Looking Forward to South Africa Modeling, Analyzing and ...€¦ · South Africa R. C. Deutsch Introduction The FIFA World Cup The World Cup Draw Purpose of This Study Modeling the

LookingForward to

South Africa

R. C. Deutsch

IntroductionThe FIFA World Cup

The World Cup Draw

Purpose of ThisStudy

Modeling theWorld CupAssessing theStrength of theTeams

Modeling theOutcome of a Game

Simulating the WorldCup

ResultsMost LikelyTournament

Analyzing the Draw

Group-by-GroupAnalysis

Predictions

Conclusions

Looking Forward to South AfricaModeling, Analyzing and Predicting the 2010 FIFA World Cup

Roland C. Deutsch

April 14, 2010

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Contents

1 Introduction

2 Modeling the World CupAssessing the Strength of the TeamsModeling the Outcome of a GameSimulating the World Cup

3 ResultsMost Likely TournamentAnalyzing the DrawGroup-by-Group AnalysisPredictions

4 Conclusions

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Facts about the World Cup

The world’s largest (single sports) event

World-wide impact is only rivaled by the Olympic games

204 federations entered the qualification roundsstarting in 2007

By November 2009, the 32 finalists were determined

Final schedule is determined by the World Cup Draw(Dec 5, 2009)

The World Cup Draw is watched by approximately asmany viewers worldwide as the Super Bowl

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

The Tournament Set-Up

Group Stagethe 32 finalists were divided into 8 groups à 4 teamsRound-robin tournament within each groupWin = 3 points, Draw = 1 point, Loss = 0 pointsThe two teams with the most points from each groupadvance to the knockout stage (various tie-breakers)

Knockout StageFour rounds:Round of 16, Quarter-Final, Semi-Final, FinalThe advancing teams are arranged in a pre-determinedsingle elimination bracketIn the Round of 16, group winners are paired up withrunner-upsIn case of a draw, first two 15-minute overtime periods,then penalty shoot-out if needed.

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Qualified Countries

Figure: Qualified nations (in green)

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R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

The World Cup Draw

The 32 teams were arranged in 4 pots.For each group a team was selected from each potNot more than one team from any continent per groupexcept for Europe

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R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

The Result of the Draw

Pot Group A Group B Group C Group D1 RSA (85) ARG (6) ENG (7) GER (5)2 MEX (18) KOR (48) USA (11) AUS (24)3 URU (25) NGA (32) ALG (29) GHA (38)4 FRA (9) GRE (16) SVN (49) SRB (20)

Pot Group E Group F Group G Group H1 NED (3) ITA (4) BRA (1) ESP (2)2 JAP (40) NZL (83) PRK (91) HON (35)3 CMR (14) PAR (21) CIV (19) CHI (17)4 DAN (27) SVK (33) POR (10) SUI (13)

Table: The eight first round groups of the 2010 FIFA World Cup.Oct ’09 FIFA rank in parentheses.

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Purpose of This Study

Assess the impact of the draw on the 32 teams.Who got lucky?Who did not?

Expected performance for each team.

Comparing expected performance pre- and post-draw.

Predicting the outcome of the World Cup

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Assessing the Strength of the Teams

To determine the relative strength of each team 4 ratingsystems were used

FIFA/Coca-Cola World Ranking (FIFA Rating)World Football Elo Rating (Elo Rating)ESPN’s Soccer Power Index (SPI Rating)A rating derived from the decimal odds for an outrightwin collected from 6 online bookmakers (BookieRating)

All ratings were collected on March 4, 2010.

To assess the strength of teams in a penalty shoot-out, apenalty-kick rating was computed as a weighted proportionof wins from a default 1-1 record and the historical record.

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

General Idea

Relating the ratings of two teams, A and B, towin-draw-loss probabilities for team A.

Standardize the rating to mean 0 and variance 1Compute the match rating as mA,B = rA − rB .

Model should be symmetric and . . .. . . for teams of equal strength, the probabilities for awin and a loss should be equal.

Use single game odds from bookmakers from all 48 firstround games.Match them up with the corresponding match ratingsfrom the Bookie Rating.To ensure symmetry, the bookmaker’s favorite wasalways listed first.Convert decimal odds into probabilities.

