Moments with Maddon: Playing Match-ups and Pinch-Hitting

In some of the recent "Moments with Maddon" scenarios, we've had to determine if it'd be better to pinch-hit for a batter, to let the batter swing away, or to go with another strategy like sacrificing. Instead of debating about another scenario today, I want to take a bit of time and review what the stats say about pinch-hitting. How do you determine when it'd be better to pinch-hit for a batter than to let them swing away?

Well, the answer to that question should be fairly obvious: when the pinch-hitter provides a better chance of not getting out than the batter at the plate. Or to look at it another way, the pinch hitter should have a better chance at providing positive offensive value to your team than the current batter. That doesn't necessarily mean that they will produce, but just that they have a better chance of it.

To measure which player is better in a given situation, I'm using Weighted On-Base Average (wOBA) since it captures all the different offensive contributions a player provides and weighs them in accordance to their actual run value. So now the question becomes, which player has a better wOBA in the situation at hand?  We don't want to compare players' career wOBA averages, since some players are significantly better depending on if they're facing a righty or lefty. As a refresher, here are the career wOBA platoon splits for all the batters on the Rays:

* Joyce, Rodriguez, and Brignac excluded due to lack of major league at-bats.

**The color grouping are approximate, merely to give you an idea of if a player's wOBA is above or below league-average and by how much. 

But wait! According to these numbers, Kelly Shoppach is apparently Albert Pujols against left-handed pitchers; that can't be true, right? Before we take these numbers as gospel, we need to perform some regression.

When looking at these splits, it's important to realize that even when you use career splits, they can still be affected by sample size issues. Since Shoppach has played most of his career as a back-up, he's only accumulated 258 plate appearances against lefty pitchers (compared with 785 PA against righties). So going forward, should we expect Shoppach to have a .419 wOBA against lefties (his current split value) or a .338 wOBA (his career average)? The answer is somewhere in-between. We can't ignore the fact that Shoppach has performed that well against lefties over 258 PA, but we need to regress that number back towards his career average since it's a relatively small sample.

As a general rule, the more plate appearances a player has, the less regression needs to take place. For example, if a player only has 3 PA against lefties, you have to assume that their talent level against lefties is their career average since you don't have enough plate appearances to draw any conclusions. If a player has 3,000 PA against lefties, though, then you can assume that their split wOBA will represent their talent level well.

And now, here are the Rays' regressed platoon splits:

Excellent!  So now we have a really good idea of what "talent level" to expect from each batter in a given situation. Obviously if the Rays are facing an ace pitcher, scale all the wOBAs down a tad; if they're facing a scrub, give them a bit of a boost. Longoria and Zobrist both look pretty awesome regardless of who's on the mound, while Bartlett, Shoppach, Blalock, Pena, Burrell, and even Crawford see some platoon differences. Like some guy mentioned on FanGraphs recently, I really hope Maddon doesn't have Bartlett lead off against righties. Looking at this data, a Crawford/Bartlett lead-off "platoon" might be a good option.

Okay. Now that we have an idea of the talent level for each player, we can start to see who makes sense as a pinch-hitter in what situation. Out of the players likely to be on the bench, Shoppach looks like the best option against lefties and Blalock the best against righties. So if Bartlett goes up to the plate against a righty, does this mean that it'd make sense to pinch-hit for him with Blalock? Well...not quite. Although Blalock has a higher overall expected wOBA against righties than Bartlett, we need to take into account that pinch-hitters typically see a 10% decrease in their performance (according to "The Book"). With that in mind, let's see how the Rays look when we lop 10% off of each of their wOBAs:

If we pinch-hit for Bartlett with Blalock, we'd be substituting a .333 wOBA batter with a .308 hitter, which isn't the direction we want to be moving in. In fact, this chart suggests pinch-hitting only makes sense in rather extreme situations - like when Kapler or Navarro are at the plate against righties or Blalock is up versus a lefty. This is slightly surprising to me; I wasn't expecting there to be many situations where pinch-hitting made sense, but I didn't think there'd be this few.  Try and make your own match-ups using the above charts and see what you find, but if you hold to the 10% reduction, it's tough to find a substitution that makes sense.

Of course, Joe Maddon also needs to take other things into account when making pinch-hitting decisions. He knows if a player is in a mental funk or coping with a minor injury, and he has scouting data at his disposal.  Maybe he has some reason to believe that that certain players are performing below their expected wOBAs at the moment. Maybe he wants to play mind-games with the other manager and use some game theory. There's more that goes into pinch-hitting than looking at the numbers, but they're certainly a good place to start. And I don't know about you, but they're a bit surprising. Maddon, if you're out there, be careful when you're pinch-hitting! If not done properly, you could actually be shooting yourself (slightly) in the foot.

*Regressed wOBA splits calculated using the Excel calculator found at Another Cubs Blog, which I've turned into a Google Docs calculator and can be found at the Saber Library.

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