Mid-season WPA update

With the season approaching the halfway point, I'm going to start looking at Tigers leaders in various areas. I'll start with the relief pitchers. It's difficult to measure the performance of relievers for a couple of reasons: (1) They pitch so few innings that their statistics can be influenced heavily by a couple of really bad outings. (2) Their actual value depends on game situations more than any other player. Using ERA to evaluate relievers is problematic because relievers often come in with runners on base and give up other pitcher's runs. So a pitcher could have a low ERA without actually being that effective. FIP ERA which is based on walks, strikeouts and home runs allowed rather than runs allowed is better but it still does not consider the game environments in which a reliever pitched.

In one instance, Fernando Rodney comes into the game with a one run lead and two runners on base in the 8th inning. In another game, Bobby Seay comes into the game with a 6 run lead and nobody on base. Now suppose each pitches a perfect inning. Using ERA or FIP, they would both get the same credit for that inning but Rodney's performance had more impact on the outcome of the game.

The Win Probability Added (WPA) statistic gives players (hitters, starters, relievers) credit based on the effect each play has on a team's probability of winning. These probabilities vary depending on the game score, the runners on base and the number of outs before and after each play. They are based on the results of thousands of games worth of data looking at every possible situation over and over.

More concretely, WPA works as follows. Suppose Bobby Seay comes into the game in the top of the 8th with a 2 run lead, 0 outs and a runner on first. There is a .787 (78.7%) expectancy that a team will win the game given that situation. Suppose Seay strikes out the first batter. There is now one out and the probability of winning has gone up to .848. Thus, the strikeout was worth .848-.787=.061

Now suppose the next batter after that doubles home a run. The Tigers now have a one run lead with a runner on second and one out. The probability of winning goes down to .693. So Seay loses points on that batter: .693-.848=-.155.

If you add up all the gains and losses for all the batters Seay faces you get his WPA. WPA doesn't necessarily solve the problem of small sample sizes but it is a reasonable stat for relievers because it gives more weight to plate appearances which have a strong impact on winning and losing games. Table 1 below lists The WPAs for Tigers relievers with 10 or more appearances in 2008. Table 2 lists the American League leaders with 25 or more appearances. These data were abstracted from the Fan Graphs web site.

Todd Jones is the leading Tigers reliever according to WPA (1.34) so far this year. This ranks Jones 13th in the American League. If we ranked Jones according to his by ERA (3.86) or WHIP (1.38), he would not have finished in the top 30. He ranks better on WPA because, like most closers, Jones comes into a lot of critical situations and gets positive results a lot more often than negative results. The Tigers lowest WPA (-1.41) belongs to Francisco Cruceta who, of course, is no longer with the team.

Table 1: WPAs for Tigers relievers in 2008 (through June 27)

Name	G	WPA
Jones	32	1.34
Miner	30	0.48
Rapada	14	0.32
Dolsi	17	0.13
Lopez	23	0.06
Seay	29	0.01
Bautista	16	-0.14
Cruceta	13	-1.41

Table 2: AL reliever WPA leaders in 2008 (through June 27)

Name	Team	G	WPA
Rodriguez	Angels	37	2.86
Nathan	Twins	34	2.77
Soria	Royals	33	2.66
Rivera	Yankees	33	2.39
Howell	Rays	29	2.10
Johnson	Orioles	31	1.99
Sherrill	Orioles	37	1.97
Downs	Blue Jays	34	1.90
Guardado	Rangers	31	1.73
Mahay	Royals	34	1.71

Now, which pitchers typically worked in the most pressing situations? To answer this question, we can use Leverage Index (LI) which measures how critical a given plate appearance is to determining the final result of a game. An LI of one is average. An LI of more than one indicates a high leverage plate appearance which has a potentially high impact on the outcome of the game. An LI of less than one is a low leverage plate appearance. pLI is Leverage Index per Plate Appearance.

Table 3 below lists The pLIs for Tigers relievers with 10 or more appearances so far in 2008. Table 4 lists the American League leaders with 30 or more appearances. Not surprisingly, closers dominated the AL leader board. If you noticed that Francisco Cruceta pitched in a lot of high leverage situations, you were right. Cruceta had the highest pLI (1.78) of any Tiger before he was removed from the Tigers roster. Of those still on the roster, Jones (1.35) and Freddy Dolsi (1.31) have been used in high leverage situations most often. Again, all of these data were pulled from Fan Graphs.


Table 3: Leverage Indexes for Tigers relievers in 2008 (through June 27)

Name	G	pLI
Cruceta	13	1.78
Jones	32	1.35
Dolsi	17	1.31
Miner	30	1.07
Seay	29	0.88
Bautista	16	0.79
Lopez	23	0.54
Rapada	14	0.47

Table 4: AL reliever Leverage Index Leaders in 2008 (through June 27)

Name	G	WPA
Jones	32	1.34
Miner	30	0.48
Rapada	14	0.32
Dolsi	17	0.13
Lopez	23	0.06
Seay	29	0.01
Bautista	16	-0.14
Cruceta	13	-1.41