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South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Converting Single-Game Odds

For the opening game South Africa-Mexico:

Win RSA Draw Win MEX Win MEX Draw Win RSA2.91 3.15 2.33 ⇒ 2.33 3.15 2.91

Convert the decimal odds, d, into probabilities, p, using

p = 1− (d− 1)ψ

1 + (d− 1)ψ.

ψ represents the bookmaker’s profit margin (chosen such that theprobabilities add up to 1). With this

Win MEX Draw Win RSA0.3962 0.2892 0.3146

The match rating is given bymMEX,RSA = (−0.1752)− (−0.3555) = 0.1803.

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R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Data

0 1 2 3

0.0

0.2

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0.6

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1.0

Match Rating

Pro

babi

lity

WinDrawLoss

Figure: The averaged win-draw-lossprobabilities for the better of the two teamsobtained from the decimal odds of six onlinebookmakers. Circles are determined byequation 2.

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South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

The Model

Use a logistic regression model to find the best fitting curvefor the probability of a win of the stronger team:

πW (mA,B) =exp(β0 + β1mA,B)

1 + exp(β0 + β1mA,B).

The probability of a loss of team A vs. team B is then givenby

πL(mA,B) = πW (−mA,B) =exp(β0 − β1mA,B)

1 + exp(β0 − β1mA,B).

Obviously, πD(mA,B) = 1−(πW (mA,B) + πL(mA,B)

).

For the collected data, β̂0 = −0.6111 and β̂1 = 0.6262.

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South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Fitted Model

0 1 2 3

0.0

0.2

0.4

0.6

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1.0

Match Rating

Pro

babi

lity

WinDrawLoss

Figure: The averaged win-draw-lossprobabilities for the better of the two teamsobtained from the decimal odds of six onlinebookmakers. Circles are determined byequation 2. Also displayed are the fitted curvesfor win (black), draw (red) and loss (green) asobtained from equations 4 and 4.

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South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Simulation Run 1

The model was used to simulate any match for all fourof the standardized ratingsThe World Cup tournament was simulated 10 000times for all four ratings.‘Home-field advantage’ (+0.7) to South Africa.‘Home-continent advantage’ (+0.35) to African teams.No such adjustment for Bookie rating.Ties at the group stage were resolved by random draw.Tied knock-out games were resolved by simulatingovertime and penalty-kicks.For every simulation run, each team’s final position andaverage opponent ratings were saved.

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R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Simulation Run 2

The draw fully determines the World Cup schedule.

To judge the impact of the actual draw, 1 000 alternatedraws were generated.

Same pots as the actual draw.Eliminates the effect of the actual draw.

For each alternate draws, the World Cup tournamentwas then simulated 1 000 times for all four ratings.

For each run each team’s final position and averageopponent ratings were saved.

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

The Most Likely Scenario

Figure: Most likely tournament based on all simulations

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Strength of Schedule

Figure: Actual strength of schedule rating

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South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Impact of Draw

Figure: Difference in actual strength-of-schedule ratingand expected pre-draw strength-of-schedule rating

