When asking what the most important statistic for a relief pitcher is, one could expect a variety of answers, from the commonplace (wins, saves, holds) to the relatively complex (DIPS, RSAA). In sabermetrics, you won’t get a lot of disagreement if you say that an ERA is a good starting point and that a high strikeout-to-walk ratio is always healthy. But most other people, save those who read The Hardball Times or Baseball Prospectus on a regular basis (which I imagine many of you do), don’t have a clue beyond that.

ERAs are great to use, and they tell us a lot, but I think Win Probability Added (WPA) can tell us even more. (I know this is a review for many people, but I feel compelled in this explanation to include those who may not be familiar.) WPA accounts for the criticality of an appearance, based on researched win expectancy tables for different scores and base-out situations. A run allowed to the home team in a tie game, bottom of the ninth, is (needless to say) more important than a run allowed when you’re up 12-2. Not all runs are created equal, so finding the win probability added in a situation tells us a bit more than ERA.

To understand WPA, it’s also helpful to understand its cousin, P. “P” refers to the amount of win probability that could potentially be added by a reliever if he comes into the current situation and finishes the inning without allowing a run. For reference, a bases-loaded situation in a tie game with no outs in the top of the 9th has a P of .473 (given an average NL run environment), while the same situation with two outs and no one on has a P of just .032. Also, a “save situation” 5-2 lead to start the top of the ninth is just .033.

To my knowledge, there have been few (if any) studies on pitchers’ WPA tendencies, so whether certain pitchers tend to be better performers in the clutch or not (at least better than their ERAs would suggest), I have no idea. Accounting for this crucial aspect of the game (the specific situation) does seem to make sense, though, and if nothing else, it gives Braves fans one more reason to despise Dan Kolb. At any rate, I started tracking WPA and P for the Braves out of a slight curiosity, and I’ve managed to turn it into quite an undertaking. It’s an enjoyable activity, but it’s very time-consuming, so the Braves are the only team I track.

Moving on, it’s important to understand that pitchers with high average “P” have more chances to help (or hurt) their WPA. Based on this important premise, I have started tracking several other stats to give WPA a bit more meaning. (Those of you who follow THT may have been familiar with what I’ve been talking about up to this point, but this should be new for just about everyone, unless you frequent my website.)

I account for the “P difference” by dividing WPA by P for two separate stats: WPIP and WPTP, which stand for Win Probability over Initial P and Total P, respectively. For WPIP, I simply divide by initial P, which was my starting point. For WPTP, I divide by total P, which is the P for each inning added up. The result is a rate stat that tells us how much of a pitcher’s P he is actually able to convert into WPA, which is especially useful for comparisons on the same team (where pitchers have varying average Ps). A side effect of the decision to track WPTP was a little added relevance for these stats for starting pitchers (because of the number of innings they pitch per appearance).

I track a few other made-up stats other than these, but they’re not as interesting for the purposes of this discussion. Instead, I’ll close with a few relief pitching leaderboards for comparison’s sake: saves, holds, WXRL (BPro’s version of WPA, expected wins added over replacement level), leverage (BPro’s version of P, which compares situations to the start of a game), and ERA and FIP for relievers with at least 30 innings and at least one save or hold.

 WXRL LEV ERA FIP Saves Holds Chad Cordero 4.462 Francisco Rodriguez 2.35 Mariano Rivera 0.85 Rudy Seanez 1.94 Chad Cordero 34 Scot Shields 22 Francisco Rodriguez 4.404 Bob Wickman 2.19 Chad Cordero 1.17 Mariano Rivera 1.97 Joe Nathan 28 Julian Tavarez 22 Scot Shields 3.775 Ugueth Urbina 2.19 Huston Street 1.41 Kyle Farnsworth 2.29 Jason Isringhausen 28 Ryan Madson 22 Derrick Turnbow 3.334 Joe Nathan 2.18 Mike Timlin 1.44 Francisco Rodriguez 2.35 Trevor Hoffman 27 Mike Timlin 18 Jason Isringhausen 3.301 Trevor Hoffman 2.14 Todd Jones 1.45 Brad Lidge 2.35 Mariano Rivera 25 Luis Ayala 18 Dustin Hermanson 3.298 Chad Cordero 2.07 Eddie Guardado 1.59 B.J. Ryan 2.48 Jose Mesa 25 Scott Eyre 18 Mariano Rivera 2.818 Dustin Hermanson 2.01 Dan Wheeler 1.6 Arthur Rhodes 2.56 Bob Wickman 25 Tom Gordon 18 Eddie Guardado 2.738 Scot Shields 2.01 Roberto Hernandez 1.61 Chris Reitsma 2.58 Francisco Rodriguez 24 Gary Majewski 17 Bob Wickman 2.632 Jose Mesa 1.99 Cliff Politte 1.71 Roberto Hernandez 2.61 Brad Lidge 24 Ron Villone 16 Brian Fuentes 2.593 Akinori Otsuka 1.97 Jason Isringhausen 1.73 Trevor Hoffman 2.61 Eddie Guardado 23 Juan Rincon 16

A few notable things from the data:

Several players have been getting “cheap” saves or holds: Jason Isringhausen (3rd in saves, 19th in leverage) and Julian Tavarez (T-1st in holds, 55th in leverage) for the Cardinals, and Ryan Madson (t-1st in holds, 52nd in leverage) of the Phillies. At the other end of the spectrum are players who are really earning their keep, such as K-Rod, who is just 8th in saves, but first in leverage (and consequently 2nd in WXRL).

There are a few unheralded names on the WXRL list, including Scot Shields, Derrick Turnbow, and Brian Fuentes, who really doesn’t get enough credit for the great job he does for the Rockies.

Next week, I will be fresh off my yearly trip to see the Braves in person (Saturday’s game against the Pirates). I’ll come back with a report for everyone, as well as some more relief pitching analysis.

References
The Hardball Times stats page
Baseball Prospectus stats page
You should also check out Dave Studeman’s articles on Win Probability and P at THT.

### 2 Responses “Advanced Relief Pitching Primer”

1. Larry says:

Just a general comment on P/Leverage wrt the Rockies. Since Coors Field is such a different run environment, is it possible that the P values there are substantially different than elsewhere? How tough would it be to figure that out?

2. John W says:

Great question. You’re absolutely right that the values are different there. The win expectancy chart that I use (courtesy of Dave at THT) is dynamic based on the particular run environment, so the P does in fact change a lot when it comes to Coors Field.

An example:
On May 10, Dan Kolb came into a game at Coors Field with the Braves leading 5-4 in the bottom of the ninth (of course, he blew the game). The P there was .261.

A few weeks later, on June 4, the Braves were visiting the Pirates and were ahead 1-0 entering the bottom of the ninth. PNC is still a slight hitter’s park, yet the P there was “just” .207.

I don’t really know how tough it was to figure out, since I didn’t do it myself, but I’m grateful that someone was able to do it. Thanks for bringing that up; that was a great point that I didn’t think to discuss myself.