New on SocTakes: On international rankings, FIFA vs. Elo


Photo credit: Oleg Bkhambri (Creative Commons license)

If you’ve followed international soccer for any stretch of time, you’re probably familiar with the FIFA World Ranking system. This list, calculated and maintained by FIFA, attempts to quantitatively determine which teams are the best in the world. They’ve been around in some form since December 1992, and have undergone several dramatic revisions since then. The latest such change will occur after the World Cup, with a completely new calculation method based on the Elo formula. That Elo formula is also used by the World Football Elo Ratings, a competing ranking system that I — and many others — actually prefer.

First up, how exactly does FIFA calculate its rankings? There’s a method to their madness. The core formula is:

ranking points = result points x match status x opposition strength x regional strength

Let’s break that down.

Result points refers to a simple table of points, from zero to three, depending on the final result. Zero for a loss without a penalty shootout, one for a shootout loss or a draw, two for a shootout win and three for a win without a shootout.

Match status is a bit more complicated. It’s a multiplier based on what sort of match was played, from 1x to 4x. A regular friendly match has a 1x multiplier, a World Cup or continental cup qualifier 2.5x, continental cup or Confederations Cup finals 3x (as in the tournament itself, not just the final) and a World Cup finals (see previous note) 4x.

Opposition strength is a multiplier defined as (200 – opponent ranking position)/100. Fairly straightforward, with exceptions that the top team is rounded up to 2x instead of 1.99x, and every country ranked 150th and below is set at 0.5x.

Regional strength is where stuff gets a bit odd. This is where FIFA’s subjective opinions come in and the entire confederation’s results dating back to the previous World Cup are considered. These are updated every four years. Currently, CONMEBOL leads with 1x, UEFA is second with 0.99x, and all four other regions are at 0.85x. The regional strength multiplier is defined as the average of the regional multipliers of the two teams. CONMEBOL vs. CONCACAF would be .925, for example.

And then there’s the assessment period multiplier, used to weight the rating points based on that earlier formula. This is another table of multipliers, ranging from 0.2x to 1x, with 0.2x for matches 36-48 months ago, 0.3x from 24-36 months ago, 0.5x from 12-24 months ago and 1x within the last 12 months.

And then, the matches played are run through the various formulas, and a number comes out the other end. That number, the “total points,” is the criteria by which FIFA’s rankings are determined.

This formula has been criticized since its inception, and despite numerous revisions still isn’t as impartial as it could be. With something like this, it’s possible to use purely quantitative observations without subjective decisions to determine a rankings list. That’s where Elo comes in.

Elo ratings were initially created by physicist Arpad Elo with chess as a focus. The idea is to create a formula for both absolute rankings (i.e. a player’s individual strength) and comparative rankings (i.e. how much better or worse one player is than another). This has been adopted and adapted for soccer as the World Football Elo Ratings, making a few modifications to the formula to include the necessary variables that come along with soccer.

Their formula considers the current rating of a team at the time of the match a weight index K representing the status of the match from 60 for the World Cup down to 20 for a friendly; an index based on goal differential where G=1 for a one-goal margin of victory or a draw, G=3/2 for a two-goal win and G=(11+N)/8 for a three-goal or more victory; the result of the match where W=1 for a win, 0.5 for a draw, and 0 for a loss; and the expected result of the match calculated by the difference in ratings with a 100-point boost for the home team.

There are some more complicated formulas there that I’m not going to bother transcribing into WordPress, so check out the Wikipedia article on the World Football Elo Ratings if you’re curious.

That last point, the expected result, is where the biggest advantage of Elo over FIFA lies. Not only can we say which team is the best in the world or which team is better than some other team, we can also say what we would expect the result of Team A playing Team B to be. World Football Elo Ratings also take into account every match played by international teams, giving it a predictive power that puts the FIFA ratings to shame. There was actually a study done in 2009 and published in 2013 that used both the current FIFA ratings system as well as Elo to predict the results of matches. The World Football Elo Ratings formula came out on top, while the FIFA formulas performed badly.

And before I jump into the 2018 World Cup groups, I’ll add that the FIFA Women’s World Rankings actually use a modified version of that Elo formula for their calculations instead of the FIFA formula used for the men’s teams.

So, to examine the World Cup and how these two systems apply, I’ll go group by group and give the ratings in both FIFA and Elo systems for every team. Ratings are taken from the June 7 FIFA World Ranking and June 13 World Football Elo Ratings.

Group A
Uruguay 14th (1018) 12th (1894)
Egypt 45th (649) 50th (1646)
Russia 70th (457) 45th (1678)
Saudi Arabia 67th (465) 63rd (1591)

Well, look at that, already something interesting. Russia’s FIFA rating is heavily depressed compared to their Elo. By the FIFA ratings, we wouldn’t expect Russia to be better than Saudi Arabia, but with Elo, it’s less surprising that they won, although probably not by five goals. Russia is expected to advance from the group per Elo, along with Uruguay. Saudi Arabia is predicted to outperform their FIFA ranking slightly, although they are the lowest rated team in the tournament. Egypt is the oddball as the only team rated worse by Elo than by FIFA in this group, where FIFA expects they would advance from the group while Elo says Russia goes on.

