Not to draw this off-topic thread out too long, but perhaps there are
enough interested to make it worthwhile:
> And, since my son asked me and I am basketball ignorant: Why are
> basketball scores mostly much too close to equality? The arguments
> (loose power when leading)
The relevant rule is the one that dictates that after a team scores a
basket, the ball goes back into play in the possession of the other team.
In statistical terms, this tends to create a negative correlation between
consecutive goals (counting the two teams as having opposite signs) so the
RANDOM part of the variation in differential scores is less than binomial.
To put it another way, the difference in scores (disregarding important
complications like foul shots) is essentially the difference in the number
of turnovers, where one team loses possession of the ball before scoring.
Since turnovers are relatively unusual in basketball, variance is reduced.
Of course the SYSTEMATIC part of variation due to difference in skill
could be large or small, but the top teams will often be fairly evenly
matched.
The same rule applies in football, but turnovers are more common there.
In baseball, on the other hand, scoring opportunities often arise in
clumps due to the incremental nature of pushing baserunners around the
bases (as well as more subtle factors like pitcher fatigue) so lopsidedly
varying scores (often swinging back and forth even in a short series
between the same teams) are quite common.
All of this lies in the burgeoning field of sports statistics which now
has its own ASA section, journal, etc. so I hope we won't get stuck on it
here, unless somebody writes a package! and also my excuses to the R
users at the big state university basketball powerhouses in the U.S. who
probably know much more about this than I do.
Alan Zaslavsky
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