Radioactive soccer teams

This month's Physics Today has an article about Metin Tolan's calculations to model the outcomes of more than 34,000 professional soccer games. It's worth it just for this quote:

"We approximated a soccer team by a radioactive source. A soccer team emits goals according to Poisson statistics," he says.

Here's how the modeling worked:

Calculating the probability that a team will win or lose a game by a given number of goals leads to what Tolan calls the "Bessel-function theory of football" — as soccer is called in most places outside the US. A modified Bessel function results from summing over products of probabilities expressed as Poisson distributions.

Tolan's calculations assume that goals are independent of one another, which, he says, "is reasonable for soccer, but not, for example, for basketball, because there the points are connected."

[Note: Only a physical scientist could assume that goals are independent. In a single sweep, he dismisses the entire field of sports psychology.]

Here are the results:

[F]or soccer the Bessel-function fits are good. "We have no idea why. I never would have guessed that you would find anything regular in a chaotic game like soccer," says Tolan. Bessel functions would probably not approximate minor league teams well, he adds. "The professional teams, while not of equal strength, have a certain level, and you have a sort of restricted system where not everything can happen."

Hmmmm. This raises many more questions. What does it mean to say soccer is a "chaotic" game? And how does the level of skill restrict the space of what can happen?

Anyway, if you want to place a bet, here's the hot tip:

For this year's World Cup, Tolan and his colleagues carried out 100 000 simulations based on past performance to get the probability of each team's winning the title. "Statistics cannot predict the results of a specific World Cup," says Tolan. "So this is where the fun begins." The simulations put Brazil's chance at 15% and Germany's at 10.5%, he says. But home teams tend to score an average of 0.6 to 1 additional goal per game. Incorporating that "home advantage," says Tolan, boosts Germany's chance of winning to 33%.