By Jason Wojciechowski on January 15, 2012 at 9:00 PM
I complain from time to time about the state of sabermetric glossaries, but on this point, here's a David Appelman post laying out the basics of leverage index. The upshot is that it measures the "importance" of a game situation (in win probability terms). There are all sorts of issues with LI, but as long as we're not ascribing value to players, I'm reasonably comfortable with using it as a description of the game state.
The first question is whether Devine's gap between his gmLI (the average leverage index when he enters games) and his exLI (the average leverage index when he leaves games) is unusually high. Pulling from the FanGraphs sortable leaderboards, I find that, for relievers in 2011 with a minimum of 20 IP, Devine was 41st in (exLI - gmLI) out of 251 pitchers. A quick look at the numbers reveals that Devine's gap is basically one standard deviation from the mean gap, so it's high, but not the kind of extraordinary sum that would make us wonder if something anomalous is going on.
If you pitch the late innings of close games, as Devine did:
and you pitch them well, as Devine did (six poor performances out of 26, one of those in what was already a blowout), you're going to see this kind of gap between your gmLI and your exLI as a function of Clay Davenport's observation about the end of the game's effect on win probability:
win probability is essentially a function of (run differential)/(time remaining), and time remaining becomes zero at the end. Think of how the value of 1/N changes as you change N from 100 to 0 in steps of -1, almost imperceptible differences through most of the range, accelerating rapidly as you approach zero.