037Italy 0.01 0.015 0.009

Japan 0.017 0.017 0.024Korea 0.034 0.034 0.027

Malaysia 0.044 0.044 0.034Netherlands 0.075 0.073 0.074New Zealand 0.041 0.041 0.044

Pakistan 0.03 0.03 0.037Poland 0.029 0.029 0.02Russia 0.004 0.006 0.018

Scotland 0.033 0.033 0.017South Africa 0.031 0.031 0.027

Spain 0.045 0.044 0.041USA 0.022 0.022 0.014Wales 0.026 0.026 0.016Total 1 1 1

48

B.2 Final rank matrix for the Bradley-Terry Models

Rank Team P(1st) P(2nd) P(3rd) P(4th) P(5th) P(6th) P(7th) P(8th)1 Belgium 0.211 0.154 0.152 0.101 0.165 0.113 0.079 0.0492 Netherlands 0.205 0.153 0.151 0.102 0.165 0.115 0.082 0.0513 Germany 0.20 0.160 0.184 0.130 0.124 0.099 0.076 0.0514 England 0.116 0.137 0.143 0.151 0.119 0.127 0.123 0.1075 Spain 0.101 0.122 0.107 0.115 0.143 0.147 0.141 0.1226 Ireland 0.077 0.113 0.114 0.152 0.104 0.132 0.149 0.1587 Austria 0.054 0.087 0.075 0.109 0.107 0.146 0.177 0.1998 Poland 0.036 0.073 0.074 0.139 0.073 0.120 0.174 0.263

Total 1 1 1 1 1 1 1 1

Table 27: Probabilities of each team in BT model 1

Rank Team P(1st) P(2nd) P(3rd) P(4th) P(5th) P(6th) P(7th) P(8th)1 Belgium 0.203 0.15 0.149 0.102 0.164 0.116 0.084 0.0532 Germany 0.198 0.158 0.182 0.131 0.123 0.1 0.078 0.0543 Netherlands 0.196 0.15 0.147 0.103 0.164 0.119 0.087 0.0564 England 0.12 0.138 0.144 0.15 0.118 0.125 0.121 0.1075 Spain 0.103 0.121 0.107 0.114 0.141 0.146 0.141 0.1226 Ireland 0.079 0.114 0.115 0.152 0.103 0.13 0.149 0.167 Austria 0.067 0.097 0.084 0.111 0.117 0.148 0.168 0.1748 Poland 0.036 0.072 0.072 0.138 0.071 0.117 0.173 0.272

Total 1 1 1 1 1 1 1 1

Table 28: Probabilities of each team in BT model 2

49

Rank Team P(1st) P(2nd) P(3rd) P(4th) P(5th) P(6th) P(7th) P(8th)1 Netherlands 0.202 0.162 0.166 0.120 0.154 0.111 0.074 0.0402 Belgium 0.194 0.161 0.163 0.122 0.154 0.114 0.077 0.0423 England 0.145 0.151 0.153 0.141 0.144 0.132 0.102 0.0644 Germany 0.206 0.163 0.177 0.126 0.142 0.106 0.070 0.0375 Spain 0.112 0.136 0.125 0.136 0.148 0.148 0.127 0.0886 Ireland 0.107 0.134 0.130 0.146 0.137 0.146 0.129 0.0917 Poland 0.018 0.048 0.046 0.111 0.061 0.122 0.210 0.3088 Austria 0.016 0.044 0.040 0.098 0.060 0.121 0.212 0.330

Total 1 1 1 1 1 1 1 1

Table 29: Probabilities of each team in BT model 3

C Estimates for the Generalized Linear Models

C.1 All possible linear combinations for η

(Int) ATTf ATTfl ATTb DEFf DEFb Home ∆Rank df logLik AICc delta

127 -0.057 0 0.091 0.109 0.035 0.111 0.089 -0.028 7 -1289.379 2592.917 0128 -0.094 0.023 0.088 0.099 0.036 0.115 0.091 -0.027 8 -1288.723 2593.65 0.733119 -0.047 0 0.094 0.105 0 0.143 0.089 -0.028 6 -1290.924 2593.966 1.049120 -0.082 0.022 0.091 0.096 0 0.147 0.091 -0.027 7 -1290.342 2594.843 1.92695 0.005 0 0.082 0.109 0.035 0.108 0 -0.028 6 -1291.6 2595.319 2.40296 -0.029 0.022 0.079 0.099 0.036 0.112 0 -0.027 7 -1291.04 2596.239 3.32287 0.014 0 0.086 0.105 0 0.14 0 -0.028 5 -1293.158 2596.402 3.48588 -0.016 0.02 0.083 0.096 0 0.144 0 -0.027 6 -1292.676 2597.472 4.555124 0.025 0.035 0.129 0 0.034 0.109 0.092 -0.03 7 -1291.962 2598.083 5.166125 0.049 0 0 0.168 0.039 0.1 0.074 -0.028 6 -1293.377 2598.872 5.955116 0.033 0.034 0.131 0 0 0.139 0.092 -0.031 6 -1293.385 2598.889 5.972126 0 0.028 0 0.153 0.04 0.105 0.077 -0.027 7 -1292.421 2599 6.083123 0.102 0 0.141 0 0.032 0.102 0.088 -0.032 6 -1293.543 2599.206 6.289115 0.106 0 0.143 0 0 0.131 0.089 -0.032 5 -1294.831 2599.747 6.82993 0.093 0 0 0.163 0.039 0.098 0 -0.028 5 -1294.945 2599.975 7.05894 0.048 0.026 0 0.149 0.04 0.103 0 -0.027 6 -1294.112 2600.342 7.425117 0.065 0 0 0.166 0 0.134 0.074 -0.028 5 -1295.267 2600.618 7.70192 0.09 0.033 0.121 0 0.034 0.106 0 -0.031 6 -1294.298 2600.715 7.798118 0.019 0.027 0 0.152 0 0.14 0.077 -0.027 6 -1294.387 2600.893 7.97691 0.162 0 0.133 0 0.032 0.1 0 -0.032 5 -1295.729 2601.543 8.62684 0.099 0.032 0.123 0 0 0.136 0 -0.031 5 -1295.742 2601.569 8.65285 0.108 0 0 0.161 0 0.132 0 -0.028 4 -1296.821 2601.699 8.78283 0.166 0 0.134 0 0 0.129 0 -0.032 4 -1297.03 2602.117 9.286 0.067 0.025 0 0.148 0 0.138 0 -0.027 5 -1296.069 2602.222 9.305111 0.167 0 0.072 0.092 0.086 0 0.08 -0.035 6 -1297.468 2607.056 14.13879 0.216 0 0.065 0.092 0.085 0 0 -0.035 5 -1299.274 2608.632 15.715112 0.149 0.014 0.07 0.085 0.087 0 0.081 -0.034 7 -1297.241 2608.641 15.724109 0.233 0 0 0.141 0.084 0 0.069 -0.034 5 -1300.045 2610.176 17.25980 0.2 0.012 0.063 0.086 0.087 0 0 -0.034 6 -1299.086 2610.291 17.37477 0.27 0 0 0.137 0.084 0 0 -0.034 4 -1301.397 2610.851 17.934

