Recently, there was discussion on the changes to the Pirates bullpen at the trade deadline. Courtesy of baseball-reference.com, here are the Pirates' moves after trading for Wandy Rodriguez:
July 31, 2012 - Traded Gorkys Hernandez and 2013 compensation draft pick round A to the Miami Marlins. Received Kyle Kaminska (minors) and Gaby Sanchez.
- Traded Casey McGehee to the New York Yankees. Received Chad Qualls.
As you can see, in the space of two days the bullpen lost Brad Lincoln and "gained" Chad Qualls, although they were not actually traded for each other. But did Clint Hurdle use them in the same role as relief pitchers? I concluded he did, based on an informal look at their respective game logs and the innings in which each typically made their appearances. But one particularly argumentative poster shrieked that Lincoln had been used in higher "leverage" situations, while Qualls (and after Qualls got injured, his replacement Takahashi) were not, and encouraged the reader to look up their respective leverage indexes.
Leverage index is a statistic developed by Tom Tango that helps illustrate the context of a relief pitcher's appearance:
Within a game, there are plays that are more pivotal than others. We attempt to quantify these plays with a stat called leverage index (LI). LI looks at the possible changes in win probability in a give situation and situations where dramatic swings in win probability are possible (runner on second late in a tie game) have higher LI's than situations where there can be no large change in win probability (late innings of a 12-run blowout).
The stat is normalized so that on average the leverage is 1.00. In tense situations, the leverage is higher than 1.00 (up to about 10) and in low-tension situations the leverage is between 0 and 1.0.
Tango's chart (there is a fixed Leverage Index for every inning/game situation) is here.
So over the course of a season, one would expect a team's closer and main set-up man to have an average leverage index (aLI) greater than one, while middle relievers might have an aLI around one, or a bit lower. Here's the 2012 Pirates bullpen (min. 20 appearances as a relief pitcher), ranked by aLI:
I get a hearty laugh at the idea of Clint Hurdle consulting Tom Tango's chart when choosing a relief pitcher, but based on aLI, it is clear that Hurdle didn't put Brad Lincoln in many high-pressure situations in 2012. Meanwhile, Chad Qualls had an aLI of just 0.505; does the difference between this number and Lincoln's 0.890 reflect differences in how Clint Hurdle used them, or is there another possible factor to consider?(more after the jump)
In an attempt to answer that question, let's consider the roller coaster that was the Pirates' 2012 season. We can divide it into three parts:
April/May: 25-25, 147 RS, 176 RA
June/July: 34-19, 276 RS, 215 RA
Aug/Sept/Oct: 20-39, 228 RS, 283 RA
In April/May, the Pirates had excellent starting pitching but a sub-par offense, and thus one would expect more opportunity for higher-leverage relief appearances. Likewise, one would expect somewhat less opportunity (more leads to protect, but the leads were larger) in June/July as the bats came around, but even less in Aug/Sept/Oct as the offense and starting pitching slumped (and thus there were fewer leads to protect). Thanks to Baseball Reference's season game logs, we can calculate aLI splits for any relief pitcher. However, it would be probably be a good idea to only consider the aLI splits of the two Pirates relievers whose roles in 2012 did not change, and thus do not require any speculation or assumptions:
April/May: Hanrahan 2.12, Grilli 1.74
June/July: Hanrahan 1.81, Grilli 1.92
Aug/Sept/Oct: Hanrahan 1.56, Grilli 1.46
Even though their roles did not change whatsoever, Hanrahan and Grilli saw a steep drop in aLI after the trade deadline! Now what gives here... Hurdle didn't use them differently after the trade deadline, right?
And speaking of which, we can also simply consider before and after the trade deadline:
April-July: 59-44, 423 RS, 391 RA; Hanrahan 1.96, Grilli 1.82
Aug/Sept/Oct: 20-39, 228 RS, 283 RA; Hanrahan 1.56, Grilli 1.46
By now, it should be clear that aLI is not only a function of a relief pitcher's usage/role, but also the number of high-leverage opportunities available. And when a team collapses historically like the Pirates did in 2012, a drop of 0.4 in aLI is more likely to be due to the lack of opportunities. So the next time someone tries to claim that a difference in relief pitcher leverage (during a season marred by an unprecedented collapse) only reflects the pitcher's role and the manager's use of him, kindly inform said person that their opinion is not supported by facts.