Roland C. Deutsch. April 14, 2010

Transcription

1 The FIFA World The World Draw Modeling, Analyzing and Predicting the 2010 FIFA World World Roland C. Deutsch April 14, 2010

2 Contents The FIFA World The World Draw World 1 2 World 3 4

3 Facts about the World The FIFA World The World Draw World The world s largest (single sports) event World-wide impact is only rivaled by the Olympic games 204 federations entered the qualification rounds starting in 2007 By November 2009, the 32 finalists were determined Final schedule is determined by the World Draw (Dec 5, 2009) The World Draw is watched by approximately as many viewers worldwide as the Super Bowl

4 The Set-Up The FIFA World The World Draw World Group the 32 finalists were divided into 8 groups à 4 teams Round-robin tournament within each group Win = 3 points, Draw = 1 point, Loss = 0 points The two teams with the most points from each group advance to the knockout stage (various tie-breakers) Knockout Four rounds: Round of 16, Quarter-Final, Semi-Final, Final The advancing teams are arranged in a pre-determined single elimination bracket In the Round of 16, group winners are paired up with runner-ups In case of a draw, first two 15-minute overtime periods, then penalty shoot-out if needed.

5 Qualified Countries The FIFA World The World Draw World Figure: Qualified nations (in green)

6 The World Draw The FIFA World The World Draw World The 32 teams were arranged in 4 pots. For each group a team was selected from each pot Not more than one team from any continent per group except for Europe

7 The Result of the Draw The FIFA World The World Draw World Pot Group A Group B Group C Group D 1 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 H 1 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. Oct 09 FIFA rank in parentheses.

8 The FIFA World Assess the impact of the draw on the 32 teams. Who got lucky? Who did not? The World Draw World Expected performance for each team. Comparing expected performance pre- and post-draw. Predicting the outcome of the World

9 The FIFA World The World Draw World To determine the relative strength of each team 4 rating systems 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 outright win collected from 6 online bookmakers (Bookie Rating) All ratings were collected on March 4, To assess the strength of teams in a penalty shoot-out, a penalty-kick rating was computed as a weighted proportion of wins from a default 1-1 record and the historical record.

10 General Idea The FIFA World The World Draw World Relating the ratings of two teams, A and B, to win-draw-loss probabilities for team A. Standardize the rating to mean 0 and variance 1 Compute the match rating as m A,B = r A r B. Model should be symmetric and for teams of equal strength, the probabilities for a win and a loss should be equal. Use single game odds from bookmakers from all 48 first round games. Match them up with the corresponding match ratings from the Bookie Rating. To ensure symmetry, the bookmaker s favorite was always listed first. Convert decimal odds into probabilities.

11 Converting Single-Game Odds For the opening game -Mexico: The FIFA World The World Draw World Win RSA Draw Win MEX Win MEX Draw Win RSA 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 the probabilities add up to 1). With this Win MEX Draw Win RSA The match rating is given by m MEX,RSA = ( ) ( ) =

12 Data The FIFA World The World Draw World Probability Win Draw Loss Match Rating

13 The Model The FIFA World The World Draw World Use a logistic regression model to find the best fitting curve for the probability of a win of the stronger team: π W (m A,B ) = exp(β 0 + β 1 m A,B ) 1 + exp(β 0 + β 1 m A,B ). The probability of a loss of team A vs. team B is then given by π L (m A,B ) = π W ( m A,B ) = exp(β 0 β 1 m A,B ) 1 + exp(β 0 β 1 m A,B ). Obviously, π D (m A,B ) = 1 ( π W (m A,B ) + π L (m A,B ) ). For the collected data, ˆβ 0 = and ˆβ 1 =

14 Fitted Model The FIFA World The World Draw World Probability Win Draw Loss Match Rating

15 Simulation Run 1 The FIFA World The World Draw World The model was used to simulate any match for all four of the standardized ratings The World tournament was simulated times for all four ratings. Home-field advantage (+0.7) to. 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 simulating overtime and penalty-kicks. For every simulation run, each team s final position and average opponent ratings were saved.

16 Simulation Run 2 The FIFA World The World Draw World The draw fully determines the World schedule. To judge the impact of the actual draw, alternate draws were generated. Same pots as the actual draw. Eliminates the effect of the actual draw. For each alternate draws, the World tournament was then simulated times for all four ratings. For each run each team s final position and average opponent ratings were saved.