50

107 0.287 0 0.116 0 0.079 0 0.08 -0.038 5 -1300.433 2610.951 18.034108 0.241 0.025 0.107 0 0.083 0 0.082 -0.037 6 -1299.642 2611.403 18.486110 0.208 0.018 0 0.131 0.086 0 0.07 -0.034 6 -1299.657 2611.433 18.51678 0.248 0.016 0 0.128 0.086 0 0 -0.034 5 -1301.069 2612.222 19.30575 0.336 0 0.11 0 0.079 0 0 -0.038 4 -1302.247 2612.551 19.63476 0.293 0.023 0.101 0 0.082 0 0 -0.037 5 -1301.529 2613.143 20.225122 0.342 0.058 0 0 0.038 0.083 0.065 -0.034 6 -1302.952 2618.024 25.10790 0.375 0.056 0 0 0.038 0.082 0 -0.034 5 -1304.162 2618.408 25.491114 0.356 0.057 0 0 0 0.117 0.066 -0.034 5 -1304.736 2619.557 26.6482 0.39 0.054 0 0 0 0.116 0 -0.034 4 -1305.956 2619.968 27.05189 0.552 0 0 0 0.036 0.066 0 -0.037 4 -1308.429 2624.915 31.998121 0.529 0 0 0 0.036 0.067 0.056 -0.037 5 -1307.524 2625.133 32.216106 0.473 0.046 0 0 0.076 0 0.061 -0.039 5 -1307.605 2625.294 32.37774 0.501 0.044 0 0 0.076 0 0 -0.039 4 -1308.667 2625.39 32.47381 0.562 0 0 0 0 0.098 0 -0.037 3 -1310.049 2626.132 33.215113 0.539 0 0 0 0 0.099 0.056 -0.037 4 -1309.145 2626.346 33.42973 0.627 0 0 0 0.068 0 0 -0.04 3 -1311.481 2628.996 36.079105 0.606 0 0 0 0.068 0 0.055 -0.041 4 -1310.631 2629.318 36.401103 0.456 0 0.067 0.059 0 0 0.077 -0.043 5 -1311.849 2633.784 40.86799 0.522 0 0.097 0 0 0 0.077 -0.044 4 -1313.116 2634.288 41.37171 0.502 0 0.06 0.059 0 0 0 -0.043 4 -1313.539 2635.135 42.21867 0.568 0 0.09 0 0 0 0 -0.044 3 -1314.812 2635.657 42.74104 0.456 0 0.067 0.059 0 0 0.077 -0.043 6 -1311.849 2635.818 42.901100 0.509 0.008 0.093 0 0 0 0.078 -0.044 5 -1313.02 2636.125 43.208101 0.515 0 0 0.105 0 0 0.067 -0.042 4 -1314.114 2636.286 43.36869 0.549 0 0 0.101 0 0 0 -0.042 3 -1315.387 2636.808 43.89172 0.503 -0.002 0.061 0.06 0 0 0 -0.043 5 -1313.535 2637.155 44.23868 0.558 0.007 0.087 0 0 0 0 -0.044 4 -1314.748 2637.553 44.63664 -0.509 0.043 0.087 0.195 0.043 0.197 0.094 0 7 -1311.978 2638.116 45.199102 0.511 0.004 0 0.103 0 0 0.067 -0.042 5 -1314.096 2638.276 45.35970 0.547 0.002 0 0.1 0 0 0 -0.042 4 -1315.382 2638.82 45.90356 -0.498 0.042 0.091 0.191 0 0.237 0.095 0 6 -1314.223 2640.565 47.64863 -0.458 0 0.093 0.218 0.042 0.194 0.091 0 6 -1314.227 2640.572 47.65532 -0.443 0.041 0.078 0.196 0.043 0.195 0 0 6 -1314.501 2641.122 48.20555 -0.449 0 0.097 0.214 0 0.233 0.091 0 5 -1316.336 2642.756 49.83931 -0.396 0 0.084 0.218 0.042 0.192 0 0 5 -1316.58 2643.245 50.32862 -0.417 0.048 0 0.249 0.046 0.188 0.08 0 6 -1315.594 2643.307 50.3924 -0.432 0.04 0.082 0.192 0 0.234 0 0 5 -1316.76 2643.605 50.68830 -0.369 0.046 0 0.245 0.046 0.186 0 0 5 -1317.443 2644.97 52.05323 -0.388 0 0.088 0.214 0 0.231 0 0 4 -1318.687 2645.431 52.51498 0.694 0.029 0 0 0 0 0.06 -0.045 4 -1319.124 2646.304 53.38766 0.722 0.027 0 0 0 0 0 -0.045 3 -1320.162 2646.357 53.4465 0.787 0 0 0 0 0 0 -0.046 2 -1321.212 2646.44 53.52354 -0.4 0.047 0 0.247 0 0.23 0.08 0 5 -1318.222 2646.53 53.61397 0.765 0 0 0 0 0 0.055 -0.046 3 -1320.339 2646.711 53.79461 -0.353 0 0 0.279 0.045 0.184 0.075 0 5 -1318.378 2646.841 53.92429 -0.309 0 0 0.274 0.045 0.182 0 0 4 -1320.021 2648.098 55.18122 -0.352 0.045 0 0.244 0 0.229 0 0 4 -1320.05 2648.158 55.2453 -0.338 0 0 0.277 0 0.225 0.075 0 4 -1320.887 2649.83 56.91321 -0.295 0 0 0.272 0 0.224 0 0 3 -1322.493 2651.02 58.103

51

60 -0.354 0.075 0.179 0 0.039 0.207 0.097 0 6 -1326.037 2664.192 71.27552 -0.345 0.074 0.181 0 0 0.242 0.098 0 5 -1327.844 2665.773 72.85628 -0.288 0.074 0.171 0 0.039 0.204 0 0 5 -1328.716 2667.516 74.59920 -0.279 0.072 0.173 0 0 0.24 0 0 4 -1330.545 2669.147 76.2359 -0.225 0 0.212 0 0.035 0.204 0.092 0 5 -1333.666 2677.417 84.551 -0.22 0 0.213 0 0 0.236 0.092 0 4 -1335.173 2678.402 85.48527 -0.164 0 0.203 0 0.035 0.202 0 0 4 -1336.063 2680.183 87.26619 -0.159 0 0.205 0 0 0.234 0 0 3 -1337.564 2681.161 88.24448 -0.239 0.034 0.052 0.216 0.161 0 0.075 0 6 -1344.021 2700.161 107.24446 -0.194 0.037 0 0.25 0.159 0 0.067 0 5 -1345.34 2700.765 107.84847 -0.202 0 0.056 0.236 0.158 0 0.073 0 5 -1345.453 2700.991 108.07314 -0.157 0.036 0 0.247 0.159 0 0 0 4 -1346.644 2701.344 108.42716 -0.193 0.033 0.045 0.217 0.16 0 0 0 5 -1345.644 2701.373 108.45615 -0.158 0 0.049 0.236 0.158 0 0 0 4 -1346.994 2702.044 109.12745 -0.15 0 0 0.274 0.157 0 0.064 0 4 -1346.995 2702.046 109.12913 -0.116 0 0 0.27 0.157 0 0 0 3 -1348.194 2702.423 109.50658 0.037 0.115 0 0 0.043 0.19 0.06 0 5 -1348.241 2706.568 113.6526 0.067 0.113 0 0 0.043 0.189 0 0 4 -1349.292 2706.64 113.72350 0.051 0.114 0 0 0 0.229 0.061 0 4 -1350.442 2708.94 116.02318 0.081 0.112 0 0 0 0.228 0 0 3 -1351.503 2709.04 116.12244 -0.052 0.07 0.154 0 0.161 0 0.078 0 5 -1360.839 2731.763 138.84612 -0.005 0.07 0.148 0 0.161 0 0 0 4 -1362.631 2733.319 140.40243 0.067 0 0.184 0 0.156 0 0.075 0 4 -1367.576 2743.208 150.29125 0.396 0 0 0 0.039 0.178 0 0 3 -1368.997 2744.028 151.11111 0.112 0 0.177 0 0.156 0 0 0 3 -1369.217 2744.468 151.5557 0.379 0 0 0 0.039 0.179 0.042 0 4 -1368.479 2745.015 152.09817 0.406 0 0 0 0 0.213 0 0 2 -1370.825 2745.667 152.7549 0.389 0 0 0 0 0.214 0.042 0 3 -1370.323 2746.68 153.76310 0.291 0.104 0 0 0.155 0 0 0 3 -1378.632 2763.299 170.38242 0.27 0.105 0 0 0.155 0 0.048 0 4 -1377.955 2763.966 171.0499 0.582 0 0 0 0.145 0 0 0 2 -1395.226 2794.47 201.55341 0.569 0 0 0 0.145 0 0.034 0 3 -1394.878 2795.79 202.87337 0.326 0 0 0.248 0 0 0.069 0 3 -1403.411 2812.855 219.93839 0.29 0 0.042 0.219 0 0 0.076 0 4 -1402.515 2813.086 220.1695 0.362 0 0 0.244 0 0 0 0 2 -1404.845 2813.706 220.78938 0.306 0.022 0 0.234 0 0 0.072 0 4 -1402.849 2813.754 220.83740 0.273 0.02 0.04 0.208 0 0 0.079 0 5 -1402.047 2814.179 221.2627 0.336 0 0.034 0.22 0 0 0 0 3 -1404.243 2814.521 221.6046 0.346 0.019 0 0.231 0 0 0 0 3 -1404.404 2814.842 221.9258 0.323 0.017 0.032 0.21 0 0 0 0 4 -1403.88 2815.816 222.89936 0.452 0.056 0.136 0 0 0 0.086 0 4 -1417.339 2842.735 249.8184 0.506 0.054 0.129 0 0 0 0 0 3 -1419.519 2845.073 252.15635 0.537 0 0.161 0 0 0 0.08 0 3 -1421.601 2849.235 256.3183 0.585 0 0.153 0 0 0 0 0 2 -1423.497 2851.01 258.09334 0.721 0.088 0 0 0 0 0.059 0 3 -1430.797 2867.628 274.7112 0.748 0.086 0 0 0 0 0 0 2 -1431.834 2867.685 274.7681 0.967 0 0 0 0 0 0 0 1 -1443.104 2888.213 295.29633 0.952 0 0 0 0 0 0.042 0 2 -1442.572 2889.161 296.244

