Monday, June 12, 2006

the statistics of goals and the physics of soccer balls

One of the types of things that statistics can tell you about is whether events happen independently, or instead whether an event causes another event. Take soccer, for instance. As reports, there's been a longstanding assumption that the first team to score a goal will tend to score more goals. It's certainly the case that if you have two teams, and one is better than the other, that the better team is more likely to both score first and to win. That's not very interesting. The question is whether a consequence of scoring that first goal in fact makes the scoring team better (and/or the other team worse) for the rest of the game. Put a little more technically, is the probability of scoring a goal dependent on whether or not you've previously scored a goal?

Several mathematicians (and soccer fans) from the UK and Germany crunched the numbers and have an answer. It turns out that yes, scores turn out to be more asymmetric than you would expect, and so having a lead improves your odds of additional scores.

(Note that most streaks, in other sports, turn out not to be real, but are just chance events. Steven Jay Gould talked about this a lot. "Hot hands" in basketball, for instance, don't really exist. On the other hand, DiMaggio's 56-game hitting streak is so unlikely that it should never have happened, but it did.)

Another thing that may make scores a bit larger for this World Cup compared with earlier series is that they've changed the ball. Instead of being made up of hexagons and pentagons, all stiched together, the new ball is more uniformly round, and is glued together. As National Geographic News reports, there's some concern that the smaller number of seams (14 panels instead of 32) may make the ball swerve more in the air, like a non-spinning knuckleball in baseball. (The single seam on a baseball causes the ball to act asymmetrically, and thus erratically, unless it's spinning.) Goalkeepers are concerned, naturally.

Perhaps today's 3-0 loss by the U.S. team to the Czechs may have had something to do with one or both of these effects...



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