FIFA Foe Fun!
Tim Chartier! Mark Kozek! Davidson College Whittier College
Michael Mossinghoff! Davidson College • Group E: Switzerland, Ecuador, France, Honduras.
• “Switzerland is the top seed, based on FIFA’s flawed rankings, but might only be the third-best team.” FIFA Rankings Oct. 2013
• Basis for World Cup groupings.
1 Spain 1513 13 USA 1040 2 Germany 1311 14 Portugal 1036 3 Argentina 1266 15 Greece 983 4 Colombia 1178 16 Bosnia-Herz. 925 5 Belgium 1175 17 Côte d’Ivoire 917 6 Uruguay 1164 18 Croatia 901 7 Switzerland 1138 19 Russia 874 8 Netherlands 1136 20 Ukraine 871 8 Italy 1136 21 France 870 10 England 1080 22 Ecuador 862 11 Brazil 1078 23 Ghana 860 12 Chile 1051 24 Mexico 854 Nov. 2013
• Portugal beats #25 Sweden twice, jumps from #14 to #5 in November ranking.
• Belgium loses to #4 Columbia and #44 Japan, drops from #5 to #11.
• FIFA rankings are volatile!
• Had groupings been based on November ratings, Portugal would have had better draw.
• Similar: Switzerland and Italy. FIFA’s Method
• FIFA/Coca-Cola World Ranking.
• A team is awarded points for winning matches.
• A team’s ranking depends on its average points obtained per year, over four years.
• Points are based on opponent, type of match, and age of match.
• Large variation: one win may be worth from 85 to 2400 points, even without aging effect. FIFA Ranking
• Fix a team X.
• Let yk = time period starting k years ago and ending k ⎼ 1 years ago.
• Let gk = number of games played by X during
yk, and let ck = min(1, gk/5).
• Let ak = ck・(average number of points earned
per match over yk).
• Total points for X = a1 + .5a2 + .3a3 + .2a4. Points per Match
• Points = M・I・T・C.
• M (match outcome):
• 3 for normal victory,
• 2 for shootout victory,
• 1 for shootout loss or tie,
• 0 for normal loss. Points per Match
• Points = M・I・T・C.
• I (importance):
• 1 for Friendly,
• 2.5 for World Cup or Confed.-level Qualifier,
• 3 for Confed. Final or Confederations Cup,
• 4 for World Cup match. Points per Match
• Points = M・I・T・C.
• T (opponent strength):
• Usually: 200 ⎼ opponent ranking.
• Exception 1: Min value for T is 50.
• Exception 2: Top is worth 200 (not 199). Points per Match
• Points = M・I・T・C.
• C (Confederation strength): C = average value of the confederation weight for the two teams.
• UEFA & CONMEBOL: w = 1.
• CONCACAF: w = 0.88.
• AFC & CAF: w = 0.86.
• OFC: w = 0.85. Confederation Weight • Compute winning average (1 per win, .5 per draw) in inter-confederation matches in each of last three World Cups.
• Compute mean m of these three values.
• E.g., UEFA: .51, .76, .59 produces m = .62.
• Set m0 = max m over all confederations.
1/4 • w = max(.85, (m/m0) ).
• CONCACAF: w = max(.85, (.37/.63)1/4) = .88.
• OFC: w = max(.85, (.17/.63)1/4) = .85. Oddities
• Sharp drops in age weights.
• M: Winning penalty shootouts: worth 2?
• I: Big jump from Friendly weight (1) to WC Qualifier (2.5). Host nation plays no WCQ’s!
• T: No discernment among bottom 60 teams. No team has T = 199.
• C: fudge factors. New Rankings
• Several systems: Colley, Massey, and Elo.
• Similar to FIFA in some respects:
• Use all matches for past four (or more) years.
• Weight match based on game type, age.
• Unlike FIFA:
• More conservative weights on match type.
• Smoothed age weights. Colley Method
• Wesley Colley (2001), astrophysicist.
