Soccer rankings: farewell FIFA, hello Elo?

Wales are the eighth best men’s football team in the world – one place behind the mighty Brazil – according to this month’s publication of the FIFA/Coca Cola World Rankings. Y Dreigiau have leapfrogged cross-border rivals England to achieve their highest ever ranking. This is a fantastic achievement for a team who were outside the top 100 only a couple of years ago.

Wales 2011

Wales national football team ready to play Bulgaria in 2011. Wales were outside the world’s top 100 at the time and have now reached 8th. CC BY-SA 3.0 (click for details).

Ranking national sides is important because it helps determine World Cup seedings, while it can even influence decisions on players’ work permits (just ask Jason Scotland). The FIFA ranking system has, however, come under criticism for perceived oddities. For example, five-time world champions Brazil fell to 22nd before they hosted the 2014 World Cup, a tournament for which they were favourites to win. How might this have happened?

The FIFA ranking procedure is based on a weighted average of ranking points accumulated in matches over the past four years. Ranking points in each match are determined by its result, its ‘importance‘ (e.g. a World Cup game is more important than a friendly match) and the relative strength of the opponent and their confederation (e.g. CONMEBOL teams in South America have a higher multiplier than AFC teams in Asia). This explains Brazil’s lowly position prior to the World Cup: as hosts and automatic qualifiers, they could not take part in high-point-scoring qualification matches and only played unimportant low-point-scoring friendlies.

Similarly, A good ranking can be maintained by teams that minimise the number of friendlies played, since these matches are worth relatively few points and can bring the average ranking points down. It has been suggested that Switzerland did this to ensure a seeding at the 2014 World Cup. Both Romania and Wales’s current high rankings have also been helped by having played very few friendly matches.

What’s the alternative?

The Elo rating system (that’s Elo not ELO) was developed for chess but has been applied successfully elsewhere. It’s been in the news recently, as FiveThirtyEight has produced historical Elo ratings for NFL and NBA teams, from which the best (highest-rated) teams of all time can be calculated.

The Elo rating system, like the FIFA system, is point-based and relates to a match’s importance and result. The key difference is that points are swapped from one team to another based on relative rankings, goal difference and the ‘win expectancy’, a predictive measure of each team’s likelihood of victory. More points will be exchanged when there is an upset (e.g. the United States gained a relatively large 56 points when they beat England 1-0 in the 1950 World Cup). A list of results, points traded and a table of ratings is kept diligently up to date at elorankings.net.

How do the two ranking systems compare?

FIFA vs Elo

Focusing on FIFA’s top 10, there are a few discrepancies compared to the Elo system. Largest of these – and made very obvious by the ridiculous chart below – was Wales, who are ranked number 8 by FIFA, but 43 by the Elo method (a huge difference of 31 places). Belgium and Portugal both have an advantage of seven places in the FIFA rankings, while Brazil and Chile lose out by four ranking positions and England three.

There is relatively good agreement for Argentina, Germany, Colombia and Spain, who are all one place different between the systems. World champions Germany lose out on FIFA’s top spot to their World Cup final adversaries Argentina, though Elo corrects this by reversing their positions. It probably makes sense that the recent World Cup winners should occupy the number one position.

FIFAtop10_LadderPlot_Oct2015

Wow, Wales really breaks this ladder plot of the FIFA/Coca Cola men’s top 10 and their rankings under the Elo system.

It’s interesting that all teams in FIFA’s top 10 are from either the CONMEBOL (South American) or UEFA (European) confederations; confederations with the highest multipliers in the ranking procedure. The rise of Wales may be partially due to a string of good results against the high-mulitplier UEFA sides they’ve faced in qualifying for next summer’s European championship. Relatively speaking, lower-ranked nations in other confederations would not be rewarded with as many points when doing well against the top teams in that confederation. Elo does not include a confederation multiplier and instead relies on team strength and the likelihood of winning; perhaps this is a better approach.