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Group A

Stage

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FIFA Rating

Group A

RSAMEXURUFRA

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Elo Rating

Group A

RSAMEXURUFRA

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SPI Rating

Group A

RSAMEXURUFRA

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Bookie Rating

Group A

RSAMEXURUFRA

Figure: Simulated Probabilities Group A

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Group B

Stage

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Group B

ARGKORNGAGRE

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Elo Rating

Group B

ARGKORNGAGRE

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Group B

ARGKORNGAGRE

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Group B

ARGKORNGAGRE

Figure: Simulated Probabilities Group B

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Group C

Stage

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Group C

ENGUSAALGSVN

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Elo Rating

Group C

ENGUSAALGSVN

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Group C

ENGUSAALGSVN

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Group C

ENGUSAALGSVN

Figure: Simulated Probabilities Group C

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Group D

Stage

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Group D

GERAUSGHASRB

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Group D

GERAUSGHASRB

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Group D

GERAUSGHASRB

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Group D

GERAUSGHASRB

Figure: Simulated Probabilities Group D

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Group E

Stage

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Group E

NEDJAPCMRDAN

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Group E

NEDJAPCMRDAN

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Group E

NEDJAPCMRDAN

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Group E

NEDJAPCMRDAN

Figure: Simulated Probabilities Group E

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Group F

Stage

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Group F

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Group F

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ITANZLPARSVK

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Group F

ITANZLPARSVK

Figure: Simulated Probabilities Group F

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Group G

Stage

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Group G

BRAPRKCIVPOR

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Group G

BRAPRKCIVPOR

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Group G

BRAPRKCIVPOR

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Group G

BRAPRKCIVPOR

Figure: Simulated Probabilities Group G

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Group H

Stage

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Group H

ESPHONCHISUI

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Group H

ESPHONCHISUI

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Group H

ESPHONCHISUI

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Group H

ESPHONCHISUI

Figure: Simulated Probabilities Group H

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Most Likely Finals

FIFA Rating Elo Rating SPI Rating Bookie Rating

BRA-ESP 0.082 BRA-ESP 0.081 BRA-ESP 0.039 BRA-ESP 0.054ESP-FRA 0.028 BRA-ITA 0.031 BRA-POR 0.019 BRA-ITA 0.028BRA-POR 0.024 BRA-NED 0.029 BRA-NED 0.019 ESP-ITA 0.020BRA-ITA 0.022 ESP-NED 0.023 BRA-CIV 0.017 ESP-FRA 0.019ESP-NED 0.022 ENG-ESP 0.023 ESP-NED 0.016 ESP-NED 0.019BRA-NED 0.017 BRA-POR 0.021 BRA-ITA 0.016 ENG-ESP 0.019ENG-ESP 0.016 ESP-MEX 0.015 ENG-ESP 0.015 BRA-POR 0.018ESP-POR 0.015 BRA-CHI 0.014 ARG-NED 0.013 BRA-CIV 0.017ARG-ESP 0.013 ESP-ITA 0.014 CHI-ESP 0.013 ARG-BRA 0.017ESP-ITA 0.012 GER-NED 0.013 ARG-BRA 0.012 ENG-ITA 0.016

Table: Top 10 final match lineups for the four ratings with theirsimulated probabilities.

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

Most Likely Winners

FIFA Rating Elo Rating SPI Rating Bookie Rating

(1) ESP 0.227 (1) BRA 0.224 (1) BRA 0.150 (1) ESP 0.168(2) BRA 0.172 (2) ESP 0.167 (2) ESP 0.128 (3) BRA 0.146(3) NED 0.080 (3) NED 0.103 (5) ARG 0.078 (5) ITA 0.091(7) FRA 0.066 (4) ENG 0.069 (4) NED 0.077 (4) ARG 0.089(4) ITA 0.059 (5) ITA 0.056 (3) ENG 0.076 (2) ENG 0.082(5) GER 0.055 (6) GER 0.048 (7) POR 0.048 (7) NED 0.072(6) POR 0.046 (7) ARG 0.046 (10) ITA 0.044 (8) FRA 0.068(9) ARG 0.036 (8) MEX 0.040 (6) GER 0.043 (6) GER 0.060(8) ENG 0.033 (10) FRA 0.032 (9) URU 0.043 (9) POR 0.042(10) GRE 0.033 (11) POR 0.028 (14) CIV 0.040 (10) CIV 0.037

Table: Top 10 most likely winners for the four ratings with theirsimulated probabilities.

LookingForward to

South Africa

R. C. Deutsch


The World Cup Draw






Analyzing the Draw


Predictions

Conclusions

What Can We Expect Come June?

The draw leveled the field more than expected

Brazil and Spain have unfavorable draws

Chances of France and Italy were boosted

Very open World Cup, possibly leading to a largenumber of upsets

Brazil and Spain remain firm favorites

Brazil-Spain final is most likely

Documents

Looking Forward to South Africa Modeling, Analyzing and ...€¦ · South Africa R. C. Deutsch Introduction The FIFA World Cup The World Cup Draw Purpose of This Study Modeling the