From: cabanrf@wkuvx1.bitnet
Newsgroups: rec.sport.baseball
Subject: Re: Plexiglass Cracks
Date: 21 Jan 93 17:58:56 CST
Organization: Western Kentucky University, Bowling Green, KY

In article <1993Jan20.090415@IASTATE.EDU>, tloughin@IASTATE.EDU (Thomas M Loughin) writes:
> Get out the earplugs, folks, she's about to blow...
> 
> In article <1993Jan19.170007.5082@wkuvx1.bitnet>, cabanrf@wkuvx1.bitnet writes:
>> While scanning the net, I started thinking about the Plexiglass
>> Principle, as promulgated by Bill James.  I asked if anyone had
>> done more work with this and never got a response so I designed
>> the little study below to provide a test of this principle.

Upon further reflection, I didn't test the principle (yet ! ;-))  I
tested an implication which was inherent in Bill James' statement.
Specifically, the second statement quoted.


>> 
>> In his 1982 Abstract James says "all things in baseball have a
>> powerful tendency to return to the form they previously
>> held.......As applied to teams note how consistently an up is
>> followed by a down and vice versa:"  What Bill appears to be
>> implying is that at time T, the performance at time T minus 2 is
>> a better predictor of performance than other years.

What I tested was the second statement, not the first. 

> No one, not even someone misinterpreting James' intimations, should 
> sensibly think that is true.  What he is referring to, albeit perhaps 
> obtusely, is the simple statistical principle of "regression toward the 
> mean."  This is not in any way to be confused with the notions of 
> improvement or decline.  
> 


Wait a minute.  Are you saying that a performance at time T is neither
an improvement nor a decline from the performance at time T-1?  ;-) 
I'm sure that's not the case.  But when you put this in terms of
looking at the team for time (T+1) then it is either an improvement or
a decline (or they stay the same)  So when we are talking about
performance we're talking about an improvement or decline.



> Regression toward the mean suggests that observations following one 
> which has a large deviation from the mean (average) tend to be closer 
> to the mean that their predecessor.  Sons of 6'8" fathers tend _on 
> average_ to be shorter than their fathers, just as those of 5'1" 
> fathers tend to be taller.  This is not to say that _every_ son of a 
> tall father will be shorter, just that an even-money wager is 
> well-placed on "shorter." 

Yes, but why?  Is what is being said like this (trying to paraphrase
from above).  The observation at time T-1 occupies an extreme position
in terms of the distribution of the won/loss percentages.  Therefore
it is likely that the NEXT observation will not be so extreme.

> 
> In baseball, this manifests itself as sudden changes in the observed 
> level of a team or player.  When a team goes from last to first 
> _without having made substantive changes in that direction_, they are a 
> good bet to drop back down to the previously-established level of 
> performance, assuming that no further changes are made in the next 
> year.  Nobody with a brain and a calculator expects Brady Anderson to 
> repeat his numbers of last year.  He just hasn't changed himself _that_ 
> much.  However, that doesn't necessarily imply that he hasn't 
> established some new level of performance for himself.  It just isn't 
> likely to be as radically different from his career numbers as last 
> year was.  
> 
So if I wanted to predict his performance this year, his career
numbers should be a better predictor than last years performance? 
That's what I thought too, but the regression said nope.


>> Taking the 1978-1990 seasons I constructed a dataset where each
>> year had the last 5 years won/loss percentages. 
> 
> Excellent! Attack the problem with numbers.  Set up a study to prove 
> (or disprove) a hypothesis.
> 
>> Using a multiple regression with performance at time T as the
>> dependent variable and the teams performance at times T minus one
>> through five as the independent variables gave the following
>> results:
>> 
> Well, it was a nice idea, anyway.  This isn't going to help show much 
> of anything that we didn't already know, and it certainly isn't likely 
> to turn up anything contrary to the regression toward the mean 
> principle. 
>  
> Your individual observations are not going to exhibit anything near the 
> independence required for this type of analysis.  To wit:  in one 
> observation you use Boston's 1990 results as Y, believing that 1989, 
> 1988, and so forth might be good predictors.  In the next observation, 
> you use that same 1989 result as Y, and in the next, 1988.  In order to 
> get ANY kind of reliable analysis results, you'll need INDEPENDENCE 
> among your Y-values.  You just don't have it here.  Instead, you're 
> predicting essentially the same things over and over again.   
> 
Concur.  I was expecting a LOT of multicollinearity.  But look there. 
We don't have it.  Frankly, I expected every one of the variables to
be in there and significant due to multi.  I put the output in at
least partially because of that.


