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Re Working Batter Game Scores

May 30, 2023
                                 Re-Working Hitter Game Scores


            You may remember. . . or may not; I don’t talk about it a lot. . . .but you may remember that two or three years ago I finally hit upon a way to figure a "Game Score" for a hitter,   The mistake that I had been making, which prevented me from being able to make this work for 30-some years after I developed the pitcher’s Game Score, was trying to center hitter’s Game Scores at 50.  Doing that contradicts the essential nature of a hitter’s production, which is not symmetrical by games.

            Basically, a Hitter’s Game Score as I developed it at that time, was:


                        + 10 for each run that he created,

                        +5 for a run scored,

                        +5 for an RBI

Conceptually simple, and it works.   To make it work, I had to invent a way to estimate Runs Created by a Hitter in a game, but that was worth doing for its own reasons.  An average game by a hitter is at 25.0, which is where it has to be, and virtually all games are between zero and a hundred.  

            However, an issue with this structure is that a hitter starts out at 15 and, in an "average" game, works his way up to 25.  Baseball teams historically score 4.50 runs per game, or something very, very close to that.  The average hitter in a 9-man offense creates 0.50 runs per game, which also means that the average hitter SCORES 0.50 runs per game, and drives in most of those, so an average hitter in an average game will come in at 15 + 5 + 2.5 + 2.5.   More or less. 

            But this is different than the structure of PITCHER game scores.   In a pitcher’s Game Score the pitcher starts out at 50, and goes up or down depending on the good or harm that he does for his team.  On average you start out at 50; you end up at 50.   For a hitter, you start out at 15 and end up at 25. 

            Neither approach could exactly be described as "right" or "wrong"; it is just what you are happy with.   The "right" answer is that which most accurately answers the question "How good a game was this, for the hitter?"  Sometimes I don’t like the pitcher’s system, starting in the middle.  It implies that if you don’t do anything, you’re average.   A starting pitcher starts the game, walks the first three hitters, gives up a grand slam and is taken out of the game; his Game Score is 29.  Doesn’t seem right.  He hasn’t done ANYTHING to help his team win; it seems like that should be a zero, or near-zero. 

            But that’s the exceptional case; mostly, starting in the middle works OK for that purpose.   The problem on the other end. . .an average Game Score for a hitter is designed to be 25, but it is actually 24.3, because more than nine players are used in an average game.  A defensive replacement who doesn’t have an at bat in the game gets a Game Score of 15.  Maybe it would be better if he was at 25, since 25 is the neutral score here?

            This bothers me in a case like Jerry Lynch.   Jerry Lynch was a very good left-handed hitter in the National League on my childhood, but his defensive limitations limited him to the role of pinch hitter/reserve outfielder. In 1958, when he had his career high in at bats (420), he hit .312 with power.   In 1961, when Frank Robinson was the NL MVP and led the league in OPS and OPS+, Lynch batted only 181 times but drove in 50 runs, registering a higher OPS and higher OPS+ than Robinson did.  Lynch that year was actually mentioned in MVP voting, with 30% of regular playing time.  In 1964, batting just 297 times, he hit 16 homers and drove in 66 runs. 

            But because he often batted only once a game, Lynch’s average Game Score, for his career, was only 22.1, which is in the Mark Belanger range.   That bothers me.  So I am thinking about changing the Game Score method to a system that starts out at 25, and ends up at 25 for an average hitter in an average game.  Have not decided whether to push the button on this or not, but here is the system that I am thinking of going to.  A hitter’s Game Score is


                     &nb​sp;  + 8 for each run that he created,

                        +3 for a run scored,

                        +3 for an RBI

                   &​nbsp;    +1 for Reaching On An Error

                        MINUS 2.5 for each out that the hitter is responsible for


            The practical effects of the change are as follows:


(1)   It is a little bit more complicated than the original formula.  That is a negative, but then real life is complicated,

(2)  It changes from a system based 50/50 on "real runs" (Runs Scored and RBI) and "expected runs" (Runs Created) to a system that is 57% based on Runs Created and 43% on Runs Scored and RBI.  I’m OK with that change, don’t regard it as either a positive or a negative.

(3)  It reduces very slightly the number of "out of range" Game Scores, which are Game Scores less than zero or greater than 100, and also creates a slightly more even balance between them.  Those things are both positives, but very small positives since less than one game in 2,500 is out of range. 

(4)  It gives the hitter a little bit of credit for reaching on an error, which I like. 

(5)  It changes from a system that goes up as at bats go up to a system that in essence filters out replacement level, going up only when the batter’s contribution is on balance positive. 


In the original system, outs are accounted for because making outs reduces a batter’s runs created.  In this system that is still true, but there is an additional penalty for the out itself, which offsets the fact that the starting point is 10 points higher.

I experimented with/developed the alternative system using a spreadsheet of batter games logs which runs from 1939 to 1993 and includes 324,745 batter games representing the careers of more than 200 hitters.  (I have several files like that.  I love messing around with batter Game Logs.)  In the original system there were 135 "out of range" games, of which 134 were OVER 100 and one was less than zero.   In this system there are 126 out of range game scores, of which only 10 are OVER 100, and 116 are less than zero.   So. . . a lower total (126 to 135) and better balance (116 – 10 versus 134 – 1.)   

