It's the time of year when managers start thinking about games that will actually count. Positional battles are heating up, because decisions need to be made. Opening Day starters are being named. Variations in lineups are being considered, for facing righties, lefties, and Pat Venditte. Your favorite team has spent the spring trying to decide between two players, both of whom are relative unknowns. Due to the 50/50/90 rule (when you have a 50/50 chance of getting something right by chance, you will get it wrong 90 percent of the time), they will pick the wrong utility infielder and the other guy will become a decent starter for some other team.
One thing that managers also have to do around this time is set their starting rotation. Opening Day starters can't pitch all 162 games, Old Hoss Radbourn notwithstanding, and managers need to figure out who will pitch game two, then three, then four, and then the rest of them. In general, the best strategy would seem to be to have the best guy go first, then the next-best guy, then the next-best guy, and so on.
But wait a minute: managers often talk of wanting to structure their rotation such that two similar pitchers never appear back-to-back. You'll often hear managers talk about needing to split their left-handed starters (although the fact that righties pitch back-to-back all the time never seems to bother them). The standard explanation is that if a team sees two lefty starters in a row, it will get used to the spin of a left-handed pitch and be better hitters for it. So, managers take extra care to split their lefties, or their sinkerballers, or their guys with short last names.
Warning! Gory Mathematical Details Ahead!
I took all events from 2003-2012. (So, for the initiated, we won't be having any statistical power problems, will we?) I looked at all starting pitchers who faced at least 250 batters in their capacity as starters during that year. I classified each by three criteria: handedness was the easy one. The other two I borrowed from baseball-reference.com: power vs. finesse pitchers and ground ball vs. fly ball pitchers. I grouped all pitchers within each year by whether they were in the top third, middle third, or lower third of the percentage of their batters faced who struck out or walked, for the power/finesse dimension. Then I did the same three-group division for their ratio of groundballs to fly balls. Chopping any continuous variable into discrete groups is always risky, but in the interests of putting together pitcher types, this will have to do for now.
For all games, I figured out who the starting pitcher that the other team had seen the night before was, in terms of our three criteria, and whether the pitcher was a match on any of the three criteria (and also if he was a match on all three). The "match" variable was coded dichotomously (aka, 0 and 1).
I used an old favorite: my modified binary logistic method for studying patterns within outcomes. I calculated a batter's K/PA rate within a season, the pitcher's K/PA rate (using only what he had done as a starter), as well as the league's K/PA rate (intentional walks and pitchers batting were not considered). Using these three numbers, one can create an estimate of the probability that particular plate appearance will end in a strikeout using the odds ratio (OR) method. First, convert the raw probabilities into odds ratios (prob / (1 – prob)), and use the formula
expected OR = batter OR * pitcher OR / league OR
Taking the natural log of the expected OR, and you have a fantastic control variable to stick in a logistic regression.
For all plate appearances in which a batter who logged at least 250 PA in the season in question faced off against a starter who had faced at least 250 batters in his capacity as a starter, I coded all plate appearances as to whether they ended in a strikeout or not. I followed a similar process, complete with creating a control variable, for walks, hit batsmen, singles, doubles/triples, home runs, and outs on balls in play. I created several logistic regressions in which I first entered the control variable created above. This controlled for the strikeout simply being the result of a strikeout artist facing off against Russell Branyan. Adding other variables into the mix revealed whether they had any predictive power beyond simple expectations based on batter/pitcher matchups.
I added in one of those other variables: Was the starting pitcher on the mound tonight of the same handedness as the starting pitcher that the team faced last night. I even specifically coded so that games that followed a day off were not considered.
In addition, I coded for whether the specific plate appearance featured a platoon advantage for the pitcher (both pitcher and batter were of the same hand) or the batter (they saw the world from different sides of the handedness spectrum).
If the idea that seeing a same-handed pitcher had some extra predictive power (in either direction) over what happened in a plate appearance, over and above what we might expect from the relative talents of the batter and pitcher, then our "match" variable would have come out significant.