>> First, the best predictor, among these variables is THE PREVIOUS
>> YEARS PERFORMANCE!! By itself it explains about 12% of the
>> variance in won/loss percentage.  If you add two years ago, you
>> explain another 2% of the variance.
>> 
> What this means is that there are more teams that show small changes  
> in performance than there are those that change drastically from year 
> to year.  I'm not a bit surprised; it does nothing to refute James' 
> argument.   
> 
Like I said in my reply, I'm not sure you can draw this conclusion
from that output.  What you say here is intuitively obvious and
believe it or not I agree with your statement.  But I don't trust
intuition ;;-).  Not since I drafted Julio Franco last year.  (Hey he
looked healthy!!)


>> Third, neither one is any great shakes as a predictor of
>> performance (r-square of .14)
>> 
> Makes ya wonder what _would_ work, don't it?
> 
Sure does, but I'm young.  

>> To conclude:  We have statistical evidence that the plexiglass
>> principle does not hold true for teams (which is what the
>> original analysis was based upon.)  We have anectdotal evidence
>> that the plexiglass principle does not hold true.  I think the
>> plexiglass principle needs a HARD look.
>   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>> 
> That's true.  
> 
Let me rephrase that:  We have statistical evidence (weak but still
evidence) that a portion of the arguement that Bill James used as
support for the PP is wrong.

> What I'd like to see is the following:
> 
> Go through the books and find teams whose winning percentages took 
> "big" jumps (up or down) from one year to the next.  Then look at their 
> next year's results.  THIS is what the "plexiglass principle" is 
> _really_ about.  Define "big" in some suitable way that you aren't 
> including practically everyone in the analysis.  Maybe use several 
> definitions, so we can find out how much effect there is (if any) for 
> different-sized jumps.  
> 
I havn't done this yet but it can be done.  A big part of my problem
is that I only have 14 years of data for the majors.  Anyone have a
LOT of data.  Get me the data and I'll run it.

> Take differences (Y2-Y1) and (Y3-Y2), where the Y's are the yearly 
> winning percentages.  Let's see what that tells us.  Anyone care to try 
> it?
> 
See if this helps.  Ill use a year as an example:  I created a
variable  DIFF= 1989-1988.  I then did a regression with T as the
dependent variable and diff as the independent variable.  The results
were no significant relationship between Diff and T. 

Thinking that the problem required a nominal type approach I did a
recode and checked to see if there was a relationship between the
change from (year T-2 to year T-1 ) and (year T-1 to T).  Again no
significant relationship (p.=.78).

What I have not done yet was two things.

Select only those cases where there is a large movement in the W/L
percentage.  (How will we define large?  I really dislike throwing out
data to make a hypothesis fit.)  Thendo the regression.

Do the regression using factor scores.  This will eliminate
multicollineatity.
   
> C'mon, it'll be fun!
> 
Concur, that's why I did it.

>> Statistical analysis attached for your information.
> Good Idea!
> 
> Let me make it clear:  I'm all in favor of this effort.  The 
> implementation and interpretation just missed the mark.  The answer's 
> out there somewhere.  We'll find it eventually.
> 
> -Tom
Ok, so there were some goofs.  But I still think that the basic idea
of testing this "Principle" is valid.  Principles are like laws.  They
need a LOT of evidence in their favor.  The piece by Jammes that I
cited had only 4 years worth of data, and it doesn't test the
principle (ok so I didn't either, yet).  It merely said, look at this
pattern.  This pattern holds true.  That's good as far as it goes. 
What it doesn't say is when does the pattern not hold true and whether
the pattern is due to chance or is there something of a causal nature
at work here.  These ideas can be tested, so lets do it.

BTW, why did you assume that I would flame to a response?
I put this on the net for discussion in the hopes of establishing
something that folks would regard as a definitive test of the PP.


-- 
Roy F. Cabaniss......................*Wait till Tommy meets the Lord and
Western Kentucky University..........*finds out that He's wearing pinstripes.
All opinions contained herein........*Gaylord Perry (talking about Lasorda)
Are all mine own, and that's the sin.*Baseball, what a way to spend a day!!
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