From: genetic+@pitt.edu (Dr. Dave)
Newsgroups: rec.sport.baseball
Subject: Re: Better Than Runs II
Date: 1 Oct 92 21:19:56 GMT
Organization: Department of Industrial Engineering

First, the drivel:

Thus whined IOR@SLACVM.SLAC.STANFORD.EDU (Thomas Hyer):
 
>Please, people, if you don't understand what I'm saying,
>do me a favor -- assume it's you, not me.
>
> [...]
>					Sherri Nichols
>and Dr. Dave should now go and look up `thought experiment').

If you want people to understand what you're saying, then say
what you mean.  If you want people to take your thought
experiments seriously, pick one that's relevant to the question
you're addressing.  The one you used before illustrated the
effect of variance in run scoring, not the decreasing marginal
value of additional runs.

Now, the real stuff:

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

It depends on the variance.  Are you talking about being spotted 2 runs at
the start of every game, or scoring an extra two runs per game, on average?
From the calculations below, it looks like you mean the former.  Am I failing
to understand you again?

>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:


>  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?

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

Honest question here: do you mean extra runs per game, or total extra runs?

[stuff deleted]

>If I think of anything further, I'll post it.  I would like
>to hear feedback from people who understand the problem.

How discriminating of you.

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.

The first gives probabilities for winning as a function of inning and number
of runs ahead/behind.  These also assume equal opposition.  The second is a
mixture of various topics, including the first attempt to assign situational
values to particular batting outcomes, based on their effect on various
probabilities.   It also extends the first paper, and examines various
managerial decisions (sac bunt or not, steal or not, etc.) in light of 
expected returns and probability of scoring at least one run.

-- 
       David Tate        |"Out of the dugout endlessly swinging,
 dtate@unix.cis.pitt.edu | Out of the manager's throat, the sound fundamentals,
 Prof. of Story Problems | Out of the six-month season..."            
 Member ORSA, TIMS, SABR | 	Walt "Lefty" Whitman