December 10, 2005

On maths and football

And how they don't go together

I promised a rant about the World Cup seeding, so here we go. Intuition tells you the toughest teams in the world at the moment are Brazil, Argentina, Czech Republic, England, and the Netherlands. Germany need more than one world class player [Ballack] to belong in that group, and the fact that PSV has beaten Milan twice this year says all about the current state of Italy. I just don't know the Mexican team well enough to say anything about them, but I think if you wish to include them, then include South Korea as well – they've actually made an impact!

But that's just [reasoned] intuition.

Here comes what I guess FIFA call maths and stats. The seeding list is half based on the country's world cup history, and half on the country's world ranking over the past few years. Let's pretend that ranking makes sense and see what happens next.

The ranking points

Ranked first by the end of the year gives you 32 points, second is worth 31 and it goes like that for a while, though the lowest ranked teams [somewhere beyond the 50th spot] still get a point. Since the world ranking system is a bit shady, and the top 10 teams are usually of about equal strength, this seems a fair enough allocation of points, and indeed gave fair results [with Germany and Italy indeed ending up lower, though the USA would have been seeded if only ranking were considered. Maybe a more scaled system would be better for this ranking? Say, if you beat a team higher you get more points and if you draw with a team lower you lose points or something. Anyone got Sepp's number?]. From the top of my head seeding based on ranking only would have given Brazil, Czech Rep, Argentina, the Netherlands, France, Spain, Mexico, USA. Seems the ranking's got a dislike of England…

World Cup history points

Only 1998 and 2002 counted towards these points, which kind of makes sense. There's no reason to include any older tournament, and as some '98 players [Cocu, Beckham, Zidane, Ronaldo] are still going strong, there's no reason to exclude that tournament [also, exclusion would skew the results even worse than they are now]. Brazil is the obvious number 1 in this case, being runner up and winner over those two games. But then what happens?

To compare the results to the ranking points, the max is 32 for winning the tournament. Then, as past performance do not guarantee future results, a ratio of 2:1 for the 2002:1998 games is applied, which sounds fair enough [supposedly, this is where the Netherlands were screwed, but don't worry, worse is yet to come]. The point allocation then is 32 for the winner, 31 for the runner up, 30 for the 3rd spot etcetera. Indeed, they manage to distinguish between the teams who reached the quarter finals, and even those who only reached the second round still gain a significant amount of points. Thus, England get an astronomical 20-odd points for reaching the second round in 1998 [sorry about picking on England, it was just a result that sticked out], hardly less than Argentina who beat them, or the Netherlands who beat Argentina, and less than 10 points apart from France, who won the trophy! And it gets worse.

The worst team advancing from the group stage still gets 17 points, equivalent to being ranked 16th of the world. Even ranking third in the group stage gives you 9 points, and being last is still worth 8. Thus, for merely being in the world cup, you can boost your total by 8 points. Hence we got an average team like Paraguay leaping past Portugal and Czech Republic.


I can't say I can think of a better system, but a ranking with Spain being 6th and their group winners Serbia and Montenegro somewhere in the 40s can't be right. I already suggested a heavier penalty for losing to or drawing with a lower ranked team. Points of the rich will go to the poor! Or maybe some sort of ladder system. Taking the ranking at a specific point [December] of the year is also unfavorable to teams who play more during the summer. An average rank over the past few months would be fairer.

The World Cup history system is even more ridiculous. It implies that if a country is to win a Cup and the next run doesn't manage to enter the tournament [quite likely for a European team], it will gain as many points as a team that didn't enter the first tournament, but reached the second round in the latest tournament. Kind of like the Netherlands and, say, Senegal [or Sweden, for that matter].

A system more discrete such as the Grand Prix credits would make more sense. The winner should get considerably more points than the runners up – if only because of the added value of actually winning the cup. Then semifinalists definitely should get far less points than the two finalists, and the same disparity should go between them and quarterfinalists. And why the distinction between quarterfinalists themselves? Why do Japan deserve 7 more points than Paraguay for reaching the second round in 2002? I don't remember one team any better than the other.


It doesn't really matter. It makes sense the Netherlands get some penalty for not being there in 2002 [and hence causing it to be the most boring tournament in history], and they're in an amazing group now so I don't really mind. Rather this than having been seeded and ending up with, say, Ecuador, Costa Rica, and Poland. A Grand Prix like system with a similar ratio between the two cups might have landed the Netherlands in the unseeded group as well. Still, if you decide to publish the draw pot procedure online, have some common sense and make sure your system does as well.

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