Let's talk about relief pitcher meltdown management (SETTLE DOWN GUYS JEEZ).
What should you do when your ace RP has a "meltdown", i.e., he gives up a few jacks, blows the save and the game? It can ruin your ottoneu day: 1 inning pitched, and -10 points to show for it. How do you respond- do you treat it like a freak incident and keep him in the lineup? Or do you bench him for his next few appearances, assuming that one meltdown often leads to another?
To figure out the best strategy, I took a look at how the RP's on my team historically have followed up on "meltdown appearances". To start, I gathered the game logs (and corresponding point scores) of each pitcher over the last few years from their FanGraph pages. Then, I took a look at what the point scores would have been if I had benched the player for 1 appearance after a "meltdown" (which I initially defined as an appearance earning <0 points*). I did the same for a strategy that benched a player for 2 appearances immediately following a meltdown.
Obviously, you end up with lower points overall if you bench your player vs. when you don't bench your player, but I assume I can make up those innings elsewhere, so I actually care much more about what this does to my points per inning pitched (p/IP). Here's Brandon League ('11-'12) as an example:
Overall p/IP: 7.4
p/IP excluding the first appearance after each meltdown: 7.7
p/IP excluding the first two appearances after each meltdown: 7.9
So, this is kind of cool- there IS an effect, for League at least**. By benching him for 1 or 2 appearances after he has a meltdown, I can increase my p/IP. AND the effect was consistent over the two years (it showed up in 2010 as well, but he wasn't a closer then, which complicates things).
Okay, but who is going to replace the IP League loses from being benched? And how good does that replacement player have to be to outperform what League would have done if he had NOT been benched? Here's how League performed during the time he was "benched":
p/IP of the first appearance after each meltdown: 4.8
p/IP of the first two appearances after each meldtown: 5.4
Okay, that's pretty easy to replace. My sixth man, Ronald Belisario, scored 7.1 p/IP last year. Good, so I've done it! The *new* new market inefficiency! League championship, here I come!
Wait, one step further, though- we can easily calculate how many IP League would lose from being benched based on the previous years (~5 if benched 1 app., ~9 if benched 2 app.), and we know the difference in p/IP, so let's calculate how many points this brilliant strategy will earn me over the course of the season:
Benched 1 app. after meltdown: 5 IP * (7.1 - 4.8) = 11.5 points!
Benched 2 app. after meltdown: 9 IP * (7.1 - 5.4) = 15.3 points!
So, does it pay to micromanage Brandon League's meltdowns? Blrrrrrrrrrrt!
In conclusion, if you're anticipating a close race, and you have some time on your hands, it's a worthwhile strategy to consider.
The end!
* I tested different "meltdown" thresholds as well, and found that, for my group of RP's, a threshold of -2 points maximized return from these post-meltdown-benching strategies.
** My group of pitchers show a variety of optimal post-meltdown-benching strategies- Mariano Rivera, Luke Gregerson, and Joel Hanrahan show no "post-meltdown" effects; I can maximize points from Belisario and Aroldis Chapman (RP status pending...) by sitting them 1 appearance; and League and Mark Melancon are best sat 2 appearances.
