Subject: Re: Eck vs Rickey (was Re: Rickey's whining again)
From: smith@ms.uky.edu (Brian Smith)
Expires: Sat, 1 May 1993 04:00:00 GMT
Distribution: usa
Organization: University Of Kentucky, Dept. of Math Sciences
Lines: 169

In article <6998@blue.cis.pitt.edu> genetic+@pitt.edu (David M. Tate) writes:
>I've read all of the followups to this, but I thought I'd go back to the
>original article to make specific comments about the method:
>
>
>jao@megatest.com (John Oswalt) said:
>>
>>He has obtained the play by play records, in computer readable
>>form, for every major league baseball game for the past several years.
>>He devised an algorithm which I call "sum-over-situations", and wrote
>>a computer program to calculate every major league players contribution
>>using it.  It works like this:
>>
>>Look at every "situation" in every game in a baseball season.  A
>>situation is determined by inning, score, where the baserunners are,
>>and how many outs there are.  For each situation, count how many
>>times the team eventually won the game that the situation occured in,
>>and divide by the number of times the situation came up, to come up with
>>a "value" for that situation.
>
>This was first done by George Lindsey in the late '50s/early '60s, and
>reported in 
>
>	Article:	An Investigation of Strategies in Baseball
>	Author:		George R. Lindsey
>	Journal:	Operations Research
>	Issue:		Volume 11 #4, July-August 1963, pp. 477-501
>
>Later, Pete Palmer did the same thing using simulated seasons to generate
>a larger set of data to avoid the kind of small-sample anomalies that other
>people have worried about.  He reported this in _The_Hidden_Game_of_Baseball_
>(with John Thorn).  Gary Skoog modified the method a bit and did some work
>on what he called a "Value Added" measure based on these situational values.
>His were based directly on marginal runs, though, not on win probabilities.
>These results, as applied to the 198? season, were reported in one of the
>Bill James Baseball Abstract books (1987?  Help me out here, somebody...)
>
>>For example, a situation might be inning 3, score 2-0, runner on second
>>and no outs.  There were 4212 regular season major league games last
>>year.  (With the Rockies and Marlins, there will be more this year.)
>>Say this situation came up in 100 of those, and the team ahead won
>>75 of them.  Then the value of this situation is 0.75.
>
>[Description of method: look at change in win probability based on the at bat
> plus any baserunning, and credit/debit the player by that amount each time
> he gets a plate appearance.]
>
>>Now, for each player, sum up all his at-bat and base-running values
>>for the season to obtain an overall value for that player.  Obviously
>>the sum of all players' values for each game, and for the season as a
>>whole, will be 0.
>
>That's only because you always credit +x to the batter and -x to the pitcher;
>there's no validation involved.
>
>OK, there's a very big problem here that nobody has yet commented on: you're
>adding *probabilities*, and probabilities don't add.  Runs you can add; the
>total team runs breaks down into how many runs Joe contributed plus how many
>runs Fred contributed, etc.  But probabilities don't work that way.  If Bob
>increases his team's chance of winning by 1% in each of 400 PAs, that does
>not mean that Bob increased his team's chance of winning by 400%.  In fact,
>it doesn't mean *anything*, because the units are screwy.

I agree and disagree.  John is saying that the batters efforts will result
in 4 more wins then losses.  While you are probably correct that 400%
does not mean 4 more wins then losses, it means something.  I would
rather have a player who increased my teams chances of winning by 1% in
each of 400 PAs then I would a player who increased my chances of winning
by .5% in each of 400 PAs.  Thus, there appears to me to be an obvious
positive association between John's statistic and winning games.  Thus,
before you disregard this stat, it appears to me that further study must
go into what sort of relationship there is.

