A Different Approach

We have been discussing here the relative "value" of batting in each batting order position.  I suggested in an article posted here a week or two ago that the hitter most valued by his team would bat in the cleanup spot, thus that cleanup (batting 4^th) is the highest-valued position.  My outline went 4-3-1-2-5-6-7-8-9, with the values for those as 10-9-8-7-6-5-4-3-1. 

In response to this, some of you have suggested that batting third is actually more valuable—a higher-valued spot—than batting cleanup, and various pieces of evidence have been introduced to validate this.   But it occurred to me on Saturday (September 5) that there is a different way to approach the problem.

Let us consider these two games.   Sal Bando and Rick Monday were teammates at Arizona State, were both drafted by the Kansas City A’s, and were teammates with the Kansas City A’s and the Oakland A’s.   Rick Monday, on April 20, 1969, and Sal Bando, on June 24, 1974, had what might be considered identical games.   Both of them, in those games, went to bat five times.  Both of them walked, singled, homered, grounded out, and flied out, in both cases to right field; the only difference is that Bando’s ground ball was to third and Monday’s was to first, but this fact is otherwise without consequence.  Identical games. 

This is not really unusual; I have in my game logs more than 600 games in which a player went to the plate five times, walked, singled, homered, and made two outs which were not strikeouts.  Sal Bando had that exact game 4 times in his career, and Monday had it four times; Ken Singleton had that game 9 times.  But when Bando had this game, on June 24, 1974, he scored two runs and drove in 5 runs.  When Monday had that game in 1969, he scored only one run and drove in only one run—the home run.  

Bando was hitting third in his game.

Monday was hitting eighth. 

There are theoretical runs, which are the runs created by your singles, doubles, triples, etc., and there are ACTUAL runs or, not to prejudice the discussion, what we could call Resulting Runs, which are runs scored and RBI.  Suppose that we compared games which are identical or functionally identical in terms of the hitter’s individual production or theoretical runs, but coming from different spots in the batting order.  Would it not seem logical to you, at least on the level of intuitive logic, that when a player is placed in the most important positions in the batting order, he would produce more actual runs or resulting runs (Runs Scored and RBI) then when he has identical production, but placed in a less critical position in the batting order? 

It seemed logical to me; I don’t know if it is clear yet what I have done.  But I took my Game Logs, which now include 357,000 player game lines, and I extracted from them the player’s:

1)     Batting Order Position,

2)     Runs Scored,

3)     RBI, and

4)     Runs Created.

I sorted the data by (1) batting Order Position, and (2) Runs Created, so that all of the games in which a player batted sixth and created 2.61 runs in the game were next to one another, in descending order below the games in which a player batted 6^th and created 2.62 runs in the game, and above the games in which a player batted 6^th and created 2.60 runs in the game.  I just picked those numbers out of the air, but if you are curious, there were 5 games in the data in which a player batted 6^th and created 2.62 runs in the game, 10 games in which a player batted 6^th and created 2.61 runs in the game, and 18 games in which a player batted 6^th and created 2.60 runs in the game.

From there, I formed moving averages, with 1001 games in each group—the focus line, the 500 games above this line, and the 500 games below this line.   The moving average moves constantly downward, from 3.46 runs created per game at the top of the chart to negative .79 runs created per game at the bottom of the chart.   But at some point it must cross the line 2.60 runs created per game.   There is a series of averages which look like this:

And the one we are focused on now is 2.600136, which represents 2.60 Runs Created per game in our study.  

In the 1001 games in which 6^th-place hitters created an average of 2.60 runs per game, they scored 1.470 runs, and drove in 1,977.  On the other hand, in the 1,001 games in which 5^th-place hitters created an average of 2.60 runs per game, they scored 1,566 runs and drove in 2,013.   And in the 1,001 games in which 7^th place hitters drove in 1,001 runs, they scored 1,479 runs—actually nine more than they scored while batting 6^th--but drove in only 1.867.   Let me chart that:

In fact, let’s expand the chart to include the other batting order positions—understanding that "2.60 Runs Created" is no more important than 2.50 Runs Created or 1.47 Runs Created or any other number; it’s just an exemplar. 

2.60 Runs created in a game is a very good game, and there aren’t enough 8^th or 9^th-place hitters in my data to get 1001 hitters creating that number of runs.   I have, however, 533 8^th-place hitters in that group, and if you expand that data to 1,001 games, it would work out to 1,480 runs scored—basically the same number as the 6^th- and 7^th-place hitters—but only 1,780 RBI, down another hundred. 

It would appear from this data, then, that more actual runs are produced by a hitter having a game of this quality in the 4^th spot than in the 5^th spot, more in the 5^th spot than in the 6^th spot, more in the 6^th spot than in the 7^th spot, and more in the 7^th spot than batting in the 8^th position.  This is, of course, exactly consistent with our expectations, and it is consistent with the initial layout of the value of the positions that I suggested last week.

However, the values in the chart from top to bottom are not ENTIRELY consistent with that chart.   We can measure the actual-vs.-theoretical value of run production by adding the Runs and RBI together, and dividing by the Runs Created.   We can call this the Productivity Ratio.  The layout of position values that I had suggested was this:

But based on the Productivity Ratios, I get a somewhat different order:

Before we go any further, let me acknowledge that this is not anyone’s last word on the subject.  Simulation studies have repeatedly shown that the order in which players bat in the lineup has minimal impact on the team’s runs scored, and there are no doubt many differences between Runs Scored/RBI and impact on the team.   But let’s not get intellectually constipated by the things that we think we know.   Let’s face the question direction.   Can you explain to me, in clear language which can be traced to mathematical measurements, why you would NOT want to put your best hitters in the positions in the order where they would produce the most actual runs?   If there are offsetting values to using your best hitters in the third spot, rather than the fourth, what EXACTLY are they?  What EXACTLY are the benefits of doing it the other way?   And "more opportunities to bat" doesn’t count, because that would be accounted for in the method that I have used. 

And one more point.  I understood anyway, and I suppose that I have understood since I was eleven years old, that a hitter will drive in more runs when he is hitting 4^th than when he is hitting third, but will score more runs when he is hitting third.  But what I did not understand, until now, is that the gain in RBI from hitting cleanup is like five times larger than the loss in runs scored—maybe MORE than five times, I don’t know.   This chart compares #3 and #4 hitters along a more extended spectrum:

The data shows that if a player does not have a productive day, then there is little or no difference between his hitting 3^rd and 4^th, but that if he DOES have a productive day, he will be involved in quite significantly more runs if he bats 4^th than if he bats third—and also, that the more productive he is, the larger the difference is between having him in the third spot and having him in the fourth spot.  

The data shows that

1)     Given a known and constant amount of production from the hitter,

2)     He will drive in significantly more runs from the 4^th spot than the third,

3)     He will score essentially as many, and

4)     This is the crucial point, the difference increases the better his day is. 

So if your hitter—any hitter—has more run production impact from the 4^th spot than the 3^rd spot, and if that gap increases as the hitter becomes more productive within a given game, then why would you NOT bat your best hitter in the spot where he has the most impact?   Why should we not regard the 4^th spot as the most critical spot in the batting order?

Thanks for reading.