FIFA Rankings,new verses old.

[tachyon1]

I've had a quick look at how the new fifa rankings compare with the old ones.

The old ratings did a reasonable job of predicting the outcome between two teams.The respective ratings of each team in themselves wern't really important,but the difference between them was.If you regressed the results of previous tournament games against the difference in rankings of the two teams you found the relationship between the two was fairly constant.Provided you allowed for a continental advantage of around 0.4 of a goal,regular HFA,and reduced the ratings of Concacaf and Asia by upto half a goal,you found the net difference in fifa ratings when multiplied by about 0.008 gave the expected goal supremacy for that particular match up.From goals supremacy it was a short step to win/draw/loss probabilities.

To use the Czech Rep(772) verses USA(756) WC game as an example.

Czech Rep fifa rating 772 + Continental advantage 50(0.38 of a goal)+53(Concacaf overvaluation of 0.4 of a goal) minus USA rating 756 = 119

Therefore Czech Rep ahead by 119 rating points,multiply by 0.0076(current value of the constant)=0.9 of a goal.

That equated to a CRep win probability of about 58%,a draw prob of about 26% and a USA win prob of about 16%.Most decent rating system had the Czech Rep win prob. between 54 and 58%.

Moving on to the new ratings.Unfortunately we only have the post WC figures.However,one feature of a decent ratings system is that whereas it will give a higher weighting to most recent results,these recent ratings should only gradually affect a teams current worth.For example if a team beat it's previous rating by an average of a goal a game for say seven games,it's base rating should only move relative to it's rating at the start of the run by around 0.2 of a goal.If the team at the end of this outstanding run could go back and play itself at the start of the run then it's win probability would only increase from 35% to about 39%.

No team in the WC got even close to this kind of run,therefore if the new fifa rankings are to have any predictive power it should be safe to use the new post WC ratings to evaluate the chances of the teams in the WC matches that have just taken place.

Therefore we only have games involving teams from the top fifty or so places.If these new rankings are going to follow the same pattern as the previous ones then the regression constant is obviously going to be different.It looks as though it's going to be in the region of 0.002,that gives you 0.1 of a goal being equivalent to 50 new ranking points.

Taking the same Czech Rep vs USA game

Czech Rep 1223 + Continental advantage 190 minus USA rating 933=480

Czech Supremacy=480*0.002=0.96 of a goal.That compares well with the 0.9 supremacy value derived from the old rating...with one significant difference.It appears the new fifa rating has addressed the overrating of concacaf.You no longer have to fudge for it.It's no longer there for Iran,SA,Japan either.These teams(and their neighbours) have plummetted in the ranking partly because they had a poor WC,but mostly because their confederation appears to have been re rated.

Overall the new ratings appear perform to a similar level as the old ones from a predictive point of view,but only time and more games and ratings will tell.

Zero ratings for a loss and the lack of goal difference slightly worries me.

[Hosehead]

Tachyon1, thanks for the interesting analysis. How did you get the win/draw/loss probabilities from a goal differential? Don't you need a total goals scored estimate?

Like you, I am also a bit unsure of removing goals or goal differential. Embedding the conference normalization as a static value does not seem the best choice but I am glad it is being recognized. At least FIFA is trying to be more open about their rankings, so I suppose that's a start.

[tachyon1]

Hi Hosehead,

quite right,you do need a figure for total goals,but there's a fairly clearly established relationship between goal supremacy and total goals.

In international football,if you've got two equally matched teams(goal supremacy=0),then you're going to get around 2.5 goals on average in that game.

If one team is superior by say 2.3 goals then your expected total goals rises to about 3.3 goals.

In other words the closer the match is likely to be the less total goals it will have,the bigger the mis match then the more goal laden it will be.

Some teams can appear to deviate from this behaviour and you can use individual team scoring styles to slightly modify these base numbers.But usually you're just seeing fleeting runs of apparently unusual scores that often don't repeat longterm.

Armed with a supremacy and a total goals figure you can easily work out the goals expectanion for each team in the match up.

Lets say A verses B;A is superior by 0.8 goals,total goal are expected to be 2.6.

Therefore A-B=0.8
and A+B=2.6

Add these together you get 2A=3.4(the B's cancel each other out)
Therefore A =1.7 goals and hence B=0.9 goals.

Then you just stick these goal averages into a Poisson to generate win/draw/loss fgures of 54%,27%,19%

I think you're spot on with your comment on goal difference,it's going to greatly hurt teams who reach the finals of major competitions and then struggle.

Losing 1-0 to a dodgy 93rd minute penalty to the soon to be crowned world champions,as Australia did,is surely worth some ranking points.It smacks a bit of dumbing down

T.

[Hosehead]

I assume the data concerning goal supremacy vs. expected total goals has been tabulated in a chart or otherwise approximated, but I can't find a discussion of it when searching the forums.
Can you point me to where this is discussed? Also how is goal supremacy determined? You've shown an example in your initial post of how to determine it from FIFA rankings. Is there a way to determine it solely from previous results, or would that start to tread on a more complicated algorithm (like Voros' iterative solution).
thanks for your help.

[tachyon1]

I assume the data concerning goal supremacy vs. expected total goals has been tabulated in a chart or otherwise approximated, but I can't find a discussion of it when searching the forums.
Can you point me to where this is discussed? Also how is goal supremacy determined? You've shown an example in your initial post of how to determine it from FIFA rankings. Is there a way to determine it solely from previous results, or would that start to tread on a more complicated algorithm (like Voros' iterative solution).
thanks for your help.

Hi Hosehead,

regards using previous results,try this method.

You'll need,firstly the average number of goals per game that a team scores and allows against an average opponent at a neutral venue.

In a league where everyone plays everyone else,then a simple average over a representative number of games is a good start.Around thirty games is a decent benchmark for one of the major european leagues.You can give more weight to recent games if you wish.

Next you need the average score between two average sides at a neutral venue.That's easy,you just take the average number of goals scored in a reprsentative number of games,and halve it.So if a league has 2.5 goals per game,then such a match up would end up on average 1.25-1.25.

Lastly you need the average number of goals scored by home sides and the average number of goals cored by away sides.In a typical English league home sides score about 1.45 goals/game compared to 1.05 for away sides.

Now the number crunching.

Team A at home to team B.

Lets say Team A scores 1.5 goals/game and allows 1.1 goals/game.
Team B scores 1.1 goals/game and allows 1.5 goals/game.

Average team verses average team at a neutral venue =1.25-1.25.

Home sides average 1.45 g/g
Away sides average 1.05g/g.

Hence
Team A scores at 1.5/1.25 times the rate of an average side at a neutral venue.
Home sides score at 1.45/1.25 of an average side.
Team B allows goals at 1.5/1.25 of an average side.

Multiply these rates together and team A would expect to score at 1.6704 times the rate of an average side at a neutral venue.

An average side scores 1.25 goals per game at a neutral venue,so multiply the 1.6704 scoring rate of team A at home to team B and you'd expect team A to score 2.088 goals at home to team B.

Go thru the same process for away side team B and you'll get them in for 0.813 goals.

Then stick these numbers into a poisson to get home/draw/away probabilities of 65%,21%,14%.(also notice that the supremacy for team A is about 1.2 goals and the total goals for the game has increased to 2.8 goals,compared to 2.5 goals or an evenly matched game).

If strength of schedule is an important issue,then a least squares approach may work better.

You'll end up with a ranking system expressed in terms of goals and it's fairly easy to maintain once it's up and running.

T.

[yoni]

i don´t understand Brazil is the best , was the best and will be the best

yoni