• One of the BCS algorithms for college football.
• Main idea: change winning percentage to account for strength of schedule.
• N teams; team i has unknown rating ri.
• Mandate that average rating is always 1/2.
• At start of season, everyone gets 1 in win column and 1 in loss column, so winning percentage is 50%. Colley Method • Assume no ties for now.
• Suppose team i has Wi wins, Li losses, and has
played Gi games.
• Let Oi denote the set of opponents of team i.
• Over time, the average rating of the opponents of team i should be near 1/2:
1 1 rj . Gi ⇡ 2 j O X2 i Colley Method
Wi +1 So: ri ⇡ Gi +2 W L G 1+ i i + i = 2 2 Gi +2
Wi Li 1+ 2 + j O rj 2 i . ⇡ Gi +2P This produces the linear system: W L (G + 2)r r =1+ i i . i i j 2 j O X2 i We write Cr = b. Colley Method
• C is symmetric, and positive definite.
• The system always has a unique solution.
• The mean rating is 1/2.
• Can weigh games by importance, age, …
• Ties: count as half a win and half a loss.
• Can weigh PSO win anywhere between tie and win. Type Weight
• Friendly = 1,
• Continental qualifier = 1.25,
• Continental tourn. or Confed. Cup = 1.5,
• World Cup qualifier = 2,
• World Cup match = 2.25. Age Weight 1.0 1
0.8
0.6 .50 FIFA 0.4 .30 .20 0.2 Smoothed 0 .008 1 .054 2 .283 3 .717 4 .946 5 • Total area (nearly) preserved. • Keep five years now for smoother aging. Additional Adjustments
June 9, 2013: World Cup Qualifier.
0-3
• Ignore disqualifications. Additional Adjustments
June 28, 2011: World Cup Qualifier.
• Ignore disqualifications. Weighted Colley
1 Brazil 1.058 ⬆️ 2 13 Uruguay 0.849 ⬇️ 6 2 Spain 1.008 ⬇️ 1 14 Switzerland 0.842 ⬇️ 8 3 Argentina 0.975 ⬆️ 2 15 Côte d’Ivoire 0.823 ⬆️ 8 4 Germany 0.951 ⬇️ 2 16 Russia 0.823 ⬆️ 3 5 Colombia 0.934 ⬆️ 3 17 Italy 0.814 ⬇️ 8 6 Belgium 0.929 ⬆️ 5 18 Ecuador 0.813 ⬆️ 8 7 Chile 0.883 ⬆️ 7 19 Ukraine 0.810 ⬇️ 3 8 Portugal 0.876 ⬇️ 4 20 Greece 0.810 ⬇️ 8 9 England 0.872 ⬆️ 1 21 Japan 0.780 ⬆️ 25 10 USA 0.869 ⬆️ 3 22 Croatia 0.776 ⬇️ 4 11 Netherlands 0.859 ⬆️ 4 23 Bosnia-Herz. 0.776 ⬇️ 2 12 France 0.859 ⬆️ 5 24 U.A.E. 0.775 ⬆️ 48
• Last column: Change from current FIFA rank. Colley: Group of Death!
Gp 1 2 3 4 Third Avg Rk Gap A 1 22 25 48 25 24.0 25.0 B 2 7 11 37 11 14.3 19.5 C 5 15 20 21 20 15.3 13.0 D 9 13 17 34 17 18.3 15.0 E 12 14 18 46 18 22.5 16.0 F 3 23 27 29 27 20.5 17.0 G 4 8 10 3 0 10 13 15.5 H 6 16 26 4 1 26 22.3 19.5 Massey Method • Ken Massey (1997), undergraduate student.
• Now consults for the BCS.
• Main idea: a game outcome is a noisy measurement of one team’s superiority over another.
• Measurement: if team i beats team j by p points
then record ri – rj = p.
• Produces inconsistent system.
• Use least squares. Massey Method
• Massey matrix: M = C – 2IN.
