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 e ff ect.
FIFA Ranking • Fix a team X . • Let y k = time period starting k years ago and ending k ⎼ 1 years ago. • Let g k = number of games played by X during y k , and let c k = min(1, g k /5). • Let a k = c k ・ (average number of points earned per match over y k ). • Total points for X = a 1 + .5 a 2 + .3 a 3 + .2 a 4 .
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 m 0 = max m over all confederations. • w = max(.85, ( m / m 0 ) 1/4 ). • 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 r i . • 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 W i wins, L i losses, and has played G i games. • Let O i 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 r j ≈ 1 X 2 . G i j ∈ O i
Colley Method r i ≈ W i + 1 So: G i + 2 = 1 + W i − L i + G i 2 2 G i + 2 1 + W i − L i + P j ∈ O i r j 2 . ≈ G i + 2 This produces the linear system: r j = 1 + W i − L i X ( G i + 2) r i − . 2 j ∈ O i We write C r = 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 1.0 0.8 0.6 .50 FIFA 0.4 .30 .20 0.2 Smoothed 0 1 2 3 4 5 .008 .054 .283 .717 .946 • 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 ⬆️ 2 ⬇️ 6 1 Brazil 1.058 13 Uruguay 0.849 ⬇️ 1 ⬇️ 8 2 Spain 1.008 14 Switzerland 0.842 ⬆️ 2 ⬆️ 8 3 Argentina 0.975 15 Côte d’Ivoire 0.823 ⬇️ 2 ⬆️ 3 4 Germany 0.951 16 Russia 0.823 ⬆️ 3 ⬇️ 8 5 Colombia 0.934 17 Italy 0.814 ⬆️ 5 ⬆️ 8 6 Belgium 0.929 18 Ecuador 0.813 ⬆️ 7 ⬇️ 3 7 Chile 0.883 19 Ukraine 0.810 ⬇️ 4 ⬇️ 8 8 Portugal 0.876 20 Greece 0.810 ⬆️ 1 ⬆️ 25 9 England 0.872 21 Japan 0.780 ⬆️ 3 ⬇️ 4 10 USA 0.869 22 Croatia 0.776 ⬆️ 4 ⬇️ 2 11 Netherlands 0.859 23 Bosnia-Herz. 0.776 ⬆️ 5 ⬆️ 48 12 France 0.859 24 U.A.E. 0.775 • Last column: Change from current FIFA rank.
Colley: Group of Death! 1 3 Gp 2 4 Third Avg Rk Gap 22 48 1 25 A 25 24.0 25.0 2 7 11 37 B 11 14.3 19.5 5 15 20 21 C 20 15.3 13.0 9 13 17 34 D 17 18.3 15.0 18 12 14 46 E 18 22.5 16.0 29 3 23 27 F 27 20.5 17.0 8 10 3 0 4 G 10 13 15.5 6 16 26 4 1 H 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 r i – r j = p . • Produces inconsistent system. • Use least squares.
Massey Method • Massey matrix: M = C – 2 I N . • Solve M r = v , where v i = (total points scored by team i ) – (total points scored on team i ). • Problem: M is singular. • Obvious reason: all equations were for di ff erences of ratings. N X r i = 0 . • Alter system: replace one row with i =1 • 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 di ff erential 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 di ff erential to 4. • Ensure connectivity.
Omisions!
Weighted Massey ⬆️ 2 ⬆️ 6 1 Brazil 3.633 13 Russia 2.304 ⬆️ 3 ⬇️ 7 2 Argentina 3.126 14 Uruguay 2.202 ⬇️ 1 ⬆️ 6 3 Germany 3.031 15 Bosnia-Herz. 2.187 ⬇️ 3 0 4 Spain 2.940 16 Ukraine 2.123 ⬆️ 3 ⬆️ 13 5 Colombia 2.875 17 Serbia 2.038 ⬆️ 11 ⬆️ 5 6 France 2.670 18 Côte d’Ivoire 2.019 ⬆️ 7 ⬇️ 6 7 Chile 2.620 19 USA 1.991 ⬆️ 7 ⬇️ 11 8 Netherlands 2.616 20 Italy 1.984 ⬆️ 1 ⬇️ 15 9 England 2.541 21 Switzerland 1.942 ⬆️ 1 ⬇️ 2 10 Belgium 2.528 22 Mexico 1.866 ⬇️ 7 ⬇️ 5 11 Portugal 2.354 23 Croatia 1.836 ⬆️ 14 ⬆️ 8 12 Ecuador 2.306 24 Sweden 1.712 • Last column: Change from current FIFA rank.
Massey: Group of Death! 1 2 Gp 3 4 Third Avg Rk Gap 23 45 1 22 A 23 22.8 22.5 4 7 8 54 B 8 18.3 25.5 5 18 27 32 C 27 20.5 18.0 9 20 44 14 D 20 21.8 20.5 6 12 21 56 E 21 23.8 29.5 15 47 2 30 F 30 23.5 30.0 11 19 2 6 3 G 19 14.8 15.5 10 13 28 5 7 H 28 27.0 31.0
Build Your Own! • FIFAfoefun.davidson.edu. • Build personalized rating of international FIFA teams using your selected parameters. • Age weights. • Colley or Massey. • Value of win in penalty • Number of years to use. shoot-out. • Type weights. • Max score di ff erential • 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.
Recommend
More recommend
