Roland C. Deutsch. September 28, 2011

Transcription

1 The Analyzing and Reviewing the 2010 FIFA Setup Roland C. Deutsch September 28, 2011

2 The Setup

3 The Setup Spain wins the FIFA for the first time.

4 The tournament is over... The... it is time for a little statistical review: Surprises Upsets Setup The US team s performance

5 The Set-Up The Setup Group Stage 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 Stage 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.

6 Assessing the Strength of the Teams The Setup 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 June 1, 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 as of June 1, 2010.

7 General Idea The Setup 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.

8 Converting Single-Game Odds For the opening game South -Mexico: The Setup 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 = ( ) ( ) =

9 Data The Setup Probability Win Draw Loss Match Rating

10 The Model The Setup 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 =

11 Fitted Model The Setup Probability Win Draw Loss Match Rating

12 Top 10 Most The Setup FIFA Elo ESP-SUI ESP-SUI FRA-RSA FRA-RSA ITA-NZL SVK-ITA SVK-ITA ENG-ALG KOR-GRE ITA-NZL RSA-MEX RSA-MEX PAR-NZL SRB-GHA CIV-POR POR-BRA NZL-SVK ENG-USA JAP-CMR PAR-NZL

13 Top 10 Most The Setup SPI Bookie ENG-ALG ESP-SUI ESP-SUI ITA-NZL ITA-NZL SVK-ITA FRA-RSA ENG-ALG SVK-ITA FRA-RSA PAR-NZL PAR-NZL SRB-GHA FRA-MEX DAN-JAP GER-SRB RSA-MEX ENG-USA AUS-SRB JAP-CMR

14 Simulating the The Setup The model was used to simulate any match for all four of the standardized ratings The tournament was simulated times for all four ratings. Home-field advantage (+0.7) to South. Home-continent advantage (+0.35) to n 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 was saved.

15 Group Stage The Setup Expected Negative Upset Positive Upset Group Stage Performance Group A Group B Group C Group D URU ARG USA GER MEX KOR ENG GHA RSA GRE SVN AUS FRA NGA ALG SRB Group E Group F Group G Group H NED PAR BRA ESP JAP SVK POR CHI DAN NZL CIV SUI CMR ITA PRK HON

16 Knockout Round URU ARG URU ARG KOR USA URU GER MEX GER The GHA GHA NED GER ENG NED ESP PAR Setup NED PAR SVK JAP NED ESP BRA ESP BRA ESP CHI POR

17 Computing Performance P-values The Setup To evaluate each team s performance, we can use Performance P-values: USA FIFA SPI Elo Bookie Win Final Semi Final Quarter Final Round Group Third Group Fourth P Value

18 Computing Performance P-values The Setup To see whether a team was overachieving, we compute P(matching or exceeding actual result) USA FIFA SPI Elo Bookie Win Final Semi Final Quarter Final Round Group Third Group Fourth P Value

19 Computing Performance P-values The Setup To see whether a team was underachieving, we compute P(matching or falling short of actual result) USA FIFA SPI Elo Bookie Win Final Semi Final Quarter Final Round Group Third Group Fourth P Value

20 Overachieving 0.0 Group A Group B Group C Group D The Setup P(Matching or Exceeding Actual Result) RSA ARG ENG GER MEX KOR USA AUS URU NGA ALG GHA FRA GRE SVN SRB Group E Group F Group G Group H NED ITA BRA ESP JAP NZL PRK HON CMR PAR CIV CHI DAN SVK POR SUI

21 Underachieving The Setup P(Matching or Falling Short of Actual Result) Group A Group B Group C Group D RSA ARG ENG GER MEX KOR USA AUS URU NGA ALG GHA FRA GRE SVN SRB Group E Group F Group G Group H NED ITA BRA ESP JAP NZL PRK HON CMR PAR CIV CHI DAN SVK POR SUI

22 Mission Accomplished or Chance Missed? The Setup

23 Mission Accomplished or Chance Missed? Performance USA Performance USA The Simulated Probability Post Group Post Draw Pre Draw QF SF F 1st Simulated Probability Post Group Post Draw Pre Draw QF SF F 1st Stage FIFA Rating Stage Elo Rating Performance USA Performance USA Setup Simulated Probability Post Group Post Draw Pre Draw Simulated Probability Post Group Post Draw Pre Draw QF SF F 1st QF SF F 1st Stage SPI Rating Stage Bookie Rating

24 Mission Accomplished or Chance Missed? The big picture... The Setup URU NED MEX URU ARG JAP RSA URU ARG DAN FRA KOR MEX CMR URU GER ARG USA GER PAR KOR GHA GER SVK GRE GHA NED ENG NZL NGA ITA ESP USA BRA ENG NED ESP PAR POR SVN NED PAR CIV ALG SVK JAP PRK NED ESP GER BRA ESP ESP GHA BRA ESP CHI AUS CHI POR SUI SRB HON

25 Despite being featured in the biggest upset of the tournament, Spain is a worthy winner. The Setup Given that Holland eliminated Brazil, a Holland - Spain final was most likely. Uruguay, Germany, Ghana, Japan, South Korea had the most surprising performances. Italy, France and most n teams disappointed. Team USA did extremely well in the group stage, but missed a big chance for a deep run.