Leveraging the Braves bullpen

WPA is a stat that lends itself well to the analysis of relief pitching.  Along those lines, Sal Baxamusa has an interesting article up on The Hardball Times about reliever leverage so far in the 2007 season.  If you’ve been reading this site for a while, you might remember that relievers used to be the entire focus of what I did with WPA stats.  Back then (okay, it was just lasy year), I had to input the play-by-play for each game myself, so I burned out by May and effectively abandoned that blog.  You can read those archives here if you go back far enough in the “Braves” category.

That’s neither here nor there, because today we’re talking about reliever leverage in 2007.  Baxamusa used what he calls “gLI” (and what FanGraphs calls gmLI) to represent the leverage of the game situation when a reliever enters the game.  As he said, a player shouldn’t get points for making a game closer after he comes in, so that’s probably the best way to do it.  I used “P” for this last year, and although I think P does a better job when you’re trying to determine how much win probability is possible to achieve in a situation, gLI should be adequate.

What’s really nice about gLI is that it allows you to see how the manager is using the reliever.  Is he only used for blowouts, or only in tight games?  That’s an easy question to answer with gLI or even pLI (which averages LI for each plate appearance/batter faced).  What’s more interesting to me is this: is the best reliever used in the most crucial situations?

Ideally, the best reliever would be used in the highest-leverage situations, at least on average.  However, that’s not always the case, in this ERA of bullpen specialization.  Most teams now follow the usage pattern that Tony La Russa popularized in the 80s and 90s, which means that you use your closer in a save situation regardless of what common sense might dictate.  What we’ll use to determine a pitcher’s usage pattern is gLI/Team LI, or the team’s average LI when that pitcher enters compared to the rest of the team (1.00 being average, as with LI itself).

There are two things that inherently factor into this rating:

1. The quality of the reliever
2. The quality of the rest of the bullpen

Actually, you could reduce that to one factor, if you want to call it “relative quality of reliever” or something similar to that.  By using gLI/Team LI (I’ll call it G/T to save column space), you can level the playing field for each team.  As Baxamusa points out in his article, Team LI for relievers varies (right now) between 1.54 (White Sox) and 0.65 (Mariners).  The Braves’ Team LI is 1.11, almost right in the middle, but some relievers on other teams would be penalized for playing on a team that doesn’t play close games.  G/T eliminates that bit of variability.

Obviously a manager can’t use his best reliever for every close game, but ideally, the G/T rankings would correspond to the team’s depth chart, from the best reliever to the worst.  I’ll be tracking this from here on out in a special section for relievers (below the total pitching stats).  The current stats for the Braves are listed below, through Tuesday’s game (sorted by gmLI).

This isn’t all that surprising, as Wickman and Soriano have taken the bulk of the high-leverage situations.  They’re nowhere near the league leaderboard in G/T, though, indicating that Bobby might be able to get a little more mileage out of them in tough games.  Perhaps more importantly, he should hold back on using them in those “save situations” with a three-run lead in the ninth.  This is also nothing new.

Gonzalez is an interesting story, coming in below the team’s average gLI despite being a top-notch reliever.  I haven’t looked at the specifics, but I suspect that Cox is using him more against lefty-dominated lineups and choosing to use Yates in similar situations against right-handed batters.  If that’s the case, he’s more than a bit misguided.  Gonzalez has held righties to an OPS of .615 in his career, and while his OPS vs LHB is better (.555), that doesn’t make him anything less than a dominant pitcher against RHB.

Regardless of why Cox uses Gonzalez in less-crucial situations, there’s no good reason for it.  Cox could split the high-leverage situations more evenly, or he could reduce his use of someone like Oscar Villarreal, who is right behind Gonzalez in G/T.

Having said all that, properly deploying your relief corps is not as easy as it sounds, and my hunch is that Bobby Cox isn’t the worst manager at doing so, nor is he even close.  My goal is to quantify the manager’s impact in this area at some point in the future.  You’ll notice above that I’m reviving what I call a player’s and manager’s Usage Score (USG, not to be confused with the basketball version), so let me explain that.

Previously, I used leverage stats based on “P” to calculate USG.  As I said already, I don’t have the time to go through each game play by play anymore, so I’m deferring to FanGraphs and their stats, which are based on Leverage Index.  That requires a bit of a workaround, but here’s the basic idea:

USG compares a pitcher’s actual G/T (theoretically, the manager’s view of that reliever’s relative quality) with a performance-based theoretical G/T.  Coming up with that theoretical G/T is the tricky part, but right now, I’m using pWPA/LI (Leverage-adjusted WPA per plate appearance) as the basis for it.  I just take the team-worst pWPA/LI and add it to the pWPA/LI for each player, and then I compute the player’s performance above average on the 1.00 average scale used for G/T.  That’s where I’m getting what’s labeled as tG/T (theoretical G/T) above.  Then, I simply subtract the actual G/T from the theoretical value, yielding negative values for relievers who should be used in less-crucial situations and positive values for the opposite.  It’s an imperfect method, but for now it gets the job done.

You’ll also notice the number 45 on the “Totals” line for USG, and obviously that’s not the total of those numbers.  It is, however, a weighted total for USG, based on the number of games pitched for each reliever.  I used the absolute value of USG for this calculation, since an error is an error no matter which way it goes.  That number, theoretically, represents some abstract total of errors that Bobby Cox has made in deploying his staff.  The ideal there would be zero, but it would also be virtually impossible to achieve.  There’s also really no way of comparing it to anything without running numbers for every other MLB team, which is way too much work for me.  This should do for now, as it does a decent job telling us which Braves relievers could be used more optimally.