I have been campaigning for Carlos Gomez to bat 9th (or be demoted to AAA) for some time now. To get a more objective look at the benefits of such a move I decided to do some number crunching. I want to stress that I've completely disregarded the mental aspects of baseball in the following - I'm exclusively working with the stats here.

My question is this: How many extra runs per game will the Twins score if Gomez gets to bat 9th from this point of the season and out, while Denard Span is moved to the lead-off spot?

The method

In order to arrive at an answer I go straight to The Book. In this, the authors calculate the average number of runs scored for each possible outcome of a plate appearance. They really put a lot of care into adjusting for a variety of things, including the typical situation in which each outcome is realized as well as the ball-strike count. The results are displayed in a table on p. 28 (e.g. a HR is worth 1.397 runs on average, a single is worth 0.475 runs, a caught stealing is worth -0.467 runs above what an average team would score in the inning, etc.).

The extreme case

Now, to first consider the extreme case, I focused solely on Gomez' batting and base-stealing in June and July. I looked up his splits on MLB.com and typed them into a spreadsheet where I multiplied each stat with its run value above average, as mentioned above. The bottom line was that Gomez has cost the Twins 19 offensive runs compared to the average in 194 June/July plate appearances, or 0.100 runs per PA.

Doing the same thing for Span, I found that since his call-up he has added 1 run above average in 97 PA, which is 0.013 runs per PA.

The Book also lists the average number of plate appearances per game for each lineup slot (p. 122). In AL parks, the lead-off hitter gets 4.83 PA per game, while the no. 9 hitter gets 3.90 on average. Thus, moving Gomez down to the 9th slot would give him approximately 0.93 less PA per game.

Since his performance in June and July indicates that he costs the Twins 0.1 runs per PA, moving Gomez to the bottom of the batting order would thus yield 0.093 runs extra per game for the Twins. Similarly, moving the slightly-above-average Span to the lead-off spot would add 0.012 runs per game.

Thus, the total added run value of switching Gomez and Span in the batting order is 0.105 runs per game.

via cache.lifehacker.com

The projected case

Now, obviously, no-one truly believes that Gomez will be as horrible the rest of the season as he has been in June and July. And Span will probably regress a bit towards the mean (he seems to already be doing so). Consequently, I used The Hardball Times' in-season Marcel projection spreadsheet to generate a more reasonable batting and base-stealing expectation for both players.

I went through the exact same steps as above, and the results were as follows: Gomez is projected to cost the Twins 0.038 runs per PA compared to the average while Span is projected to be almost exactly average. This means that a batting order swap would yield an extra 0.031 runs per game for the Twins.

In conclusion

The added run value was much smaller than I expected, even in the extreme case. Batting Gomez 9th would just barely amount to half a win extra over the remainder of the season. Of course there are many other ways to change the batting order, like moving Casilla and Mauer up a spot. This would most likely be worth more in terms of run value added, but I consider it unlikely that Gardy would consider this option.

I still think Gomez should be moved to the bottom of the batting order - if nothing else it might help restore his mental balance to have some pressure taken off his shoulders. What are your thoughts?

Note: The stats considered in the above analysis were 1B, 2B, 3B, HR, HBP, unintentional BB, SH, SO, SB, CS and outs on batted balls.