FIFA Foe Fun! Tim Chartier Mark Kozek Davidson College Whittier - - PowerPoint PPT Presentation

FIFA Foe Fun!

Michael Mossinghoff Davidson College

Tim Chartier Davidson College Mark Kozek Whittier College

• Group E: Switzerland, Ecuador,

France, Honduras.

• “Switzerland is the top seed, based on

FIFA’s flawed rankings, but might

• nly be the third-best team.”

1 Spain 1513 2 Germany 1311 3 Argentina 1266 4 Colombia 1178 5 Belgium 1175 6 Uruguay 1164 7 Switzerland 1138 8 Netherlands 1136 8 Italy 1136 10 England 1080 11 Brazil 1078 12 Chile 1051 13 USA 1040 14 Portugal 1036 15 Greece 983 16 Bosnia-Herz. 925 17 Côte d’Ivoire 917 18 Croatia 901 19 Russia 874 20 Ukraine 871 21 France 870 22 Ecuador 862 23 Ghana 860 24 Mexico 854

FIFA Rankings

• Oct. 2013
• Basis for World Cup groupings.

• 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
• btained 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 = 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 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 = 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
• f the confederation weight for the two teams.
• UEFA & CONMEBOL: w = 1.
• CONCACAF: w = 0.88.
• AFC & CAF: w = 0.86.
• OFC: w = 0.85.

Points per Match

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.
• w = max(.85, (m/m0)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 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%.

• 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 Gi X

j∈Oi

rj ≈ 1 2.

Colley Method

ri ≈ Wi + 1 Gi + 2 = 1 + Wi−Li

2

+ Gi

2

Gi + 2 ≈ 1 + Wi−Li

2

+ P

j∈Oi rj

Gi + 2 . (Gi + 2)ri − X

j∈Oi

rj = 1 + Wi − Li 2 .

So: This produces the linear system: 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.

Colley Method

Type Weight

• Friendly = 1,
• Continental qualifier = 1.25,
• Continental tourn. or Confed. Cup = 1.5,
• World Cup qualifier = 2,
• World Cup match = 2.25.

1 2 3 4 5 0.2 0.4 0.6 0.8 1.0

Age Weight

FIFA .20 .30 .50 Smoothed .717 .283 .054 .008 .946 1

• Total area (nearly) preserved.
• Keep five years now for smoother aging.

June 9, 2013: World Cup Qualifier. 0-3

• Ignore disqualifications.

Additional Adjustments

June 28, 2011: World Cup Qualifier.

• Ignore disqualifications.

Additional Adjustments

1 Brazil 1.058 ⬆️ 2 2 Spain 1.008 ⬇️ 1 3 Argentina 0.975 ⬆️ 2 4 Germany 0.951 ⬇️ 2 5 Colombia 0.934 ⬆️ 3 6 Belgium 0.929 ⬆️ 5 7 Chile 0.883 ⬆️ 7 8 Portugal 0.876 ⬇️ 4 9 England 0.872 ⬆️ 1 10 USA 0.869 ⬆️ 3 11 Netherlands 0.859 ⬆️ 4 12 France 0.859 ⬆️ 5 13 Uruguay 0.849 ⬇️ 6 14 Switzerland 0.842 ⬇️ 8 15 Côte d’Ivoire 0.823 ⬆️ 8 16 Russia 0.823 ⬆️ 3 17 Italy 0.814 ⬇️ 8 18 Ecuador 0.813 ⬆️ 8 19 Ukraine 0.810 ⬇️ 3 20 Greece 0.810 ⬇️ 8 21 Japan 0.780 ⬆️ 25 22 Croatia 0.776 ⬇️ 4 23 Bosnia-Herz. 0.776 ⬇️ 2 24 U.A.E. 0.775 ⬆️ 48

Weighted Colley

• 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
• f ratings.
• Alter system: replace one row with
• OK as long as there is a path between any two

teams.

N

X

i=1

ri = 0.

January 29, 2014: Friendly.

• Ignore disqualifications.
• Count penalty shoot-outs as weak wins.

