A while ago I wrote a post about one of the most unenlightened areas of baseball strategy: the use of pitchers. I proposed eliminating the distinction between starting pitchers, middle relievers, and closers in favor of a system that just uses a set of pitchers, each pitching different total numbers of innings, but no single pitcher pitching more than a few innings in a game; in other words, a starter would now throw two innings every few games instead of seven innings every five games.
The advantages of this, as I see it, are four fold.
1) If you're an NL team, you can pinch hit for your pitchers whenever they come up.
2) Pitchers don't have to throw 100 pitches in a game.
3) Batters never get to see the same pitcher twice in a game, and so can't get used to their pitches.
4) You can get the pitcher-batter match-ups you want all the time, instead of being stuck with your same pitcher the first three times through the lineup.
In the first post I estimated the size of effect (1): pinch hitting for you pitcher every time would let you score about 0.2 more runs per game, translating into about 3.2 wins per season (the difference between a .500 team and a .520 team).
Now I'm going to look at effects (2) and (3).
In order to evaluate how much you gain by not having your pitchers stay in the game too long--both in terms of fatigue, and in terms of batters not getting use to pitchers--what you really want to know is whether pitchers got less effective each time through the lineup.
It's not trivial to find a way to do this without inviting statistical bias*. In the end, what I came up with was the following: how do pitchers' statistics change between the first time they face a batter in a game, and the second time? In particular, I'm only looking at cases where the same batter had two at bats against the same pitcher in a game, and neither of the at bats ended in a sacrifice bunt or intentional walk (as those aren't good measures of pitcher skill).
So, what were the results?
Well, in 2012 pitchers allowed an OPS of .769 the first time the saw a batter, but .797 the second time; results from 2011 were similar, with a gain of about 30 points of OPS. What that means is that pitchers did get worse the second time the saw a hitter, probably from a combination of fatigue and from the hitter having seen their pitches once before.
And something to note here is that the pitches that a pitcher throws in one game are just 3% of what they throw in a year--this fatigue is not coming from the fact that pitchers are throwing 200 innings in a year, but form the fact that they have to throw 100 pitches in a night. In other words, it's fatigue that could potentially be fixed just be spreading a pitchers' innings out more.
It's hard to get a good estimate of how well hitters did the third time they saw a pitcher because by then a number of pitchers have left the game, leaving a biased sample behind. But it's interesting to note that overall--not controlling for anything--in 2012, batters gained 36 points of OPS the second time they saw a pitcher (similar to the 28 points I found), but then gained yet another 29 points of OPS the third time they saw a pitcher.
So there's reason to believe that, even controlling for other factors, in addition to the 28 points batters gained the second time they saw a pitcher they probably gained another 25 or so the second time.
How much does his matter? Well, using wOBA to calculate the runs lost over the course of a season, a team could get about 5.6 more wins if their pitchers only pitched once through the lineup each game**.
This calculation, of course, isn't perfect. Who knows how it is on a pitchers arm to throw two innings every other game; no pitchers have every really done it, so all we have is speculation. And maybe it's the case that pitchers don't actually have to get worse as the night goes on, but they only have so much gas in them for a season and decide for some reason to throw harder at the beginning of nights than at the end.
But I think it's a reasonable approximation, and 5.6 wins isn't nothing. Including the 3.2 wins from pinch hitting, so far we've gotten 8.8 extra wins each season from switching pitchers more often--the equivalent of one MVP player.
*Problems with other methods are the fact that it's non-random on which days pitchers last more than two times through the order and that there could be correlations between whether a pitcher sees a hitter more than once and how good both the pitcher and the hitter are.
**Assuming that the fact that pitchers already see hitters for the first time once counteracts the fact that they also often see them a third time, and that the difference between first and second times is a reasonable average to take.