52

C.2 Most likely outcomes for the 2019 Eurohockey Cham-pionship

game Team 1 Team 2 P(win) P(Draw) P(Loss)1 Belgium England 0.852 0.075 0.0732 Belgium Spain 0.88 0.064 0.0563 Belgium Wales 0.987 0.006 0.0034 England Spain 0.482 0.155 0.3625 England Wales 0.883 0.063 0.0546 Spain Wales 0.846 0.08 0.074

Table 31: game results in group A according to GLM 3

game Team 1 Team 2 P(win) P(Draw) P(Loss)1 Netherlands Germany 0.513 0.168 0.3192 Netherlands Ireland 0.852 0.077 0.0713 Netherlands Scotland 0.97 0.018 0.0114 Germany Ireland 0.776 0.107 0.1175 Germany Scotland 0.943 0.034 0.0236 Ireland Scotland 0.722 0.121 0.157

Table 32: game results in group B according to GLM 3

Group A Team P(1st place) P(2nd place) P(3rd place) P(4th place)1 Belgium 0.864 0.109 0.022 02 England 0.078 0.485 0.38 0.0523 Spain 0.053 0.38 0.483 0.084 Wales 0 0.022 0.11 0.863

Table 33: Group A according to Generalized Linear Model 3

53

Group B Team P(1st place) P(2nd place) P(3rd place) P(4th place)1 Netherlands 0.589 0.348 0.058 0.0042 Germany 0.374 0.499 0.114 0.0113 Ireland 0.034 0.137 0.638 0.194 Scotland 0.001 0.015 0.189 0.793

Table 34: Group B according to Generalized Linear Model 3

D R code

1 ##First imported the Dataset ##23 CountryL [,2]<-0 ## Games played4 CountryL [,3]<-0 ## Goals5 CountryL [,4]<-0 ## Goals conceded6 CountryL [,5]<-0 ## Wins7 CountryL [,6]<-0 ## Draws8 CountryL [,7]<-0 ## Losses9 CountryL$ELO <-c

(2246 ,2231 ,2079 ,1908 ,1765 ,1681 ,1551 ,1228 ,1133 ,1067 ,1030 ,1028 ,953 ,843 ,839 ,765 ,740 ,675 ,638 ,618 ,552 ,503 ,484 ,433 ,404 ,246 ,273)

10 CountryL$ELO17 <-c(1640 ,1825 ,1683 ,1845 ,1461 ,1700 ,1357 ,1214 ,1178 ,1015 ,1143 ,895 ,930 ,658 ,720 ,733 ,898 ,711 ,523 ,613 ,542 ,533 ,412 ,310 ,358 ,256 ,321)

11 for (i in 1:27){12 for (j in 1:712){13 if (Data_SET_field_hockey[j,1] == CountryL[i,1]){14 CountryL[i,2] <-CountryL[i,2] + 115 CountryL[i,3] <-CountryL[i,3] + Data_SET_field_hockey[j,3]16 CountryL[i,4] <-CountryL[i,4] + Data_SET_field_hockey[j,4]1718 if(Data_SET_field_hockey[j,3]>( Data_SET_field_hockey[j,4]))19 {CountryL[i,5] <-CountryL[i ,5]+1}2021 if(Data_SET_field_hockey[j,3] == (Data_SET_field_hockey[j,4]))22 {CountryL[i,6] <-CountryL[i ,6]+1}2324 if(Data_SET_field_hockey[j,3]<( Data_SET_field_hockey[j,4]))25 {CountryL[i,7] <-CountryL[i ,7]+1}26 }27 if (Data_SET_field_hockey[j,2] == CountryL[i,1]){28 CountryL[i,2] <-CountryL[i,2] + 129 CountryL[i,3] <-CountryL[i,3] + Data_SET_field_hockey[j,4]30 CountryL[i,4] <-CountryL[i,4] + Data_SET_field_hockey[j,3]3132 if(Data_SET_field_hockey[j,3]<( Data_SET_field_hockey[j,4]))33 {CountryL[i,5] <-CountryL[i ,5]+1}3435 if(Data_SET_field_hockey[j,3] == (Data_SET_field_hockey[j,4]))36 {CountryL[i,6] <-CountryL[i ,6]+1}3738 if(Data_SET_field_hockey[j,3]>( Data_SET_field_hockey[j,4]))39 {CountryL[i,7] <-CountryL[i ,7]+1}40 }41 }42 }43 CountryL$ATTG <-CountryL$Goals / CountryL$Gamesplayed44 CountryL$DEFG <-CountryL$GoalsAgainst / CountryL$Gamesplayed4546 ##Adding home advantage to all games.47 ## 1 means team 1 plays at home48 ## 0 means both teams do not play at home49 ## -1 means team 2 plays at home

54

5051 Data_SET_field_hockey$Home <-052 for (i in 1:712) {53 if (Data_SET_field_hockey[i,8] == "FM") {54 Data_SET_field_hockey[i,7] <-155 }56 if (Data_SET_field_hockey[i,8] == "PL"){57 Data_SET_field_hockey[i,7] <-158 }59 }60 for (i in 59:94) {61 if (Data_SET_field_hockey[i,1] == "India"){62 Data_SET_field_hockey[i,7] <-163 }64 if (Data_SET_field_hockey[i,2] == "India") {65 Data_SET_field_hockey[i,7] <- -166 }67 }68 for (i in 95:112) {69 if (Data_SET_field_hockey[i,1] == "Netherlands"){70 Data_SET_field_hockey[i,7] <-171 }72 if (Data_SET_field_hockey[i,2] == "Netherlands") {73 Data_SET_field_hockey[i,7] <- -174 }75 }76 for (i in 188:214) {77 if (Data_SET_field_hockey[i,1] == "Australia"){78 Data_SET_field_hockey[i,7] <-179 }80 if (Data_SET_field_hockey[i,2] == "Australia") {81 Data_SET_field_hockey[i,7] <- -182 }83 }8485 for (i in 267:288) {86 if (Data_SET_field_hockey[i,1] == "India"){87 Data_SET_field_hockey[i,7] <-188 }89 if (Data_SET_field_hockey[i,2] == "India") {90 Data_SET_field_hockey[i,7] <- -191 }92 }9394 for (i in 289:321) {95 if (Data_SET_field_hockey[i,1] == "South Africa"){96 Data_SET_field_hockey[i,7] <-197 }98 if (Data_SET_field_hockey[i,2] == "South Africa") {99 Data_SET_field_hockey[i,7] <- -1

100 }101 }102103 for (i in 322:354) {104 if (Data_SET_field_hockey[i,1] == "England"){105 Data_SET_field_hockey[i,7] <-1106 }107 if (Data_SET_field_hockey[i,2] == "England") {108 Data_SET_field_hockey[i,7] <- -1109 }110 }111112 for (i in 355:361) {113 if (Data_SET_field_hockey[i,1] == "Ireland"){114 Data_SET_field_hockey[i,7] <-1115 }116 if (Data_SET_field_hockey[i,2] == "Ireland") {117 Data_SET_field_hockey[i,7] <- -1

55

118 }119 }120121 for (i in 362:379) {122 if (Data_SET_field_hockey[i,1] == "Netherlands"){123 Data_SET_field_hockey[i,7] <-1124 }125 if (Data_SET_field_hockey[i,2] == "Netherlands") {126 Data_SET_field_hockey[i,7] <- -1127 }128 }129130 for (i in 465:502) {131 if (Data_SET_field_hockey[i,1] == "Brazil"){132 Data_SET_field_hockey[i,7] <-1133 }134 if (Data_SET_field_hockey[i,2] == "Brazil") {135 Data_SET_field_hockey[i,7] <- -1136 }137 }138139140 for (i in 503:520) {141 if (Data_SET_field_hockey[i,1] == "England"){142 Data_SET_field_hockey[i,7] <-1143 }144 if (Data_SET_field_hockey[i,2] == "England") {145 Data_SET_field_hockey[i,7] <- -1146 }147 }148149 for (i in 521:542) {150 if (Data_SET_field_hockey[i,1] == "India"){151 Data_SET_field_hockey[i,7] <-1152 }153 if (Data_SET_field_hockey[i,2] == "India") {154 Data_SET_field_hockey[i,7] <- -1155 }156 }157158 for (i in 543:574) {159 if (Data_SET_field_hockey[i,1] == "Belgium"){160 Data_SET_field_hockey[i,7] <-1161 }162 if (Data_SET_field_hockey[i,2] == "Belgium") {163 Data_SET_field_hockey[i,7] <- -1164 }165 }166167 for (i in 575:608) {168 if (Data_SET_field_hockey[i,1] == "Argentina"){169 Data_SET_field_hockey[i,7] <-1170 }171 if (Data_SET_field_hockey[i,2] == "Argentina") {172 Data_SET_field_hockey[i,7] <- -1173 }174 }175176 for (i in 609:628) {177 if (Data_SET_field_hockey[i,1] == "England"){178 Data_SET_field_hockey[i,7] <-1179 }180 if (Data_SET_field_hockey[i,2] == "England") {181 Data_SET_field_hockey[i,7] <- -1182 }183 }184185 for (i in 629:652) {