In practice, 99% of the differences between the systems are small.    In the original system, the ten best games in this data are identified as:

Joe Adcock, 7-31-1954 (4 homers and a double)

Rocky Colavito, 6-10-1959 (4 homers)

Willie Stargell, 5-22-1968 (single, double, three homers and 7 RBI)

Reggie Jackson, 6-14-1969 (10 RBI, the "flat bat" game in Fenway)

Willie Stargell, 8-1-1970 (3 doubles and 2 homers)

Gus Bell, 5-29-1956 (5-for-5, 3 homers and 7 RBI)

Steve Garvey, 8-28-1977 (5-for-5, 3 doubles and 2 homers)

Smoky Burgess, 7-29-1955 (3 homers, 9 RBI)

Rico Carty, 5-31-1970 (4-for-4, 3 homers, 6 RBI and a walk)

Nate Colbert, 8-1-1971 (3 homers, 8 RBI, part of his famous double-header)


In the new system, 9 of the 10 best hitter’s games are the same, with the top 3 in the same order.  The Gus Bell game nudges up two spots, with an Ernie Banks game (8-4-1955) pushing Smoky Burgess off the list. 

On the other end of the scale there is more change.  In the old system, the only game which has a negative Game Score is the game in which Joe Torre went 0-for-4 and grounded into four double plays (7-21-1975).  In the proposed new system, that is lifted out of the bottom spot up to third-worst, ahead of a game by Manny Mota (5-24-1973) in which Mota went 0-for-9 with a strikeout and a GIDP, and a game by Luis Aparicio (8-6-1959) in which Aparicio went 0-for-8 with a double play ball AND a caught stealing after he reached on an error. 

What does it take to make a negative Game Score, in the alternate method?   There are three games in this data set in which a hitter went 0-for-6, struck out 3 times and grounded into a double play.  That combination makes a Game Score of negative 0.1.  

            I haven’t decided whether to make the change or not, and I guess I am asking for your feedback without really expecting to get anything useful.  Since none of you make any regular use of the system, you probably don’t understand the ins and outs of it well enough to have an educated opinion, but you might see an advantage or disadvantage somewhere that I didn’t see, or have some reason for a preference one way or another.  Thanks for reading, and thanks for your insight.  


COMMENTS (12 Comments, most recent shown first)

I like the proposed changes. Nothing much to add other than I found it interesting that 9 of the 10 highest scores occurred in a 17 year stretch.
2:15 AM Jun 10th
Good stuff, Bill.

At a glance....

-- I'm glad to see ROE get a nod.

-- I'm surprised to see RBIs as a counting stat. In your example, you cite the high number of RBIs Lynch had in 1961 in relation to his playing time. But at a glance, most of them came as a pinchhitter, where he was coming in with the ducks on the pond. I believe Frank Thomas actually had a higher BA with men on than Lynch.

12:31 AM Jun 1st
Raincheck: Yeah -- including most of the time that we don't realize it. :-)
11:51 PM May 31st
Reggie Jackson, flat bat, Fenway?


I can find articles about the game, nothing about a flat bat.

9:05 PM May 31st
This is all pretty top level, but it makes sense to me. I like the change. It’s pretty clear that 0-9 with a GIDP (10 outs) is worse than 0-4 with 4 GIDPS (8 outs). This system seems to do a better job with the outliers, and in a sense the outliers are what is of interest to me in a system like this.

Can this system be used to look at clusters of game as well?

Also, thank for a glimpse into the inner workings of MarisFan61’s mind. He got to the right place in the end. That is often what happens to me reading these pieces. “What about….oh, Bill is right.”
1:01 PM May 31st
It appears from your examples that you subtract for strikeouts, but don't list that in your formula. (or is that a part of Runs Created now?)
12:40 PM May 31st
Wouldn't it be best to put reached on errors in the runs created formula?
9:56 AM May 31st
In the old method:

Basically, a Hitter’s Game Score as I developed it at that time, was:


+ 10 for each run that he created,

+5 for a run scored,

+5 for an RBI

How does one get a game score <15, much less less than zero? If is the "+10 for each run that he created" ?
11:06 PM May 30th
P.S. Maybe forget my question. :-)

I can answer it, at least to my satisfaction.
And actually I'd be interested to know if this is close to the actual answer.

While Runs Created does subsume everything about the hitter's productivity, still it's a theoretical thing, which doesn't have anything like a 1:1 correlation to the hitter's impact on that particular game.
.....whereas "Runs" and "RBI's" are concrete actual things of that game.
9:22 PM May 30th
...trying to partly answer my own question:

I know that pitchers' Game Scores involve more than just how many runs they gave up (or earned runs); in fact it's mainly the other things.
And clearly a pitcher's 'goodness'/'effectiveness' would be far less well assessed if those other things weren't included.

But for batting, it's not so clear (to me) that 'goodness'/'effectiveness' isn't enough accounted for by just Runs Created.

Maybe the main part of the answer is that Game Score isn't mainly about 'goodness'/'effectiveness.'
I always thought that for pitchers, it sort of is.
7:02 PM May 30th
I like the change. I don’t have anything useful to add, but the benefits you explained seem great. Can’t come up with any negatives. Out of curiosity, what do the changes do for Lynch?
5:25 PM May 30th
Not that I mind seeing old stats like "Runs Scored" and "RBI's" in the formula, but....
Why does that part of the formula need anything besides Runs Created?
(not asking about the other parts of the formula, just this part)
3:57 PM May 30th
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