Tuesday, May 16, 2006

Black And Blue Pen

Frank Robinson has made the contention that the loss of Luis Ayala has cost the Nats six wins so far this season. Where'd he come up with that number? Is it like when he said that the loss of John Patterson has cost the team three or four wins, even though the Nats have only lost two of Mike O'Connor's starts (and only one that wasn't caused by the bullpen)?

Is he right? I dunno, but our number-crunching friends at Baseball Prospectus can help clue us in.

Let's start with Adjusted Runs Prevented, ARP. The name sounds friendly enough, and it's based on a relatively simple concept. It aims to figure out how many runs a reliever allows when compared to a typical reliever.

ERA is not an especially good tool for evaluating relief pitchers. If Joey Eischen comes in with the bases loaded and allows two singles and a walk before getting the final out, he'll have allowed three runs to score without being charged for a run, despite completely failing at his job.

ARP tries to get around this by considering the context of the performance. What is the situation when the pitcher comes in? And what's the situation when he leaves? It looks at something called a run expetency table, which is nothing but a listing of how many runs a typical team scores. Here's a sample one using run totals from '99-'02. If you look at it, you see that the average team scores .555 runs per inning when there's nobody on and no one out. When the bases are loaded and nobody's out, the typical team scores 2.417 runs. Easy enough, right?

ARP's a little trickier. Using their magical stat gnomes (file photo), they've managed to produce a table which adjusts for league AND for park. Bases loaded with nobody out at RFK typically scores fewer runs than the same situation at Coors Field. We don't have access to that, so we have to nod approvingly at our Prospectus overlords and trust that they're not screwing us over.

Using the table we DO have, though, let's look at an example. It's the 6th inning, and Ramon Ortiz allows a single to Edgar Renteria and then a double to Chipper Jones. Frank trudges out to the mound to bring in Gary Majewski. With runners on second and third with no one out, the typical team scores 2.053 runs. Majewski gets Jones to fly out to deep right for a sacrifice fly, but Chipper holds at second. In a fit of tempetuousness, Frank storms to the mound to bring in Joey Eischen to face Adam LaRoche.

To figure out Majewski's stat, we look at how the state has changed. He's now leaving a game with a runner on second and one out. The typical team scores .725 runs in that situation. So when you subtract the state he entered from the state he left and account for the runs he actually allows (2.053 - .725 - 1), you see that Majewski did his job, saving .328 runs above what a typical reliever would.

When Eischen comes in, he promptly walks LaRoche on four pitches before giving up a three-run bomb to Francouer, at which point, Frank begrudgingly yanks him, handing the reigns to Bergmann. Eischen started with .725 and left with the bases empty and one out (.573) and yielded three runs. .725 - .573 - 3 = -2.848 runs worse than average. Ouch.

So let's look at some real-world results, eh?
John Rauch:       9.9
Gary Majewski: 4.5
Chad Cordero: 0.6
Mike Stanton: -0.9
Jason Bergmann: -3.1
Felix Rodriguez: -3.9
Joey Eischen: -9.9

That's pretty brutal, huh? Only Rauch and Majewski (who knew?) have been well above average. Meanwhile, Rodriguez and Eischen have been disasters, which isn't surprising if you've watched the games. It's pretty amazing to think that the difference between Rauch (who's actually the second best reliever in the NL according to this metric) and Eischen (who's the WORST reliever in the NL according to this metric) is nearly 20 runs.

Ordinarily, 10 runs saved is about equal to one win. But in the case of relievers, it's not clear that that really holds. If Eischen's giving up bombs in a game the Nats are already losing, the runs he's allowing don't really mean anything. But if he's giving up three-run bombs to Ken Griffey in the bottom of the 11th, they mean a whole lot.

Thankfully, Prospectus tries to help us there, too. They have a horribly named stat, WXRL, which aims to take those runs saved and allowed and adjust them for the context of the game situation and the actual batters faced. (So if Cordero has a 1,2,3 inning against Pujols, Edmonds, and Rolen in the 9th inning of a tie game, it's more valuable than one against Brian McCann, Brian Jordan, and Pete Orr in the 4th inning of a game the Nats trail by 17).

It also, for some Godforsaken reason which doesn't really concern me, expresses these values in terms of value over a replacement player -- the kind of player like Jason Bergmann or Sunny Kim that you can grab for nothing if injury strikes. Oh, the most important thing... it tries to convert the runs total into how many wins that pitcher has created in comparison to the waiver-wire pluckee.

Let's see how the Nats fare:
John Rauch:        .546
Chad Cordero: .294
Felix Rodriguez: -.004
Jason Bergmann: -.114
Gary Majewski: -.367
Mike Stanton: -.386
Joey Eischen: -1.094

Ouch! Even though Rauch has been the second-most effective reliever in terms of runs prevented, his contributions haven't been that valuable because of the timing of them. If you think back to the beginning of the year, for example, Rauch was coming in almost exclusively after Ramon Ortiz or Livan got their brains beaten in early in the game.

Cordero, on the other hand, has been more valuable than his stats indicate. Yeah, he hacked up the game the other night, but think about how many times he's come in this year in tie games in the 9th inning. That's VERY valuable, and this stat recognizes that keeping a game tied is almost as important (maybe even more?) than holding on to a lead. He's done more to help than hurt.

But if you add those numbers up, you get -1.671. The bullpen has cost us about two wins beyond what a gang of castoffs would, which is nowhere near the six games that Frank is pinning on Ayala. Rauch, who's been wonderfully effective, has been barely worth half a win. Relievers, especially middle relievers, just don't pitch often enough and in high enough leverage situations, to rack up that kind of effect on games.

Sure, the bullpen's stunk on ice this year. There's no denying that. But there are useful pieces there. Cordero's a solid reliever. Majewski's about where he was last year (overuse not withstanding) and Rauch can do a pretty effective Ayala impersonation -- it's just that it's taken (perhaps takING) Frank a bit too long to figure that last one out. Stanton's not great, but he has his uses, especially if you spot him. FRodo's a disaster, but he's also mopped up innings in situations where it's not really hurting the Nats.

It's probably not going to be what we had last year, but it's still a solid bullpen. Take Eischen out, and it's not bad. Supplement it with Bray or someone else, and it'll be pretty good.

But six wins good? Nope. Nice try, Frank.


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