56

186 if (Data_SET_field_hockey[i,1] == "India"){187 Data_SET_field_hockey[i,7] <-1188 }189 if (Data_SET_field_hockey[i,2] == "India") {190 Data_SET_field_hockey[i,7] <- -1191 }192 }193194 for (i in 653:673) {195 if (Data_SET_field_hockey[i,1] == "England"){196 Data_SET_field_hockey[i,7] <-1197 }198 if (Data_SET_field_hockey[i,2] == "England") {199 Data_SET_field_hockey[i,7] <- -1200 }201 }202203 for (i in 674:712) {204 if (Data_SET_field_hockey[i,1] == "Netherlands"){205 Data_SET_field_hockey[i,7] <-1206 }207 if (Data_SET_field_hockey[i,2] == "Netherlands") {208 Data_SET_field_hockey[i,7] <- -1209 }210 }211212 ### Adding data to Data Set###213 Data_SET_field_hockey$ATTG <-0214 Data_SET_field_hockey$DEFG <-0215 for (i in 1:27) {216 for(j in 1:712){217 if(Data_SET_field_hockey[j,1] == CountryL[i,1]){218 Data_SET_field_hockey[j,15] <-CountryL[i,8]219 }220 if(Data_SET_field_hockey[j,2]== CountryL[i,1]){221 Data_SET_field_hockey[j,16] <-CountryL[i,9]222 }223 }224 }225226 ##Adding game number to each game for each team##227228 Data_SET_field_hockey$NrTeam1 <-0229 Data_SET_field_hockey$NrTeam2 <-0230231 for (j in 1:27) {232 Gameno <-1233 for (i in 1:712) {234 if (Data_SET_field_hockey[i,1] == CountryL[j,1]){235 Data_SET_field_hockey[i,17] <-Gameno236 Gameno <-Gameno +1237 }238 if (Data_SET_field_hockey[i,2] == CountryL[j,1]){239 Data_SET_field_hockey[i,18] <-Gameno240 Gameno <-Gameno +1241 }242 }243 }244 ##Goals scored in Recent games put into one file##245 GamesperCountry <- matrix(0,nrow =150, ncol =27)246 colnames(GamesperCountry)<-t(CountryL [,1])247 for (i in 1:27) {248 for (j in 1:712){249 if (CountryL[i,1] == Data_SET_field_hockey[j,1]) {250 GamesperCountry[ Data_SET_field_hockey[j,17] , i ] <- Data_SET_field_

hockey[j,3]251 }252 if(CountryL[i,1] == Data_SET_field_hockey[j,2]){

57

253 GamesperCountry[Data_SET_field_hockey[j,18],i] <- Data_SET_field_hockey[j,4]

254 }255 }256 }257 ##Goals conceded in Recent games258 ConcededperCountry <- matrix(0,nrow =150, ncol =27)259 colnames(ConcededperCountry)<-t(CountryL [,1])260 for (j in 1:27) {261 for (i in 1:712){262 if(CountryL[j,1] == Data_SET_field_hockey[i,1]){263 ConcededperCountry[Data_SET_field_hockey[i,17],j]<-Data_SET_field_

hockey[i,4]264 }265 if(CountryL[j,1] == Data_SET_field_hockey[i,2]){266 ConcededperCountry[Data_SET_field_hockey[i,18],j]<-Data_SET_field_

hockey[i,3]267 }268 }269 }270271272 ##Adding form (Average Goals Scored in most recent 3 games)###273 ATTFpC <- matrix(0,nrow =150, ncol =27)274 colnames(ATTFpC)<-t(CountryL [,1])275 z<-3276 for (i in 1:109) {277 for (j in 1:27){278 for (k in 1:z) {279 ATTFpC[i,j]<-ATTFpC[i,j]+( GamesperCountry[i+k,j]/z)280 }281 }282 }283 ##Teams with less than z games get the average score for all games284 for (j in 1:27){285 if(CountryL[j,2]< z){ATTFpC[1,j]<-CountryL[j,8]286 }287 }288 ##If i+z is more than the number of games , take the result above289 for (i in 2:150) {290 for (j in 1:27) {291 if (i+z > CountryL[j,2]){292 ATTFpC[i,j]<-ATTFpC[i-1,j]293 }294 }295 }296297 ##Same thing for defensive stats , Goals conceded in most recent 3 games)###298 DEFFFpC <- matrix(0,nrow =150, ncol =27)299 colnames(DEFFFpC)<-(CountryL [,1])300 z<-3301 for (i in 1:109) {302 for (j in 1:27){303 for (k in 1:z) {304 DEFFFpC[i,j]<-DEFFFpC[i,j]+( ConcededperCountry[i+k,j]/z)305 }306 }307 }308 ##309310 for (j in 1:27){311 if(CountryL[j,2]< z){DEFFFpC[1,j]<-CountryL[j,9]312 }313 }314 ##315 for (i in 2:150) {316 for (j in 1:27) {317 if (i+z > CountryL[j,2]){

58

318 DEFFFpC[i,j]<-DEFFFpC[i-1,j]319 }320 }321 }322323324325 ##Adding long -term form (Average Goals Scored in most recent 10 - 3 games)###326 ATTFpC2 <- matrix(0,nrow =150, ncol =27)327 colnames(ATTFpC2)<-t(CountryL [,1])328 z<-10329 for (i in 1:109) {330 for (j in 1:27){331 for (k in 4:z) {332 ATTFpC2[i,j]<-ATTFpC2[i,j]+( GamesperCountry[i+k,j]/(z-3))333 }334 }335 }336 ##Teams with less than z games get the average score for all games337 for (j in 1:27){338 if(CountryL[j,2]< z){ATTFpC2[1,j]<-CountryL[j,8]339 }340 }341 ##If i+z is more than the number of games , take the result above342 for (i in 2:150) {343 for (j in 1:27) {344 if (i+z > CountryL[j,2]){345 ATTFpC2[i,j]<-ATTFpC2[i-1,j]346 }347 }348 }349350 ##Same thing for defensive stats , Goals conceded in most recent 10 -3 games)

###351 DEFFFpC2 <- matrix(0,nrow =150, ncol =27)352 colnames(DEFFFpC2)<-(CountryL [,1])353 z<-10354 for (i in 1:109) {355 for (j in 1:27){356 for (k in 4:z) {357 DEFFFpC2[i,j]<-DEFFFpC2[i,j]+( ConcededperCountry[i+k,j]/(z-3))358 }359 }360 }361 ##Teams with less than z games get the average score for all games362 for (j in 1:27){363 if(CountryL[j,2]< z){DEFFFpC2[1,j]<-CountryL[j,9]364 }365 }366 ##If i+z is more than the number of games , take the result above367 for (i in 2:150) {368 for (j in 1:27) {369 if (i+z > CountryL[j,2]){370 DEFFFpC2[i,j]<-DEFFFpC2[i-1,j]371 }372 }373 }374375 ###3 EXTRA solution ###376377 ##Adding long -term form (Average Goals Scored in most recent 10 - 3 games)###378 ATTFpC3 <- matrix(0,nrow =150, ncol =27)379 colnames(ATTFpC3)<-t(CountryL [,1])380 for (i in 1:109) {381 for (j in 1:27){382 for (k in 11: CountryL[j,2]) {383 if(i+k < 150){384 ATTFpC3[i,j]<-ATTFpC3[i,j]+ GamesperCountry[i+k,j]

59

385 }386 }387 ATTFpC3[i,j]<-ATTFpC3[i,j]/(CountryL[j,2]-i-10)388 }389 }390391 ##Teams with less than 16 games get the average score for all games392 for (j in 1:27){393 if(CountryL[j,2]< 16){ATTFpC3[1,j]<-CountryL[j,8]394 }395 }396 ##If i+16 is more than the number of games , take the result above397 for (i in 2:150) {398 for (j in 1:27) {399 if (i+16 > CountryL[j,2]){400 ATTFpC3[i,j]<-ATTFpC3[i-1,j]401 }402 }403 }404405 ##Same thing for defensive stats , Goals conceded in most recent 10 -3 games)