Continuing the theme of confederations, the plot below shows the relationship between FIFA and Elo ranks for all the 200-plus FIFA-recognised teams, split by confederation. FIFA rankings (vertical axis) broadly agreed with Elo rankings (horizontal axis) across all confederations, although the spread of the discrepancies was fairly large in some cases. CAF and CONCACAF nations tended to be ranked higher by FIFA, the few nations of CONMEBOL and OFC were generally ranked higher by Elo. In the AFC confederation, nations ranked inside the FIFA top 130 were under-scored relative to Elo rankings, while those outside the top 130 were over-scored.

FIFA vs Elo ranks, October 2015

Relationship between FIFA and Elo ranks by confederation. Dashed line indicates no difference. Nations above the line are ‘under-ranked’ by FIFA relative to Elo; they are ‘over-ranked’ below the line. Click the image to enlarge.

When collated in the table below, it is clear that the confederations differ in their mean ranking discrepancy between FIFA’s and Elo’s ranks. For example, OFC teams are an average of 26 places lower in FIFA than Elo, while CONCACAF are an average of 17 places higher. Greatest agreement between the ranking systems is for UEFA and AFC, where teams disagree by one place or lower on average.

Confederation Teams Mean StDev Max Min
OFC 10 26 44 70 -44
CONMEBOL 10 12 11 33 -1
AFC 45 0.4 25 59 -55
UEFA 52 -1 17 27 -73
CAF 52 -11 19 40 -52
CONCACAF 34 -17 26 22 -79

Certain nations were ranked very differently between the two systems. The largest 10 are shown in the table below. Interestingly, all are ranked outside FIFA’s top 120 and are ranked lower by FIFA than Elo. This hints that nations stuck at the foot of FIFA’s table might be ‘punished’ for not playing important matches in major tournaments, or else find that they are in a confederation with a relatively small multiplier for playing other teams in their confederation (e.g. 9 of the top 10 are from the AFC or the OFC).

The Elo system is perhaps more forgiving to lower-performing sides: victory or even a draw against a higher-rated side (of which there are many) could result in a great gain in points, while a loss to such opposition will result in only a small loss of points. New Zealand can consider themselves unlucky to be ranked so low in the FIFA system given that they have the largest discrepancy of any nation when compared to their position in the Elo rankings. It is unfortunate that their appearance at World Cup 2010 does not count towards their FIFA ranking position, since they went unbeaten and even finished above the fourth-seeded Italy.

Team Confederation FIFA rank Elo rank Difference
New Zealand OFC 148 78 +70
New Caledonia OFC 169 106 +63
Fiji OFC 189 127 +62
Korea DPR AFC 129 70 +59
Vanuatu OFC 201 151 +50
Syria AFC 123 76 +47
Tahiti OFC 188 141 +47
Kuwait AFC 128 86 +42
Solomon Islands OFC 197 155 +42
Gambia CAF 161 121 +40

So what?

No ranking system can perfectly capture which teams are relatively ‘better’ than any others. Football is a sport in which there are many surprises and seemingly any team can have a good crack at beating any other.

But it probably makes sense to get things in order when it comes to seeding for major competitions. A favourable draw is worth so much when trying to progress through tournaments. Oh, and that’s worth a bunch of cash, too.

Is the Elo rating system the right way to go? It certainly has its advantages and can also serve as a way of predicting match outcomes given relative team ratings. The FIFA/Coca Cola women’s rankings already use a variant of the Elo ranking. Perhaps it’s time for the men’s rankings to shift to this system too.

Whatever, we all know that the Unofficial Football World Championship rankings are the only thing that matters. Wait, what? Scotland? Maybe not.

I used R to handle the data and make the plots in this post. Contact me if you’d like any of the code.

I collected the FIFA/Coca Cola world ranking table and Elo rankings for these sides from elorankings.net (supported by Advanced Satellite Consulting). I excluded a small number of sides that did not exist in both ranking systems after taking account of spelling differences (e.g. ‘United States of America’ versus ‘USA’). I added information on each team’s membership to one of six confederations, which are largely continent-based.

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