17 The Scenario The FIFA World The World Draw World Figure: Most likely tournament based on all simulations

18 Strength of Schedule The FIFA World The World Draw World Figure: Actual strength of schedule rating

19 Impact of Draw The FIFA World The World Draw World Figure: Difference in actual strength-of-schedule rating and expected pre-draw strength-of-schedule rating

20 Group A FIFA Rating Elo Rating The FIFA World The World Draw RSA MEX URU FRA RSA MEX URU FRA World Group A Group A SPI Rating Bookie Rating RSA MEX URU FRA RSA MEX URU FRA Group A Group A

21 Group B FIFA Rating Elo Rating The FIFA World The World Draw ARG KOR NGA GRE ARG KOR NGA GRE World Group B Group B SPI Rating Bookie Rating ARG KOR NGA GRE ARG KOR NGA GRE Group B Group B

22 Group C FIFA Rating Elo Rating The FIFA World The World Draw ENG USA ALG SVN ENG USA ALG SVN World Group C Group C SPI Rating Bookie Rating ENG USA ALG SVN ENG USA ALG SVN Group C Group C

23 Group D FIFA Rating Elo Rating The FIFA World The World Draw GER AUS GHA SRB GER AUS GHA SRB World Group D Group D SPI Rating Bookie Rating GER AUS GHA SRB GER AUS GHA SRB Group D Group D

24 Group E FIFA Rating Elo Rating The FIFA World The World Draw NED JAP CMR DAN NED JAP CMR DAN World Group E Group E SPI Rating Bookie Rating NED JAP CMR DAN NED JAP CMR DAN Group E Group E

25 Group F FIFA Rating Elo Rating The FIFA World The World Draw ITA NZL PAR SVK ITA NZL PAR SVK World Group F Group F SPI Rating Bookie Rating ITA NZL PAR SVK ITA NZL PAR SVK Group F Group F

26 Group G FIFA Rating Elo Rating The FIFA World The World Draw BRA PRK CIV POR BRA PRK CIV POR World Group G Group G SPI Rating Bookie Rating BRA PRK CIV POR BRA PRK CIV POR Group G Group G

27 Group H FIFA Rating Elo Rating The FIFA World The World Draw ESP HON CHI SUI ESP HON CHI SUI World Group H Group H SPI Rating Bookie Rating ESP HON CHI SUI ESP HON CHI SUI Group H Group H

28 Finals The FIFA World The World Draw World FIFA Rating Elo Rating SPI Rating Bookie Rating BRA-ESP BRA-ESP BRA-ESP BRA-ESP ESP-FRA BRA-ITA BRA-POR BRA-ITA BRA-POR BRA-NED BRA-NED ESP-ITA BRA-ITA ESP-NED BRA-CIV ESP-FRA ESP-NED ENG-ESP ESP-NED ESP-NED BRA-NED BRA-POR BRA-ITA ENG-ESP ENG-ESP ESP-MEX ENG-ESP BRA-POR ESP-POR BRA-CHI ARG-NED BRA-CIV ARG-ESP ESP-ITA CHI-ESP ARG-BRA ESP-ITA GER-NED ARG-BRA ENG-ITA Table: Top 10 final match lineups for the four ratings with their simulated probabilities.

29 Winners The FIFA World The World Draw World FIFA Rating Elo Rating SPI Rating Bookie Rating (1) ESP (1) BRA (1) BRA (1) ESP (2) BRA (2) ESP (2) ESP (3) BRA (3) NED (3) NED (5) ARG (5) ITA (7) FRA (4) ENG (4) NED (4) ARG (4) ITA (5) ITA (3) ENG (2) ENG (5) GER (6) GER (7) POR (7) NED (6) POR (7) ARG (10) ITA (8) FRA (9) ARG (8) MEX (6) GER (6) GER (8) ENG (10) FRA (9) URU (9) POR (10) GRE (11) POR (14) CIV (10) CIV Table: Top 10 most likely winners for the four ratings with their simulated probabilities.

30 What Can We Expect Come June? The draw leveled the field more than expected The FIFA World The World Draw World Brazil and Spain have unfavorable draws Chances of France and Italy were boosted Very open World, possibly leading to a large number of upsets Brazil and Spain remain firm favorites Brazil-Spain final is most likely