From: guilford@otago.ac.nz
Newsgroups: rec.sport.baseball
Subject: Re: Cecil signs :-( :-( :-(
Date: 29 Jan 93 16:29:44 +1300
Organization: University of Otago, Dunedin, New Zealand


Fulminated <2531@blue.cis.pitt.edu>, genetic+@pitt.edu (David M. Tate):

> First of all, I'm going to ditch the word "value", because it's clear to me
> that everyone in this discussion is so firmly tied to the notion that "value"
> must always mean "replacement value" that there's no point fighting it.

Value has a pretty standard meaning, which is tied to the idea of 
opportunity cost (hence, replacement).  Maximizing your definition 
isn't going to maximize your chances of winning -- maximizing an
opportunity cost based definition will.

Example: suppose you have only 3 teams, 3 positions (1B, SS and DH), and 
a league that lasts only one year.  Suppose each team's personnel can
be described in terms of wins above or below average, as follows:  

           1B    SS     DH         

team A     8.0  -5.0    1.3       
team B    -1.0   5.0   -2.0             
team C    -7.0   0.0    0.7             

Suppose that each team has a replacement-level backup at each position,
with this level being -12.0 at 1B, -5.0 at SS and -2.0 at DH.

Notice that no trades (or coalitions) are possible: the gains from trades
have been exhausted.  Team C would like to trade their above-average DH or 
their average SS for team B's below-average 1B, but team B won't do it.
Team A would like to trade their above-average DH for team C's average
SS, but team C won't do it.

Now suppose team B has another 1B who is -1.0 versus average.  They could
use this player to get team C's DH in trade -- and would become, just
barely, the best team in the league (initially, team A is 4.3 to B's 2.0,
after this trade it would be 2.3 to 2.7).

I think the usefulness of this example is limited, but some ideas or
notions are illustrated:

1. Team B's below-average 1B is clearly more valuable, by any reasonable
definition, than any DH, even the best one, in the league.  

2. Consider a team that is thinking of trading for Whitaker or Fielder.
Suddenly, Frank Thomas becomes twice as valuable, so that the average
level at 1B rises considerably.  How does this affect this team's thinking?
I don't see why Thomas's improvement affects Fielder and Whitaker
differentially just because Fielder happens to play the same position.
And just as their relative attraction to another team shouldn't change,
it seems to me their relative contribution to the Tiger's efforts remains
unchanged as well.  I still fail to see why distance from league average
has a meaningful imputation of value.

> What I want to do is to explain wins.  I want to point to a team and say 
> "They won 87 games; what were the individual contributions to that total?"
> Now, since winning is BY DEFINITION relative to your opponents' actual
> performance, and not to some hypothetical replacement level, it seems only
> reasonable to use your opponents' actual performance as the yardstick by
> which to measure where your wins came from.  That's why I advocate the use
> of league averages (or, actually, the average of everyone in the league but
> you) as the correct baseline for this sort of analysis.  It's a retrospective
> look (as Bob Davis correctly pointed out) at what happened in the past; not
> an attempt to gauge how hard or expensive or whatever it would be to replace
> the performance of a given player.

Okay, suppose that you want "to use your opponents' actual performance as 
the yardstick by which to measure where your wins came from."   League
average does this -- it gives you a number -- just as any other baseline
does.  But it only tells you "what were the individual contributions to
that total" in a very limited and artificial way.  Suppose from one year
to the next, the only change is that the performance of every SS in the
league improves dramatically.  According to the league average metric,
their individual contributions didn't change at all.  If the only
change was that the performance of an equivalent number of players 
selected at random improved, individual contributions are going to be
very different....  

Bill Guilford