From: tedward@cs.cornell.edu (Edward [Ted] Fischer)
Subject: Re: Bases loaded walk gives Reds win in 12
Organization: Cornell Univ. CS Dept, Ithaca NY 14853
Lines: 87

In article <mssC5y5u0.4Dn@netcom.com> mss@netcom.com (Mark Singer) writes:
>
>Actually, I think the large-scale sample size is part of the problem.
>It seems to me that if we were to plot all the players in baseball
>in regard to BA vs. Clutch BA deviation we would get some kind of
>bell curve.  (The X-axis being the +/- deviation in clutch hitting
>vs. non-clutch;  the Y-axis being the number of players.)  Certainly
>there would be *some* players on the extreme ends of the bell.

Right.  Most definitely.

>My *supposition* is that if we were to find the SAME players
>consistently (year after year) at one end of the bell or the other,
>then we might be able to make some reasonable conclusions about
>*those* players (as opposed to all baseball players).

This may be the root of the confusion...

Please consider the following hypothetical with an open mind.  Note
that I am *not* (yet) saying that it has anything to do with the
question at hand.

Suppose we have a simplified Lotto game.  You pick a number from 1-10
and win if that number is drawn.  Suppose we have a large population
of people who play this game every week.

In the first year of the game, approximately 1/4 of the population
will win 7 or more times.

In the second year of the game, 1/4 of those 7-time winners will again
be 7-time winners.

In the third year of the game, 1/4 of those who won 7 or more times in
each of the first two years will win 7 again.

Suppose I started with 1024 people in my population.  After three
years, I have 32 people who have consistently, in each of the last
three years, won 140% or more the number of times expected.

Do we expect them to be big winners in the fourth year of the game?
No.  Because we know there is no skill involved.  Nothing about these
"consistent winners" can influence their chances of winning.  But
suppose we *don't* know whether or not there is a chance that skill
might be involved.  Perhaps some of the people in our population are
psychic, or something.  How would we test this hypothesis?

We can look for correlations in the population.  Now most of the
population will show zero correlation.  But our psychics should show a
high positive correlation (even if they aren't very good psychics,
they should still manage to win 7 or more times most years).  Net
result?  A small positive correlation over the entire population.

>This probably brings us to the heart of the disagreement I am having
>with others on this topic.  Must any conclusion based on statistical
>history be able to be applied broadly throughout a data base before
>it has any validity?  Is it impossible (or irrational) to apply
>statistical analysis to selected components of the data base?

Well, zero correlation is zero correlation.  You mention that Sabo has
hit poorly in the clutch over the last 3(?) years.  But if we look at
the past, we find that clutch patterns are just as likely to reverse
as they are to remain consistent.  The length of the streak doesn't
seem to make a difference to the probability that the player will be
clutch or choke the next year.  Is there any reason to expect *this*
streak to be different from past streaks?

Now if it were true that "75% of all three-year streaks remained true
to form", then we might have something useful.  But then we wouldn't
have zero correlation.  Instead we have "50% of all three-year streaks
remain true to form, and 50% of all three-year streaks reverse".  You
look at those numbers and say "three year choke streak implies more
likely to choke this year".  But it would be equally valid to look at
those numbers and say "three year choke streak implies more likely to
be clutch this year", since the probabilities are split 50-50 each
way.

>I completely accept that reasoning.  Again, what if we were to find
>the same individuals at each end of the spectrum on a consistent
>basis? 

Then we would have something useful.  And we would also have a
positive correlation.  But for every individual that exhibits such a
pattern and holds true, there is another who exhibits such a pattern
and then reverses.

Cheers,
-Valentine