Except that it didn't. For any of the outcomes.
Okay, well, maybe seeing a repeat performance from the power/finesse spectrum would give hitters an advantage. Nope.
What about groundball/flyball preferences? Does having seen all those sinkers last night make you a better hitter when you see them tonight? No.
I then coded for whether or not the opposing pitcher matched the guy from the night before on all three counts, same hand, same penchant for power, same fascination with fly balls. Perhaps a righty junkballer and a righty power arm wouldn't be similar enough to tip the batter off on what to do next to get an advantage, but maybe having all three properties match would. Did this more complete match with last night's starter predict anything? It predicted a whole lot of nothing.
It doesn't seem to matter who pitched last night or what sort of pitcher he was. Matchups generally conformed to what might be expected by seasonal averages of the batter and pitcher.
There was, however, one property of the pitcher, compared to last night's pitcher, that predicted something about how things would go: whether or not he was wearing the same uniform. I coded each game for whether the batting team was facing the same team from last night. It didn't matter who the pitcher was or what sort of approach he generally used. Teams facing off for the second game in a row were less likely to hit home runs, more likely to strike out, and more likely to be hit by a pitch. The effect sizes were small (on the order of a tenth of a percentage point), but significant, and they generally favored the pitcher.
What Does it All Mean?
Managers should have no qualms about putting two pitchers with similar styles back-to-back, according to these calculations. There simply is no reason to believe that there is any effect, positive or negative, for the batting team of seeing the same type of pitcher on consecutive nights.
On some level, the idea that there would be a practice effect that carries over from the night before makes sense. Humans are able to carry lessons from one day to the next, and practice does make perfect. So why not here? I'd submit that it's because the concept we're testing is way too simple, although its simplicity makes it easier to remember and make sense of. This shortcoming underlies about 90 percent of misunderstandings about how things really work, both in baseball and the rest of life. The idea that it makes sense to split up starters of the same type essentially assumes that the batter ends the game, goes into suspended animation, and re-emerges at 7:00 the next night without anything in the middle. That might be how it works in video games, but there are more moving parts for the real big-league batter than the model suggests.
Let's start with what tomorrow night's starting pitcher is doing tonight. If he's doing his job, he'll be watching closely what his teammate is doing and taking notes on the batters whom he'll be facing tomorrow night. Maybe he's picking apart weaknesses that he might exploit. Interesting that we see significant effects biased toward the pitcher if the pitcher gets a look at the hitters the night before (without the hitter getting a look at him).
Then there's the batter. Yes, he probably does face off against a starter two or three times, but he probably also faces off against a reliever and has to process all that information as well. After that, he goes home or back to the hotel, where he sleeps and gets up for another game the next day… the same way that he has a few thousand times before. If he's doing his job right, he'll come to the park and study up on whom he'll be facing tonight. It might be a guy similar to the one he faced last night, or someone different, and he's probably dealt with both situations before. Either way, he's probably faced a pitcher similar to tonight's starter at some point in the past. Maybe often, and it's not like he's forbidden to draw from that knowledge. And just as he's done a thousand times before, he begins preparing himself for that which he is about to face and puts last night out of his head. Then he goes and takes batting practice, which presumably his manager has arranged to be thrown by a coach who uses the same hand as tonight's starter. And that will be his most recent experience swinging a bat.
Something that every article should note: I could be wrong. It's possible that my method for classifying pitchers (looking at power/finesse and GB/FB ratio, along with handedness) is not picking up on some specific issue that I should control for. Every sabermetrician should be prepared to be proven wrong.
But the data here say that there's no after-effect from seeing the same type of pitcher as last night. So the next time you hear a manager move a superior starter back in the rotation in favor of a lesser one, and he says that you gotta keep 'em separated, don't pay him no mind. Just say, "Heeeeeeeeeeeeeeeeeeeeey, go out and play."
I promised Sam Miller I would do this study about three months ago. Sorry it took so long, Sam.