Re: Basketball pitch

["Steven M. Boker" <smb3u@xxxxxxxxxxxxxxxxxxxxxxxxx>]

There are several problems being discussed here.  First the statistics.

If we want to understand the likelihood of "D" we must incorporate both
the mean and variance of "D" into the model.  But we must also have some
sort of control against which to measure the distribution of frequencies
in the initial pitch of the chant.  Dan Levitan has suggested the
distributions of individual mean speaking pitch.  This would provide
an interesting test.  I would suggest that there is far less variance
in the "D" of the initial pitch of the chant than in the distribution
of individual mean speaking pitch.  In this way we could test the
difference between the two distributions.  An interesting comparison.

However, this brings up the second problem.  Standard statistical
techniques assume independent samples.  While each individual's mean
speaking pitch may represent an independent sample making up a
distribution, the chanting at a basketball game is highly likely to
be a self-organizing system.  The individual voices in the chant
are likely to not be independent samples.  Thus, one does not have
10,000 degrees of freedom in the distribution of pitches from the
first part of the chant.  It is not clear to me how to adjust for
this bias which will certainly reduce the variance in the pitches
in the chant other than by having a sample of people sing the chant
one at a time and comparing that variance to the variance at the
game.

Steve Boker
boker@virginia.edu