To Pinch Hit, or Not to Pinch Hit


I had the good pleasure of attending last Saturday’s game against the Red Sox with Zac and the wives. We found ourselves discussing pinch hitting situations (Zac and I, not the wives), specifically in the bottom of the eighth inning. Here’s the situation: Inge had just doubled to tie the game, plating Cabrera and moving Boesch to third. They had runners on second and third, no outs, with Gerald Laird  due up to face Hideki Okajima.

My initial thought was to bring in Johnny Damon  here in hopes that he would be better able to drive in the go-ahead run even though you would be giving up the righty-lefty advantage. In my mind, Damon’s hitting skills were so much better than Laird’s that we could expect him to drive in the run with a greater frequency. Leyland didn’t pinch hit for Laird, who struck out, and the Tigers didn’t score any more that inning. I remained intrigued by the question, so I decided to crunch some numbers.

More after the jump (spoiler alert: Jim was right, I was wrong).

My study on the subject was aided greatly by The Book  (read: I copied their methods). If you enjoy deep analysis, advanced statistics, or you just love anything that’s ultra nerdy, I highly recommend obtaining a copy. It’s also worth mentioning that when comparing offensive abilities of players I’m going to use a statistic that’s presented in The Book: weighted on-base average (wOBA). For those unfamiliar, wOBA is simply a statistic that quantifies total offensive production (kinda like OPS, but correctly weighing the values of a single, double, and the like). One beauty of wOBA is that it’s scaled to on-base percentage so you can use the same rule of thumb: above .400 is excellent, .340 is about average, and below .300 is poor.

First, I calculated career lefty-righty splits for each player (in terms of wOBA). Then, using the techniques detailed in the appendix of The Book, I regressed each player’s measured (calculated) splits toward the league average splits to determine each player’s “platoon split skill.” Brandon Inge has the biggest platoon advantage on the team, he is expected to hit lefties .031 wOBA points better than righties (this equates to .027 more runs per plate appearance, or 16 runs in 600 plate appearances).

Next, each player’s career wOBA was calculated and regressed to determine true expected talent level. From this, I was able to calculate expected platoon wOBA (vs. lefties and righties) by weighing the overall value wOBA with percentage of at-bats that were against lefties and righties (and setting the difference to be equal to the platoon split  skill calculated above). So, going back to our Brandon Inge example, he’ll be expected to hit at a .338 (wOBA) clip against left handers, but only .307 against right handers (you can see the .031 difference from above).

It has been determined (again, in The Book) that players hit worse in pinch hitting roles than they do in starting roles, so we cannot expect the same level of performance. In fact, hitters on average hit .034 points worse after riding the pine the whole game than they do when they’re starting. Applying this “pinch hitting penalty” to our righty-lefty splits we can create the following pinch hitting decision chart.

The “platoon skill” column shows each player’s ability to hit left handers better than right handers (negative numbers indicate ability to hit right handers better than left handers). The “Starter” columns list each player’s expected wOBA for each pitcher handedness in a starting role, and the “PH” columns list expected ability in pinch hitting roles.

Going back to our original question, Laird, the starter, was expected to hit .328 against Okajima (a lefty) and Damon was expected to hit only .308 against him.

Using the table, one could determine if pinch hittiting would be adventageous by finding the difference between the starter’s expected hitting ability, and the pinch hitter’s (being careful to use the correct columns).

It’s interesting to note that the best possible scenario would be inserting Miguel Cabrera  into the game for Donnie Kelly against a left handed pitcher, an advantage of .083 points. This would increase the run expectancy for that plate appearance by 7.2%.

I didn’t include Wells or Worth because we really don’t have any worthwhile MLB data on them, and I included Raburn and Sizemore, because I thought it still would be interesting. Data is as of 5/10/2010.