Newsgroups: rec.sport.baseball
Subject: Re: Better Than Runs II
From: guilford@otago.ac.nz
Date: 5 Oct 92 14:41:11 +1300
Organization: University of Otago, Dunedin, New Zealand

In article <6656@blue.cis.pitt.edu.UUCP>, genetic+@pitt.edu (Dr. Dave) writes:

> Thomas Hyer writes:

>>  Now, how many wins are two extra runs worth?  

>>First,
>>you change 10.2% of the games from outright losses to
>>outright wins.  

>>Then you add half of the games you would
>>have lost by 2, which now go to extra innings, and half
>>the extra-inning games, which you now win outright.  Thus:

This is an answer to the question, "how many wins are two extra runs
in one game worth?"  (I see no point in the loose wording).

>>  Runs    Wins		<== actually, marginal winning percentage shift?
>>  ----    ----
>>   1      .104
>>   2      .200
>>   3      .281
>>   4      .346
>>   5      .396
> 
>>That is, if a team was spotted three runs, it would win about
>>.781 of its games (against equal opposition).

> So far so good.  I have no problem with your "equal opposition" caveat,
> and never did.  The question is whether this is the correct thought 
> experiment. 
> 
> Is the assumption of a fixed bonus per game a reasonable one for modelling
> the marginal value of runs?  You're talking about the change in winning
> percentage for a team that gets 1, 2, 3, etc. extra runs per game; we can't
> compare actual history with the model's predictions for more than about 1
> run per game; how many teams are 162 runs above league average in scoring?

Actually, it's perfectly reasonable to add things up this way.  What is
the value of one run?   Truly, this one run must occur in a particular
game, so if you know the expected probability of that run turning that
game from L to W, that should give you the marginal value.

Caveat 1: You have to make sure you've calculated this expectation
properly.  In particular, runs don't occur "randomly," since teams
will make decisions (strategy, personnel) based on the score.  

Caveat 2: The value of a second run is close, but not quite the same
as, the value of the first.  Whether or not you're talking about "two
runs in one game" or "two runs in one season" becomes important.  If
it's the latter, then you have a large probability of "one run in each
of two different games," and a small probability of "two runs in one
game," and you have to aggregate properly....

Caveat 3: If you're calculating the marginal value of runs (or the
value of 1 run) at a point (e.g. a team that scores a league average
number of runs against league-average competition), then using this
to determine the value of, say, 100 runs, there may be an error involved
with simply multiplying the marginal value times 100.  E.g., what if 
the point you've calculated your marginal value at is a maximum or
minimum?

Caveat 4: Other (extant) methods are easier.

>>Now, how can we isolate the contributions of players which
>>lead to scoring 1,2,3.. extra runs?

> You might want to check out two articles by George Lindsey:
> 
> 	"The Progress of the Score During a Baseball Game", 1961,
> 	_J._Am._Stat._Assoc._ Volume 56, pp. 706-728.
> 
> 	"An Investigation of Strategies in Baseball", 1963,
> 	_Operations_Research_, volume 11, pp 477-501.

Never, ever, read up on an area before you try and do work in that area.
A bad, pointless, counterproductive idea.

Bill Guilford