# The mathematical game

It’s the first day of Europe’s Champions League football tournament but if you can’t wait for the results, no worries as Eurofootsie probably knows them all already thanks to it’s whizz-bang computer modelling.

Its computer system analyses every top-league team* in Europe’s last 50 games to come up with what it hopes is the definitive guide to which teams are the best in Europe. At present it believes the top 5 European club sides with their rating (the top team is always 100) are:

Manchester United – 92.97
Juventus – 89.36
Barcelona – 89.29

Well no great surprises there, though some eyebrows may be raised at Barcelona in fifth. See here for a more detailed explanation of how it came to this conclusion and loads of football trivia (debunking popular myths such as teams are most vulnerable to conceding a goal just after they have scored one).

Before any readers rush out to punt lots of money in online betting I should point out that its forecasting power probably still needs a little tweaking. A similar system used by The Times newspaper to predict the English premier league over the weekend forecast Arsenal, Liverpool, Bolton, Man U, Chelsea, Newcastle, Southampton, Man City, Fulham and Leeds would all win. Only six out of the ten did.

* Newly promoted teams (e.g. Wolverhampton Wanderers in the English league) don’t get a rating until they have played 25 games in the top division. In Wolves case we should probably add, ‘if they last that long’.

## 5 thoughts on “The mathematical game”

1. What is it about sports that turns otherwise math-phobic men into amateur actuarians ?
I had thought it was an american peculiarity,
but apparently not.

2. In Wolves case we should probably add, ‘if they last that long’.

Pah! We’re guaranteed 38 games…though we might well be effectively relegated after 25 at this rate.

Does the system allow for negative ratings?

3. On a more serious note, having had a look at the site, I think they place far too high a weighting on which country a side plays in (which explains why Sociedad have such a high rating). Obviously, that’s useful in stopping dominant sides in small countries (TNS in Wales, say) from getting an arbitrarily high rating from thimping part-timers week in, week out, but it seems to be a bit too much of a blunt instrument around the top with some quite mediocre sides from big leagues coming out ahead of good sides from smaller (or less rich) leagues. For instance, it ranks Bolton as higher than PSG.

But that is partly good news, as it means that Wolves won’t be competing with Faroese, Azerbaijani and Luxembourgeois sides for last place.

4. “some eyebrows may be raised at Barcelona in fifth”. Yep, we’re going for EUFA this year, so I’ll have to plump for the next best thing: Marseille. Allez les Phoceans.

5. A mathematical comment (critique): This football calculation, and the resulting ranking seems to imply that “better” is transitive with respect to football teams. A better than B and B better than C implies that A is better than C. But I’m not sure this would be the case. Not even simple dice are transitive – consider three sided dice with number of eyes:

A: 2, 2, 5
B: 3, 3, 3
C: 1, 4, 4

Which die is better (more often show more eyes than the others). Well B is better than A (which always lose on 2 and win on 5) and C is better than B (as C always win on 4 and lose on 1). Is C therefore “best”. No, C loses against A 3 times in 3 on 1 and loses 1 times in 3 on 4. C has two 4’s so C loses 3+1+1 (=5) times in 9 against A.

Hence A is better than C which is better than B which is better than A! Which one is best? You can’t make a ranking among these simple three-sided dice. How do you expect to make a mathematical ranking among things as complex as football teams!?