• Solve Mr = v, where vi = (total points scored by team i) – (total points scored on team i).
• Problem: M is singular.
• Obvious reason: all equations were for differences
of ratings. N • Alter system: replace one row with ri =0. i=1 X • OK as long as there is a path between any two teams. Adjustments
January 29, 2014: Friendly.
PSO 4-1
• Ignore disqualifications. • Count penalty shoot-outs as weak wins. Adjustments
October 14, 2010: CONCACAF Qualifier
17-0
• Ignore disqualifications. • Count penalty shoot-outs as weak wins. • Massey: set max score differential to 4. Adjustments
July 2 and 9, 2011: World Cup Qualifiers: Only matches for both since 2008!
• Ignore disqualifications. • Count penalty shoot-outs as weak wins. • Massey: set max score differential to 4. • Ensure connectivity. Omisions! Weighted Massey
1 Brazil 3.633 ⬆️ 2 13 Russia 2.304 ⬆️ 6 2 Argentina 3.126 ⬆️ 3 14 Uruguay 2.202 ⬇️ 7 3 Germany 3.031 ⬇️ 1 15 Bosnia-Herz. 2.187 ⬆️ 6 4 Spain 2.940 ⬇️ 3 16 Ukraine 2.123 0 5 Colombia 2.875 ⬆️ 3 17 Serbia 2.038 ⬆️ 13 6 France 2.670 ⬆️ 11 18 Côte d’Ivoire 2.019 ⬆️ 5 7 Chile 2.620 ⬆️ 7 19 USA 1.991 ⬇️ 6 8 Netherlands 2.616 ⬆️ 7 20 Italy 1.984 ⬇️ 11 9 England 2.541 ⬆️ 1 21 Switzerland 1.942 ⬇️ 15 10 Belgium 2.528 ⬆️ 1 22 Mexico 1.866 ⬇️ 2 11 Portugal 2.354 ⬇️ 7 23 Croatia 1.836 ⬇️ 5 12 Ecuador 2.306 ⬆️ 14 24 Sweden 1.712 ⬆️ 8
• Last column: Change from current FIFA rank. Massey: Group of Death!
Gp 1 2 3 4 Third Avg Rk Gap A 1 22 23 45 23 22.8 22.5 B 4 7 8 54 8 18.3 25.5 C 5 18 27 32 27 20.5 18.0 D 9 14 20 44 20 21.8 20.5 E 6 12 21 56 21 23.8 29.5 F 2 15 30 47 30 23.5 30.0 G 3 11 19 2 6 19 14.8 15.5 H 10 13 28 5 7 28 27.0 31.0 Build Your Own!
• FIFAfoefun.davidson.edu.
• Build personalized rating of international FIFA teams using your selected parameters.
• Colley or Massey. • Age weights.
• Number of years to use. • Value of win in penalty shoot-out. • Type weights. • Max score differential • Age weighting method. to use in Massey. Press • Alex Bellos, The Guardian, June 6.
• Wall Street Journal blog, June 10 and 12.
• Galileu, Brazilian science magazine, June 16.
• Visitors from more than 80 countries. ESPN Bracket Predictor
• T. Chartier & co.: submits brackets for NCAA basketball for testing predictive power of rankings.
• ESPN World Cup site: > 1 million entries.
• Some brackets we generate beat more than 90% of submitted brackets. Elo’s Ranking
• Created for ranking in chess.
• Adaptation for soccer.
• Each team has a rating value.
• After each match, some rating points are exchanged between the two teams.
• Number of points exchanged depends on outcome of match, weight of match, and disparity in rating points. • Suppose team i beats team j.
• Add to ri and subtract from rj: K(v ⎼ F(ri ⎼ rj)).
• K = weight of the match.
• v = value of the victory: 0.5 ≤ v ≤ 1.
• F(x) = distribution function for logistic distribution.
