From: genetic+@pitt.edu (Dr. Dave)
Newsgroups: rec.sport.baseball
Subject: Re: Cecil signs :-( :-( :-(
Date: 22 Jan 93 21:05:51 GMT
Organization: Department of Industrial Engineering

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.

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.  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.

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.  (Note for bob vesterman: I agree that
you can't compare a SS to a DH without normalizing for which one is going to
get more PA, which will favor the player with the higher absolute offense.  I
don't think that such an adjustment changes the basic point here, which is 
you want to compare with respect to average, and not w/r/t replacement level.)

On the other hand, a player's *market* value is affected not only by his use
value, but by how scarce such a use value is.  Here is where variance effects
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.  This is also why Mickey Tettleton for Jeff Robinson was
probably among the top-5 dumbest trades in history.  Not only is Tettleton's
use value exceptionally good, but his market value (should be) even higher.
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.

So, I guess I'm claiming that you should draft and trade based on market
value (as well as use value), but evaluate the team you *do* put on the field
according to use value.  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.

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.  Replacement
level tells you how badly your team's winning percentage would fall if all the
shortstops in your organization were killed by a freak meteor shower, so that
you had to go out and sign AAA players and released major-leaguers.  That has
nothing to do with your chances of winning the players you *do* have.


-- 
       David Tate        |"Something there is that doesn't love a wall,
 dtate@unix.cis.pitt.edu | That sends the screaming liner over it 
 Prof. of Story Problems | And spills the bleacher-dwellers from their seats."
 Member ORSA, TIMS, SABR |  	"Fenway Wall", Robert Frost