In Defence of The FIFA Rankings.

A good team ratings system should be capable of doing two things.Firstly,it should accurately reflect the current pecking order in the sport and secondly,the difference in the ratings between each team should allow an estimation of the actual gulf in class between each of the sides.

Which brings us neatly to the FIFA World Rankings.England lie currently third in the group of UEFA nations,trailing only Germany and multiple Champions,Spain.The Spanish have 1691 points compared to the Germany tally of 1502 and then come England on 1294.We then reach a gaggle of  five similarly rated sides headed by Italy,ending with Greece and separated by a spread of around 200 points.

Historically FIFA's attempt to quantify their sport has rarely been favourably received and the prominence of England towards the head of their current incarnation has done little to add credibility to the numbers.The Three Lions went into Euro 2012 with 1145 ranking points and they raised that total by 149 points on the back of two wins against Sweden and hosts Ukraine and 90 minute draws with Italy and France.When England opened their tournament against France a 1145 side faced off against a 964 side.

Before we can attempt to make any sense of this mysterious FIFA points system it's necessary to to qualify the components that go towards quantifying each team's chances of winning a football match.The obvious starting point is the difference in class between the sides,but there are additional minor factors most notably home field advantage,but also a continental advantage in World Cup Finals.Since the FIFA rankings morphed into their present form there have been sufficient matches played to produce a correlation between the difference in FIFA rankings teams and the actual match result.

If two teams played a continual re match the most convenient way to express the gulf in class between them would be the average of the goal difference between the sides over the re runs.To illustrate,Arsenal would quite often beat Stoke by varying margins of victory,occasionally Stoke would pinch a draw or even a win.On average Arsenal would likely to be just under a goal superior to Stoke.To test the FIFA ratings we can perform a similar process by grouping games where the difference in FIFA ratings between the sides is similar and record the average goal superiority of the higher ranked teams.In short we can turn FIFA points into goal supremacy from historical data and then use that conversion factor to convert FIFA points into goals to predict future matches.

The conversion factor I've calculated for the latest FIFA rankings requires the difference in rankings points between two teams to be multiplied by around 0.002 to convert to a goal supremacy.To illustrate,when England (1145) played France (964) at Euro 2012 the difference in ranking points was 181 in England's favour,multiplied by 0.002 gave Hodgson's side a supremacy of 36 100ths of a goal.I don't really want to turn this post into a number crunching fest and there are numerous ways to convert a goal supremacy into win,draw and loss probabilities.So I'll merely say that this size of expected supremacy equates to an England win probability of 37%,a French win probability of 34% and the remaining 29% going on the draw.

The standard way to evaluate the effectiveness of a ratings system and any predictions derived from it is to see how well it performs in out of sample matches.I therefore crunched the numbers for all of the group games of Euro 2012,produced a goal supremacy and a win,loss and draw probabilities for all 24 matches and compared their predictions to a batch of game odds on offer from a series of online books.

Match Odds Derived from FIFA Ranking Points Compared To Consensus Bookmakers Odds for Group D.

"Home" Team.	"Away" Team.	FIFA Home Win %	FIFA Away Win %	FIFA Draw %.	Home %.	Away %.	Draw %.
France	England	28	45	27	34	37	29
Ukraine	Sweden	31	43	26	42	29	29
Ukraine	France	28	46	26	25	45	30
Sweden	England	26	48	26	25	45	30
Ukraine	England	21	55	24	27	45	28
Sweden	France	34	39	27	15	60	25

Group D has been chosen to give topical interest as it involves England,but the selection has been kind to the FIFA derived odds.The bookmakers 100% odds better predict the draw between France and England,as well as the Ukraine win over Sweden.For the remaining four games the FIFA ratings are sweeter on the wins for England,France,England and Sweden.A four to two victory for FIFA is not only a  small sample triumph,but it is also a rather blunt comparison.The more confident a method is in the actual result,then the more credit it should receive.By comparing the individual win/lose/draw pre game probabilities with the post game realised probabilities,where the actual result has a probability of 1 and the two remaining outcome shake out at zero,it is possible to quantify the accuracy of each match selection.

If we run through these processes for all 24 games we find that the bookmakers odds are more enthusiastic about the game day outcome than were FIFA in 13 of the 24 games,while using the more quantified method that accounts for the level of confidence in the actual outcome on the day we find that both sets of odds perform with equal accuracy.

Bookmakers always add an overround to their prices,so anyone hoping to gain too much of an edge by using FIFA's ratings may be disappointed,but the similarity between the two sets of odds does validate Blatter's numbers,even if they fail to capture the limited tactical approach of some of it's higher rated members.