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.