From: thornley@milli.cs.umn.edu (David H. Thornley)
Subject: Re: Bonds "choke"?
Organization: University of Minnesota
Date: Tue, 6 Oct 1992 21:27:33 GMT

In <1992Oct5.212051.11815@odin.corp.sgi.com> kubey@sgi.com (Ken Kubey) writes:

>In article <GRABINER.92Oct5144048@birkhoff.harvard.edu> grabiner@math.harvard.edu (David Grabiner) writes:
>>In article <1992Oct5.144730.18495@odin.corp.sgi.com>, Ken Kubey writes:
>>
>>> In article <1992Oct4.214410.23833@midway.uchicago.edu> thf2@midway.uchicago.edu writes:
>>
>>>>Or could it be, just maybe, that if you take 270 players and have them
>>>>face the top pitching staffs in the league in short series there is
>>>>a good random chance that two of them will go 0 for 16?
>>
>>> Sure.  Note that we are really talking about 0-20.
>>> Anyone know Gene Tenace's overall BA for the years in question?  
>>
>>> If my calculator and brain are working right, the chance of a .300 hitter
>>> going 0-20 is 0.000798 or 0.0798%.
>>
>>[Tenace wasn't that good a hitter, and so the chance he would go 0-20
>> is much greater.]
>>
>>Likewise, the Bonds predicted BA is too high, and chance of an 0-20
>>streak too low; he doesn't get to face the fifth starters on last-place
>>teams.  .002 for a *specific* streak of 20 AB is probably closer.

>I think your calculations are pretty good.  A 20-30 point drop in average
>seems reasonable in the LCS.  Nonetheless, we still see that Tenace's
>0-20 was 3 times more likely than Bonds'.  While the pure numbers were
>the same (0-20), the Pirates lost more of their expected offense.

Don't forget that Bonds has faced left-handed pitching about two-thirds
of the time in the LCS, as opposed to about one-third of the time in the
regular season.  He hasn't had much of a platoon differential in the past
two years, but facing extra lefties isn't going to help him.

>>Given the number of places that you could have found an interesting
>>streak, the fact that you found one with probability .002 doesn't
>>suggest that something unusual is happening.

>I think it *does* "suggest" that something unusual is happening.
>It doesn't prove anything, but it certainly suggests something.
>.002 is still a 500-1 longshot.  Interestingly, this streak happened to
>one of the leagues most feared hitters in the most important games
>he has ever played. 

Yes, but this isn't a 500-1 longshot.  What you have done is found an
oddity in the data and pushed it for all it's worth.  Had you posted a
prediction before the 1990 NLCS that Bonds would end the 1991 NLCS tied
for the longest streak of hitless ABs with men on base, this would be a
real and legitimate longshot.  Instead, you have looked at the data ex
post facto, and carefully selected the facts that look odd.

You could have calculated the probability that Bonds would have such a low
LCS OPB or BA (SLG is more difficult to calculate).  You could have done this
under several different conditions, including RISP, runners on, LIPS, or
bases empty.  You could have done this on any of dozens of players who
have been in 10+ postseason games in the past few years.  You could have
made a cutoff of 15 AB with runners on, in which case the odds would be
less, or a cutoff of 25 AB with runners on, in which case the odds would
be less (because, I presume, a hit would be in there).

I don't know how many things I would find equally surprising if they
occurred, including Canseco failing to hit, Rickey Henderson being caught
stealing, consecutive Oakland shutouts, etc.  I suspect I could easily make
a list of over 25 surprising and significant things that could have
happened, whereas the only one that did was Bonds' streak.  

Consider dice.  I roll a die four times and get 6, 6, 2, 1, an event that
happens once in 1296 times (assuming a fair die).  It is just as likely as
getting 6, 6, 6, 6.  Now, assume we play a game in which we roll different
dice different numbers of times.  If we have a large number of dice, it's no
surprise if one does something significant, like roll 2, 3, 4, 5 or all 4s.
If one die out of 50 rolls four times and gets all 6s, how unusual is that?
You could expect that once in 25-30 games.  However, is that more significant
than rolling all 1s or 3s, or rolling a straight?  What if the die is rolled
5 times and gets 6, 6, 6, 6, 2?  Obviously, even if the probability of one
die rolling four 6s is 1 in 1296, that number is largely irrelevant to
how likely we are to see unexpected results in rolling large numbers of dice.

Now, Bonds' failures in the NLCS are significant, and certainly important
for Pittsburgh, but it's real difficult to determine their *statistical*
significance.  For the record, I think it's a statistical fluke, and that
he will do well in this NLCS.

David Thornley
"like quoting numbers to statheads" - popular proverb, replaced one about
eliminatory activity under adverse meteorological conditions c. 1995
- Encyclopedia Galactica
Newsgroups: rec.sport.baseball