###406 ##Adding long -term form (Average Goals Scored in most recent 10 - 3 games)###407 DEFFFpC3 <- matrix(0,nrow =150, ncol =27)408 colnames(DEFFFpC3)<-t(CountryL [,1])409 for (i in 1:109) {410 for (j in 1:27){411 for (k in 11: CountryL[j,2]) {412 if(i+k < 150){413 DEFFFpC3[i,j]<-DEFFFpC3[i,j]+ ConcededperCountry[i+k,j]414 }415 }416 DEFFFpC3[i,j]<-DEFFFpC3[i,j]/(CountryL[j,2]-i-10)417 }418 }419420 ##Teams with less than 16 games get the average score for all games421 for (j in 1:27){422 if(CountryL[j,2]< 16){DEFFFpC3[1,j]<-CountryL[j,9]423 }424 }425 ##If i+16 is more than the number of games , take the result above426 for (i in 2:150) {427 for (j in 1:27) {428 if (i+16 > CountryL[j,2]){429 DEFFFpC3[i,j]<-DEFFFpC3[i-1,j]430 }431 }432 }433434435 ##Adding form data to Data set##436 Data_SET_field_hockey$ATTFORM <-0437 Data_SET_field_hockey$DEFFORM <-0438 Data_SET_field_hockey$ATTFORMLONG <-0439 Data_SET_field_hockey$DEFFORMLONG <-0440 Data_SET_field_hockey$ATTG2 <-0441 Data_SET_field_hockey$DEFG2 <-0442 for (i in 1:27){443 for (j in 1:712) {444 if(Data_SET_field_hockey[j,1]== CountryL[i,1]){445 Data_SET_field_hockey[j,19] <-ATTFpC[Data_SET_field_hockey[j,17],i]446 Data_SET_field_hockey[j,23] <-ATTFpC2[Data_SET_field_hockey[j,17],i]447 Data_SET_field_hockey[j,25] <-ATTFpC3[Data_SET_field_hockey[j,17],i]448 }449 if(Data_SET_field_hockey[j,2] == CountryL[i,1]){450 Data_SET_field_hockey[j,20] <-DEFFFpC[Data_SET_field_hockey[j,18],i]451 Data_SET_field_hockey[j,24] <-DEFFFpC2[Data_SET_field_hockey[j,18],i]

60

452 Data_SET_field_hockey[j,26] <-DEFFFpC3[Data_SET_field_hockey[j,18],i]453 }454 }455 }456457 ##Adding ELO difference and World Ranking difference ###458 Data_SET_field_hockey$ELODIFF <- Data_SET_field_hockey$ELO1 - Data_SET_field_

hockey$ELO2459 Data_SET_field_hockey$RankDIFF <- Data_SET_field_hockey$WorldRanking1 - Data_

SET_field_hockey$WorldRanking2460461462 ## Data set is now completed ##463 ##Formula to predict outcome of a game##464465 Outcomematch <-function(team1 ,team2 ,distr="BT", q ,sigm , Teamlist , MODEL =

NEWMODEL3 ,modelno){466 ploss <-0467 pwin <-0468 pdraw <-0469 i<-0470 j<-0471 if (distr == "BT"){472 i<-match(team1 ,Teamlist)473 j<-match(team2 ,Teamlist)474 pwin <-q[i]/(q[i]+sigm*q[j])475 ploss <-q[j]/(q[j]+sigm*q[i])476 pdraw <-(sigm ^2-1)*q[i]*q[j]/((q[i]+sigm*q[j])*(q[j]+sigm*q[i]))477 }478479 if(distr == "BTNODRAW"){480 i<-match(team1 ,Teamlist)481 j<-match(team2 ,Teamlist)482 pwin <-q[i]/(q[i]+q[j])483 ploss <-q[j]/(q[j]+q[i])484 pdraw <-0485 }486487 if(distr == "GLM"){488 GLMresult <-GLM(team1 , team2 ,modelno , MODEL , Teamlist)489490 pwin <-GLMresult$Win1491 ploss <-GLMresult$Loss1492 pdraw <-GLMresult$Draw1493 GTM1 <-GLMresult$GTM1494 GTM2 <-GLMresult$GTM2495 }496 if(distr =="GLMNODRAW"){497 GLMresult <-GLM(team1 , team2 , modelno , MODEL , Teamlist)498499 pwin <-GLMresult$Win1/(GLMresult$Win1+GLMresult$Loss1)500 ploss <-GLMresult$Loss1/(GLMresult$Win1+GLMresult$Loss1)501 pdraw <-0502 GTM1 <-GLMresult$GTM1503 GTM2 <-GLMresult$GTM2504 }505 list("Win1" = pwin , "Loss1" = ploss , "Draw1"=pdraw , "GTM1"=GTM1 , "GTM2"=

GTM2)506 }507508 ## GLM prediction formula ##509510 GLM <-function(Team1 , Team2 , modelno , MODEL , Teamlist){511 ploss <-0512 pwin <-0513 pdraw <-0514 Goals1 <-0515 Goals2 <-0

61

516 i<-match(Team1 ,Teamlist)517 j<-match(Team2 ,Teamlist)518 Goals1 <-exp(NEWMODEL3[modelno ,1]+ NEWMODEL3[modelno ,2]*EURO2019[i,8]+

NEWMODEL3[modelno ,3]*EURO2019[i,9]+ NEWMODEL3[modelno ,4]*EURO2019[i,6]+NEWMODEL3[modelno ,5]*EURO2019[j ,10]+ NEWMODEL3[modelno ,6]*EURO2019[j,11]+ NEWMODEL3[modelno ,6]*EURO2019[j,7]+ NEWMODEL3[modelno ,7]*(EURO2019[i,12]- EURO2019[j,12])+NEWMODEL3[modelno ,8]*(EURO2019[i,2]- EURO2019[j,2]))

519 Goals2 <-exp(NEWMODEL3[modelno ,1]+ NEWMODEL3[modelno ,2]*EURO2019[j,8]+NEWMODEL3[modelno ,3]*EURO2019[j,9]+ NEWMODEL3[modelno ,4]*EURO2019[j,6]+NEWMODEL3[modelno ,5]*EURO2019[i ,10]+ NEWMODEL3[modelno ,6]*EURO2019[i,11]+ NEWMODEL3[modelno ,6]*EURO2019[i,7]+ NEWMODEL3[modelno ,7]*(EURO2019[j,12]- EURO2019[i,12])+NEWMODEL3[modelno ,8]*(EURO2019[j,2]- EURO2019[i,2]))

520521 for (z in (1:15)){522 ploss <-ploss+dskellam(-z,Goals1 ,Goals2)523 pwin <-pwin+dskellam(z,Goals1 ,Goals2)524 }525 pdraw <-dskellam(0,Goals1 ,Goals2)526527 list("Win1" = pwin , "Loss1" = ploss , "Draw1"=pdraw , "GTM1"=Goals1 , "GTM2"=

Goals2)528 }529530531 ### Model Selection for GLM ###532 library(MuMIn)533 newmodel <-glm(Score1~ATTFORM+ATTFORMLONG+ATTG2+DEFFORM+DEFFORMLONG+DEFG2+Home

+RankDIFF+ELODIFF+, data=Data_SET_field_hockey , family = poisson (),na.action = "na.fail")

534 vif(newmodel)535536 ##removed the ELO##537 library(MuMIn)538 newmodel2 <-glm(Score1~ATTFORM+ATTFORMLONG+ATTG2+DEFFORM+DEFFORMLONG+DEFG2+

Home+RankDIFF , data=Data_SET_field_hockey , family = poisson (),na.action= "na.fail")

539 NEWMODEL2 <-dredge(newmodel2)540 NEWMODEL2[is.na(NEWMODEL2)]<-0541 vif(newmodel2)542543 ##removed the DEFFFORMLONG , final models ##544 newmodel3 <-glm(Score1~ATTFORM+ATTFORMLONG+ATTG2+DEFFORM+DEFG2+Home+RankDIFF ,

data=Data_SET_field_hockey , family = poisson (),na.action = "na.fail")545 NEWMODEL3 <-dredge(newmodel3)546 NEWMODEL3[is.na(NEWMODEL3)]<-0547 vif(newmodel3)548549 ##Bradley - Terry Model , Making matrix with won games , tied games and

calculating theta ###550551 ##table with draws ##552553 CountryLBT <-CountryL[order(CountryL$Country),]554555 Gamestied <-matrix(0,nrow=27,ncol =27)556 colnames(Gamestied)<-sort(CountryL [,1])557 rownames(Gamestied)<-sort(CountryL [,1])558559 for (k in 1:712){560 for (i in 1:27) {561 for (j in 1:27){562 if (Data_SET_field_hockey[k,1] == CountryLBT[i,1] && Data_SET_field_

hockey[k,2] == CountryLBT[j,1]){563 if(Data_SET_field_hockey[k,3] == Data_SET_field_hockey[k,4]){564 Gamestied[i,j]<-Gamestied[i,j]+1565 }