1.0
0.8
0.6
0.4
0.2
-1000 -500 500 1000 World Football Elo Ratings • www.eloratings.net
• Base K value: (20, 30, 40, 50, 60) for friendly, minor tourn., WC/cont. qual. or major tourn., WC qual., WC match.
• Magnify K depending on winning margin: 1, 1.5, 1.75, 1.875, … .
• v = 1 for victory (incl. shootouts); 0.5 for tie.
• Pretend home team is rated 100 higher.
• Use all FIFA matches back to 1872! Our Elo Rating
• K = 20 for friendly; magnify by same factors used in earlier systems, e.g., K = 40 for WCQ.
• v = 1 for victory; 1/2 for tie; 2/3 for shootout victory.
• Use prior five years of FIFA matches. eloratings.net Our Elo ratings 1 Brazil 2113 ⬆️ 2 1 Spain 316 0 2 Spain 2086 ⬇️ 1 2 Brazil 307 ⬆️ 1 3 Germany 2046 ⬇️ 1 3 Germany 265 ⬇️ 1 4 Argentina 1989 ⬆️ 1 4 USA 234 ⬆️ 9 5 Netherlands 1959 ⬆️ 10 5 Argentina 217 0 6 England 1914 ⬆️ 4 6 Netherlands 216 ⬆️ 9 7 Portugal 1902 ⬇️ 3 7 Portugal 213 ⬇️ 3 8 Colombia 1897 0 8 England 186 ⬆️ 2 9 Uruguay 1895 ⬇️ 2 9 Côte d’Ivoire 182 ⬆️ 14 10 Chile 1895 ⬆️ 4 10 Chile 174 ⬆️ 4 11 Italy 1879 ⬇️ 2 11 Uruguay 173 ⬆️ 5 12 France 1869 ⬆️ 5 12 France 168 ⬆️ 5 13 USA 1832 0 13 Colombia 167 ⬇️ 5 14 Belgium 1824 ⬇️ 3 14 Nigeria 163 ⬆️ 30 15 Russia 1821 ⬆️ 4 15 Iran 159 ⬆️ 28 16 Mexico 1820 ⬆️ 4 16 Japan 158 ⬆️ 30 17 Switzerland 1820 ⬇️ 11 17 Belgium 157 ⬇️ 6 18 Ukraine 1815 ⬇️ 2 18 Greece 156 ⬇️ 6 19 Ecuador 1813 ⬆️ 7 19 Switzerland 151 ⬇️ 13 20 Greece 1796 ⬇️ 8 20 Egypt 151 ⬆️ 16 Number of Matches
40
30
20
10
20 40 60 80 100 µ = 41.6, = 21.0. Elo Summary
• Elo: seems not well suited to FIFA rankings.
• World Elo: More than a century of accumulated points.
• Ours: most games within a confederation. Local powers (USA, Nigeria, Egypt, Côte- d’Ivoire, Iran) have perhaps inflated rankings. FIFA Colley Massey WER Elo SPI 1 Spain Brazil Brazil Brazil Spain Brazil 2 Germany Spain Argentina Spain Brazil Argentina 3 Argentina Argentina Germany Germany Germany Germany 4 Colombia Germany Spain Argentina USA Colombia 5 Belgium Colombia Colombia Netherlands Argentina France 6 Uruguay Belgium France England Netherlands Netherlands 7 Switzerland Chile Chile Portugal Portugal Spain 8 Netherlands Portugal Netherlands Colombia England Belgium 9 Italy England England Uruguay Côte d’Ivoire Uruguay 10 England USA Belgium Chile Chile England 11 Brazil Netherlands Portugal Italy Uruguay Bosnia-Herz. 12 Chile France Ecuador France France Ecuador 13 USA Uruguay Russia USA Colombia Mexico 14 Portugal Switzerland Uruguay Belgium Nigeria Switzerland 15 Greece Côte d’Ivoire Bosnia-Herz. Russia Iran Portugal 16 Bosnia-Herz. Russia Ukraine Mexico Japan Ghana Thanks!