>Consider an example:  Bob hits a 2-out solo HR in the bottom of the first;
>about .12 on your scale.  He does the same thing again in the fourth, with
>the score tied, for another .14.  And again, in the seventh, with the score
>tied, for another .22.  And, finally, in the ninth to win the game by a score
>of 7-6, for a value of 0.5.  Bob hit 4 solo HR in 4 plate appearances, and
>was credited by your method with .12 + .14 + .22 + .5 = .98.  But what does
>that mean?  Was Bob 98% responsible for the win?  Certainly not; the defense
>is *always* 50% responsible (if you include pitching in that), and Bob wasn't
>pitching.  In fact, Bob was only 4/7 of the offense (which is a lot, but not
>even close to 100%).  Furthermore, what about the other 3 team runs?  Say
>they all came on solo HR by Fred; then Fred was hitting HR to tie up the game,
>which are just as valuable as HR to take the lead (see Lindsey), and Fred will
>himself have accrued a good .4 rating or so.  So Fred and Bob combined have
>amassed 138% of a win IN ONE GAME.  There's clearly a problem here.

The only problem here is an insistance that these number mean exactly
how many wins the team has.  First, we are using averages over many
seasons and applying them to one game.  Second, remember some players
performance take away from the chance of you winning.  That is a
player who gets an out gets a "negative probability" in most cases.
Thus, I'm not sure in any given game when you add up all the numbers
for a team who won that they will add up to 1 in that game.  Sometimes,
they will add up to more then one sometime, less than one.  Also,
the pitchers' bad performances (giving up 6 runs) may have given
them a large negative percentage for that game.  Also, any batter that
pulled an 0-4 night would give large negatives.  



>>Greg thinking about the right things, but his intuition is off the
>>mark.  Closers are enormously important.  The total number of runs
>>value is outweighed by when they come, or are prevented from comming.
>>The doubling which Greg allows is not enough.
>
>In another article, I proposed a test of this.  We can predict a team's 
>won/lost record quite accurately by looking at how many runs *total* they
>score and allow, without regard to when those runs score in the game.  If
>late runs are really more important than early runs, then looking only at
>late runs should lead to a *better* predictor, right?

No, but really only because you have a smaller sample size.  I would
think however, that the number of runs you score in the first inning
would be just as good as a prediction as how many runs you score 
in the last inning.  And, realize something else a closer usually
comes in in a close situation, not a blow out.  It is hard to argue
that any runs that a closer gives up in a game have equal importance
to those given up in the first inning.  Look, a closer giving up runs
often means a team will lose many games.  On, the other hand a starter
who gives up runs often still leaves his team a chance to win.  The
offence has many more outs to do something about.  But, I am not
saying all late inning situations are equally important either.  If
I am down 8 runs in the ninth, it really does not matter how many
runs my pitcher gives up in the ninth.       

>Here's another thought experiment: apply this method to basketball.  What
>you find is that points scored in the first *half* of the game have almost
>exactly no value, because no lead is safe with an entire half yet to play.
>Furthermore, the sub in off the bench who sinks the winning free throws with
>no time on the clock gets a +1.0 for the game, while the star forward who 
>scored 27 points in the first half before spraining his ankle gets a zero.
>
>Does this make sense?


No, but why would you assume that the teams probability of winning would
be 0 before the possesion in which the free throws were made.  Look,
if you are down 1 point with 5 seconds left, there is a fairly high
probability that you will win the game if you are in possesion of the
ball.  And, do not forget that somebody elses missed shots, turnovers,
fouls, bad defense, etc. caused a "negative chance" that the team
would win.
 
From reading all of the discussion on this statistic, I feel that those
who critisize it to a certain extent are doing so out of an agenda.
At first look this statistic valadates clutchness.  But, it really
does not.  Cluthness revolves around the idea that certain players
in crucial situation elevate their performance and others performance
goes down.  I've never seen convincing proof that this really happens.
So, if you assume there is no clutchness, then that means that except
for a lot of noice, this statistic has a positive association to
player performance.  There is a way to get rid of the noice if you
do not believe in clutchness.  Certainly, we could find out what
the average value of a home run is for example.  We may find for
instance, that a home run increases your chance of winning by 15%
on average while a strikeout decreases your chance of winning by 5%.
I bet if this were done we would find that this statistic was just
as good as other statistics we have for predicting wins and losses.

How do we evaluate relief pitchers?  Say John and Sam have the
exact same pitching statistics (runs, earned runs, K's, BB's,
etc.)  Both had exceptional numbers.  John, however only pitched
in closer situations, while Sam was a Mop up man.  Who was more
valuble to their team?  Probably John.  Who was the better 
pitcher?  They were probably about the same.

                                                        Brian Smith