62

566 if(Data_SET_field_hockey[k,3]== Data_SET_field_hockey[k,4]){567 Gamestied[j,i]<-Gamestied[j,i]+1568 }569 }570 }571 }572 }573 ##WON GAMES##574575 Gameswon <-matrix(0,nrow=27,ncol =27)576577 colnames(Gameswon)<-sort(CountryL [,1])578 rownames(Gameswon)<-sort(CountryL [,1])579580 for (i in 1:27) {581 for (j in i:27){582 for (k in 1:712){583 if (Data_SET_field_hockey[k,1] == CountryLBT[i,1] && Data_SET_field_

hockey[k,2] == CountryLBT[j,1]){584 if(Data_SET_field_hockey[k,3]>Data_SET_field_hockey[k,4]){585 Gameswon[i,j]<-Gameswon[i,j]+1586 }587 if(Data_SET_field_hockey[k,3]<Data_SET_field_hockey[k,4]){588 Gameswon[j,i]<-Gameswon[j,i]+1589 }590 }591 }592 }593 }594 for (j in 1:27) {595 for (i in j:27){596 for (k in 1:712){597 if (Data_SET_field_hockey[k,1] == CountryL[i,1] && Data_SET_field_

hockey[k,2] == CountryL[j,1]){598 if(Data_SET_field_hockey[k,3]>Data_SET_field_hockey[k,4]){599 Gameswon[i,j]<-Gameswon[i,j]+1600 }601 if(Data_SET_field_hockey[k,3]<Data_SET_field_hockey[k,4]){602 Gameswon[j,i]<-Gameswon[j,i]+1603 }604 }605 }606 }607 }608609 ##Calculating the theta (it is called sigm)##610611 Difference <-1612 t<-1613 Ties <-sum(CountryLBT [,6])614 sigm <-2615 m<-27616 q<-CountryLBT [,10]617 while (Difference > 1e-8){618 sigmold <-sigm619 sum1 <-0620 sum2 <-0621 for (i in 1:m) {622 for (j in 1:m){623 sum1 <-sum1 +(( Gameswon[i,j]+ Gamestied[i,j])*q[j])/(q[i]+sigm*q[j])624 sum2 <-sum2 +(( Gameswon[j,i]+ Gamestied[i,j])*q[i])/(q[j]+sigm*q[i])625 }626 }627 t<-t+1628 C<-1/(2*Ties)*(sum1+sum2)629 sigm <-1/(2*C)+sqrt (1+(1/(4*C^2)))630 Difference <-abs(sigmold -sigm)631 }

63

632633634635636 ### predicting group stage ####637 GroupResults <-function (group , distr ="BT",q ,sigm , Teamlist , modelno ){638 ProbRes <-data.frame(group ,"Prob 1st place "=rep (0,4)," Prob 2nd place"=rep

(0,4) ,"Prob 3rd place"=rep(0,4) ,"Prob 4th place"=rep(0,4))639 Matches <-t(combn(group ,2))640 MatchProb <-data.frame(" Team1"=Matches[,1],"Team2"=Matches[,2]," Team1Win

"=rep (0,6) ,"Draw"=rep(0,6),"Team2Win"=rep(0,6),"GTM1"=rep(0,6),"GTM2"=rep(0,6))

641642 for (i in 1:6) {643 probs <-Outcomematch(Matches[i,1], Matches[i,2],distr , q , sigm , Teamlist ,

MODEL=NEWMODEL3 ,modelno )644 MatchProb[i,3] <-probs$Win1645 MatchProb[i,4] <-probs$Draw1646 MatchProb[i,5] <-probs$Loss1647 MatchProb[i,6] <-probs$GTM1648 MatchProb[i,7] <-probs$GTM2649 }650651 ProbMat2 <-MatchProb[,c(3 ,4 ,5)]652 pos <-matrix (c(T,F,F,F,T,F,F,F,T),ncol =3)653 Team1Mat <-matrix(c(3,3,3,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0),ncol =3)654 Team2Mat <-matrix(c(0,0,0,3,3,0,1,0,0,1,1,0,3,0,0,0,0,0),ncol =3)655 Team3Mat <-matrix(c(0,0,0,0,0,3,0,1,0,1,0,1,0,3,0,3,0,0),ncol =3)656 Team4Mat <-matrix(c(0,0,0,0,0,0,0,0,1,0,1,1,0,0,3,0,3,3),ncol =3)657658 Epnt=c(sum(ProbMat2*Team1Mat),sum(ProbMat2*Team2Mat),sum(ProbMat2*Team3Mat)

,659 sum(ProbMat2*Team4Mat))660 ExpPoints <-data.frame("Team"=group ,"ExpPnt"=Epnt)661 ExpPoints <-ExpPoints[order(-ExpPoints$ExpPnt) ,]662 rownames(ExpPoints)<-rep (1:4)663664 for (a in 1:3) {665 for (b in 1:3) {666 for (c in 1:3) {667 for (d in 1:3) {668 for (e in 1:3) {669 for (g in 1:3) {670 PntTeam <-rep(0,4)671 TFt <-rbind(pos[a,], pos[b,],pos[c,],pos[d,],pos[e,],pos[g,])672 AllPos <-prod(ProbMat2[TFt])673 PntTeam [1] <-sum(Team1Mat[TFt])674 PntTeam [2] <-sum(Team2Mat[TFt])675 PntTeam [3] <-sum(Team3Mat[TFt])676 PntTeam [4] <-sum(Team4Mat[TFt])677 maxlen <-length(which(PntTeam == max(PntTeam)))678 if(max(PntTeam)== 9) {ProbRes[which.max(PntTeam) ,2]<-ProbRes[

which.max(PntTeam) ,2]+ AllPos679 NewPntTeam <-PntTeam[-which(PntTeam ==9)]680 NewMaxlen <-length(which(NewPntTeam == max(NewPntTeam)))681 if(NewMaxlen == 3){ProbRes[which(PntTeam!=9),c(3,4,5)]<-682 ProbRes[which(PntTeam!=9),c(3,4,5)]+ AllPos /3}683 if(NewMaxlen ==2){684 max2 <-max(NewPntTeam)685 min2 <-min(NewPntTeam)686 ProbRes[which(PntTeam == max2),c(3,4)]<-ProbRes[which(PntTeam

== max2),c(3,4)]+ AllPos/2687 ProbRes[which(PntTeam == min2) ,5]<-ProbRes[which(PntTeam ==

min2) ,5]+ AllPos}688 if(NewMaxlen == 1) {689 max1 <-max(NewPntTeam)690 ProbRes[which(PntTeam == max1) ,3]<-ProbRes[which(PntTeam ==

max1) ,3]+ AllPos

64

691 NewPntTeam2 <-NewPntTeam[-which.max(NewPntTeam)]692 NewMaxlen2 <-length(which(NewPntTeam2 == max(NewPntTeam2)))693 if(NewMaxlen2 ==2) {694 max2 <-max(NewPntTeam2)695 ProbRes[which(PntTeam == max2),c(4,5)]<-ProbRes[which(

PntTeam == max2 ),c(4,5)]+ AllPos/2 }696 if(NewMaxlen2 ==1) {697 max2 <-max(NewPntTeam2)698 min2 <-min(NewPntTeam2)699 ProbRes[which(PntTeam == max2) ,4]<-ProbRes[which (PntTeam

== max2) ,4]+ AllPos700 ProbRes[which(PntTeam == min2) ,5]<-ProbRes[which (PntTeam

== min2) ,5]+ AllPos701 }702 }703 }704 if(max(PntTeam)==7){705 if(maxlen ==2){706 ProbRes[which(PntTeam ==7),c(2,3)]<-ProbRes[which(PntTeam

==7),c(2,3)]+ AllPos/2707 NewPntTeam <-PntTeam[-which(PntTeam ==7)]708 NewMaxlen <-length(which(NewPntTeam ==max(NewPntTeam)))709710 if(NewMaxlen ==2){711 ProbRes[which(PntTeam ==1),c(4,5)]<-ProbRes[which(PntTeam

==1),c(4,5)]+ AllPos/2}712713 if(NewMaxlen ==1){714 max2 <-max(NewPntTeam)715 min2 <-min(NewPntTeam)716 ProbRes[which(PntTeam ==max2) ,4]<-ProbRes[which(PntTeam ==

max2) ,4]+ AllPos717 ProbRes[which(PntTeam ==min2) ,5]<-ProbRes[which(PntTeam ==

min2) ,5]+ AllPos}718 }719 if(maxlen ==1){720 ProbRes[which.max(PntTeam) ,2]<-ProbRes[which.max(PntTeam)

,2]+ AllPos721 NewPntTeam <-PntTeam[-which(PntTeam ==7)]722 NewMaxlen <-length(which(NewPntTeam ==max(NewPntTeam)))723 if(NewMaxlen ==1){724 max1 <-max(NewPntTeam)725 ProbRes[which(PntTeam ==max1) ,3]<-ProbRes[which(726 PntTeam ==max1) ,3]+ AllPos727 NewPntTeam2 <-NewPntTeam[-which.max(NewPntTeam)]728 NewMaxlen2 <-length(which(NewPntTeam2 ==max(NewPntTeam2)))729 if(NewMaxlen2 ==2){730 max2 <-max(NewPntTeam2)731 ProbRes[which(PntTeam ==max2),c(4,5)]<-ProbRes[which(