PSO 4-1

Adjustments

October 14, 2010: CONCACAF Qualifier

• Ignore disqualifications.
• Count penalty shoot-outs as weak wins.

17-0

• Massey: set max score differential to 4.

Adjustments

July 2 and 9, 2011: World Cup Qualifiers:

• Ignore disqualifications.
• Count penalty shoot-outs as weak wins.

Only matches for both since 2008!

• Massey: set max score differential to 4.
• Ensure connectivity.

Adjustments

Omisions!

1 Brazil 3.633 ⬆️ 2 2 Argentina 3.126 ⬆️ 3 3 Germany 3.031 ⬇️ 1 4 Spain 2.940 ⬇️ 3 5 Colombia 2.875 ⬆️ 3 6 France 2.670 ⬆️ 11 7 Chile 2.620 ⬆️ 7 8 Netherlands 2.616 ⬆️ 7 9 England 2.541 ⬆️ 1 10 Belgium 2.528 ⬆️ 1 11 Portugal 2.354 ⬇️ 7 12 Ecuador 2.306 ⬆️ 14 13 Russia 2.304 ⬆️ 6 14 Uruguay 2.202 ⬇️ 7 15 Bosnia-Herz. 2.187 ⬆️ 6 16 Ukraine 2.123 17 Serbia 2.038 ⬆️ 13 18 Côte d’Ivoire 2.019 ⬆️ 5 19 USA 1.991 ⬇️ 6 20 Italy 1.984 ⬇️ 11 21 Switzerland 1.942 ⬇️ 15 22 Mexico 1.866 ⬇️ 2 23 Croatia 1.836 ⬇️ 5 24 Sweden 1.712 ⬆️ 8

Weighted Massey

• 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.
• Number of years to use.
• Type weights.
• Age weighting method.
• Age weights.
• Value of win in penalty

shoot-out.

• Max score differential

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.

• 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%
• f submitted brackets.

ESPN Bracket Predictor

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
• utcome 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.
• 1000
• 500

500 1000 0.2 0.4 0.6 0.8 1.0

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.

1 Brazil 2113 ⬆️ 2 2 Spain 2086 ⬇️ 1 3 Germany 2046 ⬇️ 1 4 Argentina 1989 ⬆️ 1 5 Netherlands 1959 ⬆️ 10 6 England 1914 ⬆️ 4 7 Portugal 1902 ⬇️ 3 8 Colombia 1897 9 Uruguay 1895 ⬇️ 2 10 Chile 1895 ⬆️ 4 11 Italy 1879 ⬇️ 2 12 France 1869 ⬆️ 5 13 USA 1832 14 Belgium 1824 ⬇️ 3 15 Russia 1821 ⬆️ 4 16 Mexico 1820 ⬆️ 4 17 Switzerland 1820 ⬇️ 11 18 Ukraine 1815 ⬇️ 2 19 Ecuador 1813 ⬆️ 7 20 Greece 1796 ⬇️ 8

eloratings.net Our Elo ratings

1 Spain 316 2 Brazil 307 ⬆️ 1 3 Germany 265 ⬇️ 1 4 USA 234 ⬆️ 9 5 Argentina 217 6 Netherlands 216 ⬆️ 9 7 Portugal 213 ⬇️ 3 8 England 186 ⬆️ 2 9 Côte d’Ivoire 182 ⬆️ 14 10 Chile 174 ⬆️ 4 11 Uruguay 173 ⬆️ 5 12 France 168 ⬆️ 5 13 Colombia 167 ⬇️ 5 14 Nigeria 163 ⬆️ 30 15 Iran 159 ⬆️ 28 16 Japan 158 ⬆️ 30 17 Belgium 157 ⬇️ 6 18 Greece 156 ⬇️ 6 19 Switzerland 151 ⬇️ 13 20 Egypt 151 ⬆️ 16

Number of Matches

20 40 60 80 100 10 20 30 40

µ = 41.6, σ = 21.0.

• 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.

Elo Summary

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!