From: guilford@otago.ac.nz
Newsgroups: rec.sport.baseball
Subject: Re: Cecil signs :-( :-( :-(
Date: 27 Jan 93 15:08:00 +1300
Organization: University of Otago, Dunedin, New Zealand

Retorted <2356@blue.cis.pitt.edu>, genetic+@pitt.edu (Dr. Dave):

> Thus spake tedward@cs.cornell.edu (Edward [Ted] Fischer):

>>  [David Grabiner said:]

>>>I don't believe this is true, though.  The value of a player to your
>>>team does not depend on standard deviations; it depends on the number of
>>>games he helps your team win and lose.  If you trade a shortstop who
>>>slugs 50 points better than average and an average first baseman for an
>>>average shortstop and a first baseman who slugs 50 points better than
>>>average, your team will still score the same number of runs.  Since you
>>>break even on the trade, you must have traded players of the same value.

>>After some thought, I have to disagree.  The key isn't value-above-
>>average.  The key is value-above-replacement-level.  Which is
>>significantly below average.  Therefore 50 points above average is
>>more valuable at a position with a higher variance in talent.

First of all, you guys are just on the wrong track.  Start by thinking
about the entire distribution of talent at the position.  All of these
other things -- replacement level, average, variance, etc -- are just 
useful ways of describing (or summing up what is interesting about) the 
distribution.  

When you say, Fielder is x above the average, you have attached his
value to Frank Thomas's.  Is it?  If Frank Thomas left baseball to work
as a fireman, would that make Fielder more valuable?  (Notice that I'm
not trying to answer this question).

When you say, Fielder is y above replacement level, you are saying that
it doesn't matter whether all of the other 1B above replacement are
Frank Thomases or Mark Graces.  Is this true?

Average is at least a statement about a part of the distribution (the part
above replacement level), whereas replacement level is just telling you
where one point of the distribution is....

I think D Grabiner's reasoning about the 4-player swap (above) is more or
less right, but it doesn't tell us whether the average shortstop is equal
in value to the average first baseman -- it hasn't been ruled out that the
average first baseman could be equal in value to the 50 pts above average 
SS....

> We've had portions of this discussion before, but I think I've finally
> figured out how to state my case for average value in this context.  Bear
> with me...
> 
> I'm going to claim that useful things, in general, have two different kinds
> of value: use value, and market value.  In an imperfect market, these two are
> seldom the same.  

Ouch ouch ouch ouch ouch.  To begin with, it might help to think about
what kind of imperfections are plaguing this market.  Is there imperfect
information?  Transactions costs?  What?

> The classic example is a used car.  *Any* car that runs has
> a use value equal to what it would cost you to get around town if you didn't
> have a car that runs.  This is a huge amount of money.  On the other hand, a
> car's market value (what you can get for it in trade or sale) goes to zero
> long before the use value does.  This is oversimplified, but you get my drift.

Note that you might also use the words use value in a quite different way,
so that the use value goes to zero first -- like, why do most of us only
own one car?

> Now, I claim that this applies to baseball players, too.  A player's use value
> is what he does to your chances of winning when he plays.  Since winning is
> defined as scoring more runs than your opponent does, this value consists 
> solely in how much he contributes to your run differential.  Run differential
> is not a function of who the worst player in the league is, but rather of who
> is actually playing in the league.  Thus, average value at a given position
> is the relevant baseline for use value.  

Since any number (say, 0) will do for inter-positional comparisons, what
average value gives you is a method of comparing players at different
positions.  So this must mean that an average shortstop has the same
value ("use value") as an average 1B.  This in turn must mean that if
Frank Thomas hits 10 more homers, you can trade Cecil Fielder for a 
crummier shortstop without losing any runs....

> come in, so that a Ryne Sandberg or Barry Larkin has a much higher trade value
> than an equivalently above-average 1B or DH, even when having the same use
> value when played.  

Why?  If their use value ("chances of winning when he plays") is the 
same, why is the market value different here?  So the one is scarcer,
who cares if it doesn't affect the W-L columns?  

Lee Stevens use value, by your definition, is his value if Montreal
actually plays him.  His market value, I would guess, takes into account
the likelihood or opportunity costs of having someone better.  I'm not
sure I see why this is an interesting distinction....  (You haven't
established that there isn't a one-to-one relationship).

It seems to me though, that "value" as it is being used in this thread
is neither of these two types of value.  Market value, as noted here, 
will depend on what a player is going to do in future years, within the 
confines of the player's contract and baseball's labor set-up.  The value 
being talked about it is more of the single-season variety.  Brian Downing 
vs. John Olerud is another issue....

> Given a choice between a Tettleton or Larkin (very similar use values last
> season) and a Fred McGriff (about the same as the other two), you go for the
> catcher or SS because you expect another McGriff to come along in a year or
> three, whereas you may not see another Tettleton in your tenure as GM.

If Fred is helping you win as much as the others, why not?  Do McGriffs 
have shorter careers, or are there more of them?  If there are more of them,
why is their use value equal?  

> If you're only looking ahead one season, there'd be
> no reason to consider scarcity effects, and thus no reason to use anything but
> use value in your selection process.  Use values tell you what your chances of
> winning are; market values tell you about how easy/hard to improve it will be.

If McGriff's use value is as good as Tettleton's this year, why won't it 
be just as good as Tettleton's next year?

Sorry, but I think several things are being confused here.  There are
time effects, market imperfections, variances....  It all boils down to
a distribution of talent at each position, where the player is on that
distribution.  If you compare a 1B and a SS, you have to take into 
account your opportunity costs, in terms of wins or expected wins 
(depending on whether you're evaluating last year or next year), at the
respective positions, which in turn depend on what those distributions look
like....  There is no reason for an average SS to be equal in value to
an average 1B, by any definition of value mentioned or alluded to above.
Replacement level is important, because it tells you something about
your distribution and your opportunity costs that average doesn't.                                         


> And I *still* don't see why you'd ever compare to replacement level directly;
> it's the variance that you're interested, not the lower bound.  

But what information about the variance is conveyed by the average?

Bill Guilford
Newsgroups: rec.sport.baseball