PntTeam ==max2),c(4,5)]+ AllPos/2}732 if(NewMaxlen2 ==1){733 max2 <-max(NewPntTeam2)734 min2 <-min(NewPntTeam2)735 ProbRes[which(PntTeam ==max2) ,4]<-ProbRes[which(PntTeam

==max2) ,4]+ AllPos736 ProbRes[which(PntTeam ==min2) ,5]<-ProbRes[which(PntTeam

==min2) ,5]+ AllPos}737 }738 if(NewMaxlen ==2){739 max2 <-max(NewPntTeam)740 min2 <-min(NewPntTeam)741 ProbRes[which(PntTeam ==max2),c(3,4)]<-ProbRes[which(

PntTeam ==max2),742 c(3,4)]+

AllPos/2

743 ProbRes[which(PntTeam ==min2) ,5]<-ProbRes[which(PntTeam ==min2) ,5]+ AllPos}

65

744 }745 }746 if(max(PntTeam)==6){747 if(maxlen ==3){ProbRes[which(PntTeam ==6),c(2,3,4)]<-ProbRes[

which(PntTeam ==6),c(2,3,4)]+ AllPos/3748 ProbRes[which(PntTeam ==0) ,5]<-ProbRes[which(PntTeam ==0) ,5]+

AllPos}749 if(maxlen ==2){ProbRes[which(PntTeam ==6),c(2,3)]<-ProbRes[

which(PntTeam ==6),c(2,3)]+ AllPos/2750 NewPntTeam <-PntTeam[-which(PntTeam ==6)]751 NewMaxlen <-length(which(NewPntTeam ==max(NewPntTeam))752 )753 if(NewMaxlen ==2){ProbRes[which(PntTeam ==3),c(4,5)]<-ProbRes[

which(PntTeam ==3),c(4,5)]+ AllPos/2}754 if(NewMaxlen ==1){755 max2 <-max(NewPntTeam)756 min2 <-min(NewPntTeam)757 ProbRes[which(PntTeam ==max2) ,4]<-ProbRes[which(PntTeam ==

max2) ,4]+ AllPos758 ProbRes[which(PntTeam ==min2) ,5]<-ProbRes[which(PntTeam ==

min2) ,5]+ AllPos}759 }760 if(maxlen ==1){ProbRes[which.max(PntTeam) ,2]<-ProbRes[which.

max(PntTeam) ,2]+ AllPos761 NewPntTeam <-PntTeam[-which(PntTeam ==6)]762 NewMaxlen <-length(which(NewPntTeam ==max(NewPntTeam))763 )764 if(NewMaxlen ==1){765 max1 <-max(NewPntTeam)766 ProbRes[which(PntTeam ==max1) ,3]<-ProbRes[which(PntTeam ==

max1) ,3]+ AllPos767 NewPntTeam2 <-NewPntTeam[-which.max(NewPntTeam)]768 NewMaxlen2 <-length(which(NewPntTeam2 ==max(NewPntTeam2)))769 if(NewMaxlen2 ==2){770 ProbRes[which(PntTeam ==2),c(4,5)]<-ProbRes[which(PntTeam

==2),c(4,5)]+ AllPos/2}771 if(NewMaxlen2 ==1){772 max2 <-max(NewPntTeam2)773 min2 <-min(NewPntTeam2)774 ProbRes[which(PntTeam ==max2) ,4]<-ProbRes[which(PntTeam ==

max2) ,4]+ AllPos775 ProbRes[which(PntTeam ==min2) ,5]<-ProbRes[which(PntTeam ==

min2) ,5]+ AllPos}776 }777 if(NewMaxlen ==2){778 max2 <-max(NewPntTeam)779 min2 <-min(NewPntTeam)780 ProbRes[which(PntTeam ==max2),c(3,4)]<-ProbRes[which(PntTeam

==max2),c(3,4)]+ AllPos/2781 ProbRes[which(PntTeam ==min2) ,5]<-ProbRes[which(PntTeam ==

min2) ,5]+ AllPos}782 }783 }784785 if(max(PntTeam)==5){786 if(maxlen ==3){787 ProbRes[which(PntTeam ==5),c(2,3,4)]<-ProbRes[which(PntTeam

==5),c(2,3,4)]+ AllPos/3788 ProbRes[which(PntTeam ==0) ,5]<-ProbRes[which(PntTeam ==0) ,5]+

AllPos}789 if(maxlen ==2){790 ProbRes[which(PntTeam ==5),c(2,3)]<-ProbRes[which(PntTeam

==5),c(2,3)]+ AllPos/2791 NewPntTeam <-PntTeam[-which(PntTeam ==5)]792 NewMaxlen <-length(which(NewPntTeam ==max(NewPntTeam))793 )794 if(NewMaxlen ==2){

66

795 ProbRes[which(PntTeam ==2),c(4,5)]<-ProbRes[which(PntTeam==2),c(4,5)]+ AllPos/2}

796 if(NewMaxlen ==1){797 max2 <-max(NewPntTeam)798 min2 <-min(NewPntTeam)799 ProbRes[which(PntTeam ==max2) ,4]<-ProbRes[which(PntTeam ==

max2) ,4]+ AllPos800 ProbRes[which(PntTeam ==min2) ,5]<-ProbRes[which(PntTeam ==

min2) ,5]+ AllPos}801 }802 if(maxlen ==1){803 ProbRes[which.max(PntTeam) ,2]<-ProbRes[which.max(PntTeam)

,2]+ AllPos804 NewPntTeam <-PntTeam[-which(PntTeam ==5)]805 NewMaxlen <-length(which(NewPntTeam ==max(NewPntTeam))806 )807 if(NewMaxlen ==1){808 max1 <-max(NewPntTeam)809 ProbRes[which(PntTeam ==max1) ,3]<-ProbRes[which(PntTeam ==

max1) ,3]+ AllPos810 NewPntTeam2 <-NewPntTeam[-which.max(NewPntTeam)]811 NewMaxlen2 <-length(which(NewPntTeam2 ==max(NewPntTeam2)))812 if(NewMaxlen2 ==1){813 max2 <-max(NewPntTeam2)814 min2 <-min(NewPntTeam2)815 ProbRes[which(PntTeam ==max2) ,4]<-ProbRes[which(PntTeam

==max2) ,4]+ AllPos816 ProbRes[which(PntTeam ==min2) ,5]<-ProbRes[which(PntTeam

==min2) ,5]+ AllPos}817 }818 if(NewMaxlen ==2){819 max2 <-max(NewPntTeam)820 min2 <-min(NewPntTeam)821 ProbRes[which(PntTeam ==max2),c(3,4)]<-ProbRes[which(

PntTeam ==max2),c(3,4)]+ AllPos/2822 ProbRes[which(PntTeam ==min2) ,5]<-ProbRes[which(PntTeam ==

min2) ,5]+ AllPos}823 }824 }825 if(max(PntTeam)==4){826 if(maxlen ==3){827 ProbRes[which(PntTeam ==4),c(2,3,4)]<-ProbRes[which(PntTeam

==4),c(2,3,4)]+ AllPos/3828 ProbRes[which(PntTeam ==3) ,5]<-ProbRes[which(PntTeam ==3) ,5]+

AllPos}829 if(maxlen ==4){ProbRes[,c(2,3,4,5)]<-ProbRes[,c(2,3,4,5)]+

AllPos/4}830 }831 if(max(PntTeam)==3){ProbRes[,c(2,3,4,5)]<-ProbRes[,c(2,3,4,5)]+

AllPos/4}832 }833 }834 }835 }836 }837 }838 list("GroupMatchRes"=MatchProb ,"GroupProbabilities"=ProbRes ,"839 ExpectedPoints"=ExpPoints)}840841 #### After Group stage we have the post -Group stage ###842843 ###POST GROUP STAGE844845 PGStage <-function(distr2="BT",distr="BTNODRAW",q,sigm ,ListOfTeams ,POOL1 ,POOL2

,modelno){846847 ##POULE C FOR 5-8 ###

67

848 plc5to8 <-data.frame("Team"=c(PouleA19 ,PouleB19),"5th Prob"=rep(0,8),"6thProb"=rep(0,8), "7th Prob"=rep(0,8), "8th Prob"=rep(0,8))

