wOBA Addendum: How Valuable are Rajai's Legs?

No, I'm not talking about his logo-emblazoned stirrups.

Last week I wrote about wOBA and how it's calculated and used. One of the great things about wOBA is its flexibility. That run value system can be adapted to include any event you would like. Want to include intentional walks? Look up the average run value, add 0.3, multiply by 1.15, and throw it in the formula. Catcher's interference? Just do the same thing. The only reason those events aren't usually included in the standard wOBA formula is because they're so rare that they're not worth the trouble of calculating. For pretty much everybody, they'll likely make next to no difference in the end result. But unlike interference calls and non-Barry Bonds intentional walks, stolen bases and caught stealings can occur enough in some cases to matter. Lucky for us, we've got one of those rare cases.

Yeah, yeah, I know, Rickey Henderson claimed that Rajai Davis could steal 80 bases. That's not happening. But he does lead the majors with 22 steals, which puts him on pace for 68+. And he's just so blindingly quick that I see no reason for that pace to go down, provided he stays healthy.

Now, the math doesn't quite work the same as the rest of the offensive events (+0.3, ×1.15), because SBs and CSs don't take up or occur during a plate appearance, but the weights for the wOBA formula work out to be +0.25 for a stolen base and -0.50 for each time caught stealing.

If you calculate Rajai's wOBA using the standard formula, it comes out to 0.298. When you add in his 22 stolen bases and 2 caught stealings, it jumps all the way up to 0.322. That's still not exactly good (especially considering that CFers as a group generally hit a hair better than the league average of 0.325-0.330), and it's nowhere near his 2009 mark of 0.354, but the 24 point SB-fueled increase means that his baserunning has already been worth, by itself, almost four runs. Over the course of a full season, his legs are on pace to create something around twelve additional runs, or a full win plus change. Not bad at all.

 

The A's are in Fenway tonight, as Gio Gonzalez opposes a pitcher the A's know very well, John Lackey. First pitch is at 4:10 PM, rainy weather permitting.

Odds and Ends

  • Those wOBA weights really point out how small of an impact stolen bases actually have. A stolen base is worth somewhere around a third or a fourth of the value of a single. Rajai is special. Most batters don't have anywhere near the speed required to steal enough bases to make it all that meaningful. If you had to choose between a light hitting speed demon and a league average base clogger, it's almost always worth it to choose the base clogger, even if the gap in hitting ability is rather small. Even a legendary 80 SB/0 CS season would only add 30 points to a wOBA over a full year. In other words, steals are great if they're a bonus, in addition to hitting ability. If they're the only reason a player is on a team, you're probably making a roster mistake.
  • For those wondering if the weights should change from year to year due to changes in run environments (or for those who like looking at enormous monolithic tables full of numbers), take a look at this. It's a table from Tom Tango's website that shows the wOBA weights if you were to recalculate them every year. The answer? Eh, not really. The weights stay constant enough to be fine as static unchanging numbers.
  • By the way, Fangraphs's wOBA already includes SB and CS.
  • I wanted ask this question last week, but I'll ask it now: are there any other arcane stats you'd like to see tackled next? I was thinking of aiming for UZR, followed by WAR, but if there are any good recommendations, I'd be happy to handle those too.
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