A couple of weeks ago, we looked at what happens when a closer enters the game in a save situation after his team has handed him a lead with little warning. What we saw was that when a pitcher had only a short time between his team giving him the lead and his first pitch, his velocity and break tended to be a bit more erratic. The effect seemed biggest when the transition from lead to closing situation was near instant, but it quickly fell away and then died out completely around 15 minutes of warning time.
While this is an interesting observation of a pitcher's behavior, does the time a closer has to mentally prepare for a save situation actually predict anything useful about what will happen when the pitcher takes the mound? Is he less effective for his wildness? More?
Discovering the answer to that question is a little more complex than you might imagine. You always want to control for two major variables: how good the pitcher is in general and how good the hitters are whom he's facing. To do that, we're going to need to do some numerical gymnastics. So, with that said…
Warning! Gory numerical details ahead!
(Rated SPSS, because I don't use R)
I've previously shown this method in full elsewhere, so I'm going to do an abbreviated version here.
During a plate appearance, there are eight basic events that can happen: a walk, a strikeout, a hit batsman, batter reaches on an error, a single, an extra base hit (double or triple), a home run, or an out in play. You can calculate the rates at which each player ends up with each of those outcomes rather quickly.
In 2011, John Jay struck out in 16.1 percent of his plate appearances. Madison Bumgarner whiffed 22.6 percent of the batters he faced in 2011. (The two of them need to be on a team with Josh Hamilton, for the sake of fans of both baseball and the Federalist Papers.)
What are the chances that if Jay faced Bumgarner in 2011, a single plate appearance would have ended in a strikeout? A good way to estimate the odds is through the odds ratio method. We convert the probability of a strikeout for each into an odds ratio (forumula is p / (1-p); so for Jay, it's .161 / .839 = 0.191895). You can calculate the probability of a strikeout in that instance through the formula:
batter odds ratio * pitcher odds ratio / league odds ratio = expected odds ratio
If you're curious, Jay vs. Bumgarner would end in a strikeout about 19.7 percent of the time, according to the model. For our purposes here, we're going to take the natural log of the expected odds ratio and stick it into a binary logit regression, with the outcome being whether or not the plate appearance ended in a strikeout. (For those who want more technical details, they are in the article linked above.)
Now that we've controlled for what we might expect from the matchup in general, we can put other variables into our regression, like how much time the closer had to mentally prepare. I created a series of regressions looking at each outcome, then put in the "time to prepare" variable. If it is influencing the outcomes, then it will show up in the regression as significant. With a little math, you can even tell how much it will affect outcomes.
Closer preparation time didn't seem to actually matter. There was no effect of the prep time variable on any outcome. I tried it both in raw number of seconds and as a dichotomous variable cut off at the 15-minute mark. I tried controlling for a couple of other variables, but that didn't help matters either.
One thing that occurred to me was that a pitcher might feel amped up for the first batter or two, then succeed in calming himself down as he goes about his work. I isolated the first batter that each pitcher faced in a "closing" situation, then the second, then the third. There were no differences. I also looked into whether the pitcher settled down as the inning wore on and became less variable in his velocity and movement. I isolated the first five pitches he threw, then pitches 6-10, then pitches 11-15. The effects stayed consistent. Pitchers who had less time to prepare showed more variation in their pitches throughout the inning, but it didn't make any difference in the outcomes that resulted on the scoresheet. Players still struck out, walked, and hit home runs (and everything else) at roughly the same rates that they would have been expected to.
What gives? Well, there's someone else in this equation who is probably just as shocked about the whole "One team was winning, and then suddenly, the other one is" thing. I'll give you a hint: he holds a large toothpick. If it's the home team who surrendered the lead, the batter probably wasn't even thinking he'd bat again in this game. Because we can't magically make the pitcher aware of the sudden nature of this lead and make the batter believe that this is just another fifth inning at-bat, we'll never be able to untangle those two. Maybe the shock on both sides cancels each other out.
In any case, it shows something valuable. You might see that a pitcher is visibly a little shaken out there, and maybe he is. Just understand that the narrative that "He's shaken, and because of that, he will fall (or, if you work in the movie industry, rise to the occasion)" is far too simplistic. Human behavior is a really complicated thing.