849850 PossCA <-combn(PouleA19 ,2)851 PossCB <-combn(PouleB19 ,2)852 ProbCA <-c(rep(0,6))853 ProbCB <-c(rep(0,6))854 CA1 <-CA2 <-CB1 <-CB2 <-0855 for (i in 1:6) {856 CA1 <-match(PossCA[1,i],PouleA19)857 CA2 <-match(PossCA[2,i],PouleA19)858 CB1 <-match(PossCB[1,i],PouleB19)859 CB2 <-match(PossCB[2,i],PouleB19)860 ProbCA[i]<-POOL1$GroupProbabilities[CA1 ,4]*POOL1$GroupProbabilities[CA2

,5]+ POOL1$GroupProbabilities[CA1 ,5]*POOL1$GroupProbabilities[CA2 ,4]861 ProbCB[i]<-POOL2$GroupProbabilities[CB1 ,4]*POOL2$GroupProbabilities[CB2

,5]+ POOL2$GroupProbabilities[CB1 ,5]*POOL2$GroupProbabilities[CB2 ,4]862 }863 ProbCA <-ProbCA/sum(ProbCA)864 ProbCB <-ProbCB/sum(ProbCB)865866 PossC <-matrix(0,ncol=36,nrow =4)867 ProbC <-c(rep (0 ,36))868 k<-1869 for(i in 1:6){870 for (j in 1:6){871 PossC[,k]<-c(PossCA[,i],PossCB[,j])872 ProbC[k]<-ProbCA[i]*ProbCB[j]873 k<-k+1874 }875 }876 Outcome <-data.frame("group"=c(0,4), "P 5", "P 6", "P 7", "P 8" )877 for (i in 1:36) {878 Result <-GroupResults(PossC[,i],distr2 ,q,sigm ,ListOfTeams ,modelno)879 Outcome <-Result$GroupProbabilities880 for (j in 1:4) {881 plc <-match(Outcome[j,1], plc5to8 [,1])882 plc5to8[plc ,2:5] <-plc5to8[plc ,2:5]+( Outcome[j ,2:5]*ProbC[i])883 }884 }885886 ## SEMIFINALS ##887888 Semi1 <-data.frame("Team"=c(PouleA19 ,PouleB19),"Win Prob"=rep(0,8),"Lose

Prob"=rep(0,8))889 T1<-0890 T2<-0891 M<-0892 for (i in 1:4) {893 for (j in 1:4) {894 M<-Outcomematch(PouleA19[i],PouleB19[j],distr ,q,sigm ,ListOfTeams ,MODEL ,

modelno)895 T1<-match(PouleA19[i],Semi1 [,1])896 T2<-match(PouleB19[j],Semi1 [,1])897 Semi1[T1 ,2] <-Semi1[T1 ,2]+M$Win1*POOL1$GroupProbabilities[i,2]*POOL2$

GroupProbabilities [j,3]898 Semi1[T2 ,2] <-Semi1[T2 ,2]+M$Loss1*POOL1$GroupProbabilities[i,2]*POOL2$

GroupProbabilities [j,3]899 Semi1[T1 ,3] <-Semi1[T1 ,3]+M$Loss1*POOL1$GroupProbabilities[i,2]*POOL2$

GroupProbabilities [j,3]900 Semi1[T2 ,3] <-Semi1[T2 ,3]+M$Win1*POOL1$GroupProbabilities[i,2]*POOL2$

GroupProbabilities [j,3]901 }902 }903904905 Semi2 <-data.frame("Team"=c(PouleA19 ,PouleB19),"Win Prob"=rep(0,8),"Lose

Prob"=rep(0,8))

68

906 T1<-0907 T2<-0908 M<-0909 for (i in 1:4) {910 for (j in 1:4) {911 M<-Outcomematch(PouleA19[i],PouleB19[j],distr ,q,sigm ,ListOfTeams ,MODEL ,

modelno)912 T1<-match(PouleA19[i],Semi2 [,1])913 T2<-match(PouleB19[j],Semi2 [,1])914 Semi2[T1 ,2] <-Semi2[T1 ,2]+M$Win1*POOL1$GroupProbabilities[i,3]*POOL2$

GroupProbabilities [j,2]915 Semi2[T2 ,2] <-Semi2[T2 ,2]+M$Loss1*POOL1$GroupProbabilities[i,3]*POOL2$

GroupProbabilities [j,2]916 Semi2[T1 ,3] <-Semi2[T1 ,3]+M$Loss1*POOL1$GroupProbabilities[i,3]*POOL2$

GroupProbabilities [j,2]917 Semi2[T2 ,3] <-Semi2[T2 ,3]+M$Win1*POOL1$GroupProbabilities[i,3]*POOL2$

GroupProbabilities [j,2]918 }919 }920 ### 3rd/4th PLACE ##921 LoserFinal <-data.frame("Team"=c(PouleA19 ,PouleB19), "3rd place"=rep(0,8), "

4th place"=rep(0,8))922 T1<-0923 T2<-0924 M<-0925 for (i in 1:8){926 for (j in 1:8){927 if (i != j){928 M<-Outcomematch(Semi1[i,1],Semi2[j,1],distr ,q,sigm ,ListOfTeams ,MODEL ,

modelno)929 T1<-match(Semi1[i,1], LoserFinal [,1])930 T2<-match(Semi2[j,1], LoserFinal [,1])931 LoserFinal[T1 ,2] <-LoserFinal[T1 ,2]+M$Win1*Semi1[i,3]*Semi2[j,3]932 LoserFinal[T2 ,2] <-LoserFinal[T2 ,2]+M$Loss1*Semi1[i,3]*Semi2[j,3]933934 LoserFinal[T1 ,3] <-LoserFinal[T1 ,3]+M$Loss1*Semi1[i,3]*Semi2[j,3]935 LoserFinal[T2 ,3] <-LoserFinal[T2 ,3]+M$Win1*Semi1[i,3]*Semi2[j,3]936937 }938 }939 }940 LoserFinal [,2]<-LoserFinal [,2]/sum(LoserFinal [,2])941 LoserFinal [,3]<-LoserFinal [,3]/sum(LoserFinal [,3])942943 ## FINAL ##944 Final <-data.frame("Team"=c(PouleA19 ,PouleB19), "1st place"=rep(0,8), "2nd

place"=rep(0,8))945 T1<-0946 T2<-0947 M<-0948 for (i in 1:8){949 for (j in 1:8){950 if (i != j){951 M<-Outcomematch(Semi1[i,1],Semi2[j,1],distr ,q,sigm ,ListOfTeams ,MODEL ,

modelno )952 T1<-match(Semi1[i,1],Final [,1])953 T2<-match(Semi2[j,1],Final [,1])954 Final[T1 ,2] <-Final[T1 ,2]+M$Win1*Semi1[i,2]*Semi2[j,2]955 Final[T2 ,2] <-Final[T2 ,2]+M$Loss1*Semi1[i,2]*Semi2[j,2]956 Final[T1 ,3] <-Final[T1 ,3]+M$Loss1*Semi1[i,2]*Semi2[j,2]957 Final[T2 ,3] <-Final[T2 ,3]+M$Win1*Semi1[i,2]*Semi2[j,2]958 }959 }960 }961 Final[,2]<-Final [,2]/sum(Final [,2])962 Final[,3]<-Final [,3]/sum(Final [,3])963

69

964 FinalscoreTable <-data.frame("Team"=c(PouleA19 ,PouleB19),"1st place"=rep(0,8), "2nd place"=rep(0,8),"3rd place"=rep(0,8), "4th place"=rep(0,8),

965 "5th place"=rep(0,8),"6th Prob"=rep(0,8), "7thProb"=rep(0,8), "8th Prob"=rep(0,8))

966 FinalscoreTable [ ,2:3] <-Final [ ,2:3]967 FinalscoreTable [ ,4:5] <-LoserFinal [ ,2:3]968 FinalscoreTable [ ,6:9] <-plc5to8 [,2:5]969970 FinalscoreTable1 <-data.frame("Team"=c(PouleA19 ,PouleB19 ,"Total"),"1st place

"=rep(0,9), "2nd place"=rep(0,9),"3rd place"=rep(0,9), "4th place"=rep(0,9),

971 "5th place"=rep(0,9),"6th Prob"=rep(0,9), "7thProb"=rep(0,9), "8th Prob"=rep(0,9))

972 FinalscoreTable1 [1:8 ,2:9] <-FinalscoreTable [1:8 ,2:9]973974 FinalscoreTable1 <-FinalscoreTable1[order(FinalscoreTable1$X1st.place ,

decreasing = TRUE),]975976977 for (i in 1:8) {978 FinalscoreTable1 [9,i+1] <-sum(FinalscoreTable1 [1:8,i+1])979 }980 list("A"=ProbCA , "B"=ProbCB , "Possibilities"=PossC ,"Probabilities"=ProbC , "

Result"=plc5to8 ,"SF1"=Semi1 , "SF2"=Semi2 ,"LF"=LoserFinal ,"FF"=Final ,"Final"=FinalscoreTable1)

981982 }

70