Group B
Spain 10th (1126) 3rd (2044)
Portugal 4th (1274) 6th (1970)
Iran 37th (708) 21st (1798)
Morocco 41st (686) 24th (1733)

More fun in Group B! Spain is rated lower by FIFA, Iran even more so, and Morocco very much a lot even more so holy shit. Portugal has the edge in the FIFA rankings, likely because of their Euro 2016 win. We would expect Spain and Portugal to advance from either rankings, though, so Iran or Morocco making it to the knockout round would be a significant upset.

Group C
France 7th (1198) 4th (1987)
Peru 11th (1125) 10th (1915)
Denmark 12th (1051) 16th (1856)
Australia 36th (718) 32nd (1742)

Nothing particularly odd here. FIFA rates France and Australia slightly worse, while rating Denmark a bit higher. The interesting thing to me is how little there is separating France, Denmark, and Peru on both ratings; only 131 points on Elo means that we can expect a lot of close games. So far, France only narrowly beat Australia thanks to an own goal, and Denmark beat Peru 1-0. This is going to be a very tough group.

Group D
Argentina 5th (1241) 5th (1986)
Croatia 20th (945) 17th (1853)
Iceland 22nd (908) 24th (1764)
Nigeria 48th (618) 44th (1681)

Not much to see here, really. Argentina is the undisputed fifth-best team on earth, Croatia and Nigeria are slightly underrated by FIFA, while Iceland is slightly overrated likely due to their run in Euro 2016. These four teams are separated by quite a lot, making Iceland’s draw against Argentina all the more unlikely. While, at first glance, it would look like both ratings pick Argentina and Croatia to advance, Iceland is close enough to Croatia to potentially beat them and make it to the knockout round.

Group E
Brazil 2nd (1431) 1st (2142)
Switzerland 6th (1199) 14th (1890)
Serbia 34th (751) 22nd (1777)
Costa Rica 23rd (884) 31st (1744)

And here we are, finally some discrepancies. Brazil is considered a very, very good team by both formulas, nothing surprising there, while Switzerland is ranked substantially higher by FIFA than Elo. Then there’s Costa Rica and Serbia, who nearly swap positions moving from FIFA to Elo. Serbia’s failure to qualify for the 2014 World Cup hurts them badly in the FIFA rankings, while Costa Rica gets a boost from their eighth-place finish in Brazil and third-place finish in the most recent Gold Cup. That doesn’t make either of them an easy bet to advance, though, given that there’s still quite a lot of breathing room between Serbia and Switzerland.

Group F
Germany 1st (1558) 2nd (2077)
Mexico 15th (989) 18th (1850)
Sweden 24th (880) 20th (1795)
South Korea 57th (544) 40th (1714)

Iiiiiiiiinteresting. FIFA really hates South Korea. They’re exceptionally harsh on Asian teams in general, with Japan sitting in 61st. Korea actually outranks both Panama and Nigeria in the Elo ratings, despite sitting well below both on FIFA’s list. Elo tends to rate AFC higher than FIFA does, while rating CONCACAF lower, which explains the slight disparity for Mexico. Sweden is ahead of Iceland in Elo, but not in FIFA. I blame the Euro 2016 bump for that one as well. Germany is almost guaranteed a spot in the knockout stage. Almost. If they lose to Sweden or gasp Korea though, we could have some chaos. I like chaos, and I’m definitely pulling for Sweden and Korea to advance.

Group G
England 12th (1051) 7th (1948)
Belgium 3rd (1298) 8th (1939)
Panama 55th (571) 48th (1659)
Tunisia 21st (910) 49th (1657)

Here’s a potential hot take for you: I think FIFA is dramatically overrating Tunisia. There is no reasonable explanation for there to be a 28-position difference between their Elo rating and FIFA ranking. In Elo, which has shown much stronger predictive power, Panama and Tunisia are essentially level on strength, with Russia and Egypt a little bit better and worse, respectively. This seems reasonable — hell, even logical. I find it interesting that Belgium gets a five-spot boost from FIFA while England drops five. Again, when the FIFA rankings show something weird, trust Elo. This is a group that is probably predetermined.

Group H
Colombia 16th (986) 9th (1928)
Poland 8th (1183) 19th (1831)
Senegal 27th (838) 27th (1750)
Japan 61st (521) 43rd (1684)

OK, now this makes no sense to me. Elo barely rates Poland in the top 20, while they’re top 10 for FIFA. Colombia are top 10 for Elo and 16th for FIFA. You want some UEFA bias proof? Here it is. Senegal is 27th objectively. Japan, meanwhile, suffers from FIFA’s bias against AFC, like Korea above. Japan outranks Nigeria, Egypt and Tunisia in the Elo ratings, and should be viewed as a threat to advance, not as the worst team in the group. In fact, Japan is closer to Senegal than Senegal is to Poland, and the entire group is separated by only 244 points in Elo (compare to 662 in FIFA). This is going to be a very strong group, and we’ve already seen that with the current standings matching the inverted Elo order.

So, that’s a little primer on the two rating systems, an explanation of why Elo is better and a demonstration that the FIFA rankings are kind of nuts. Stay tuned to Soc Takes for more World Cup content as the tournament continues.

Follow John on Twitter: @JohnMLTX.

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