Adjusting Appearance Data for Base-Out State

It would be atypical – and therefore, interesting – for a pitcher to be used frequently in other base-out states. Moreover, we should be giving credit to pitchers who are being used in that way. An appearance where a pitcher enters with a four-run lead but the bases loaded should not be viewed in the same way as an appearance where a pitcher enters with a four-run lead in a clean inning. More than likely, the manager has two different pitchers in mind for each of these scenarios.

Adjusting the inning is easy: Credit partial innings in the event that the pitcher enters with more than zero outs in the inning. This will bump the inning component of every pitcher’s “center of gravity” up a bit, giving credit to players for working slightly later in the game when called upon mid-inning. (Note: we could also define terms in a different way, and say that a pitcher who enters in a “clean” 9^th inning is actually entering at inning 8.0, as 8 innings have been recorded prior to his entrance; however, this makes the resulting metric less intuitive.)

Adjusting the score differential doesn’t seem as straightforward at first, but fortunately, we can use the concept of RE24 to accomplish this. Given that entering in a clean inning is the default status, we will make no adjustment to the score differential for a given appearance if the pitcher entered in a clean inning. For any other base-out state, we will add or subtract the difference between expected runs in that base-out state and expected runs in a clean inning state (0 on, 0 out).

Let’s return to the three appearances shown above. As you might have guessed by now, they are not identical. Rather, they illustrate the importance of adjusting for base-out state.

If you were to ask Daniel Hudson to recall what he could about these three appearances, he’d probably feel very differently about each of them (if he remembers, anyway). In the first case, he’s coming into a clean 8^th inning, protecting a one-run lead. It was a situation he found himself in with some regularity in 2016, prior to assuming the closer’s role.

The second situation is an absolute bear. Jake Barrett has allowed a leadoff single to lead off the inning, and poor Steve Hathaway, who shouldn’t be touching this game situation with a 10-foot pole at this point in his career, has subsequently allowed a double and a walk to load the bases. Hudson has been brought in to protect a one-run lead with the bases loaded and nobody out. The opposing team has an expected run value of 2.282. While technically Hudson has been given a lead, it’s one that he would be hard-pressed to keep, even if he does everything right. The reality is that this appearance is associated with an expectation that Arizona will trail by the end of it – as you can see on the play-by-play log, the Padres have a 70.6% win probability at this point. It would be silly to give this appearance the same treatment as the first two. (Hudson, by the way, does a masterful job of escaping this situation without surrendering the lead!)

The third case is the one I want to focus on. Rather than a clean inning, Hudson was asked to get the third out of the 8^th inning, with the tying run standing on second base. While the Leverage Index at the time of entry for this appearance is higher (3.50) than in the first instance (2.17), Hudson actually has an easier job: He needs just one out instead of three, and the opposing team is expected to score fewer runs in this situation, all else being equal. In the “clean” 8^th inning, he can be expected to give up 0.481 runs, while in the two-out, runner-on-second situation, he can be expected to give up just 0.319 runs. Moreover, the chance of scoring at least one run – presumably the more important question where one-run leads are concerned – is also lower in the “higher leverage” situation. (This doesn’t even account for the batter, Hector Sanchez, who is hardly Wil Myers at the plate, and is probably inferior to the 4-5-6 hitters in the Phillies lineup, as well.)

This brings up an important distinction between leverage and run prevention. Leverage Index, certainly, is an important tool. What it measures, however, is variance in win probability for a single at-bat. Managers rarely have the luxury of giving their pitchers one-batter appearances in the regular season. Even the notoriously fleeting Javier Lopez averaged nearly three batters per appearance in 2016. Managers must therefore determine how to maximize the value of relief appearances as a whole, not just at the time when the reliever is entering the game. Leverage Index shows how much variance can arise from the current plate appearance, but a manager may very well be better served having their best pitcher throw the entirety of the 8^th inning, rather than having him get the third out in a situation that commands high leverage but still has relatively low run expectation.

Next time, we’ll look at how base-out state adjustments impacted the raw inning-score matrix data in 2016, to draw conclusions about which relievers were used most often in high-pressure, mid-inning situations, and whether that sort of usage aligns with what we’d expect from an optimal manager.