A couple weeks ago, during what turned out to be an epic pitching duel between Matt Cain and Cliff Lee, something ordinary happened -- a common occurrence that I found nonetheless intriguing. In the bottom of the eleventh inning, with Antonio Bastardo on the mound, Brandon Belt singled. Angel Pagan, on the sixth pitch of his at-bat against Bastardo, hit a groundball to third baseman Ty Wiggington. Wiggington bobbled the ball and both runners (Belt, Pagan) were safe on the play. Wiggington, accordingly, was charged with an error. Melky Cabrera then stepped up to the plate, one out in the inning, and lined a single into shallow right field to drive in the winning run.
This, of course, got me thinking about the implications of Pagan's "reached on error," which had improved the Giants' win expectancy by roughly 7%. Had he struck out, rather than put the ball in play, Melky's single would merely have advanced Belt to second base -- and the Giants would have then had runners on first and second with two outs. Who knows what would have happened next? Instead, Pagan put the ball in play. And though the result of the plate appearance dropped his overall numbers (AVG/OBP/SLG), it was a positive event.
There are cases in which "errors" are clearly the fault of the fielder, and similarly, there are cases in which the fielder is given a tough break when charged with an "error." Either way, in spite of this grey area, it all shows up in the scorebook as an error. There's no established difference. But there are a few things we know about errors that are important to recognize: they occur when the ball is put in play (duh); they're more likely to occur in the infield (i.e. on groundballs) than in the outfield, and moreover, they're more likely to occur on the left side of the infield; lastly, they're more likely to occur when the batter is speedy -- as in Pagan's case.
As such, we can deduce that certain batter skills allow errors to occur with differing frequencies. A swift, right-handed contact hitter (i.e. Angel Pagan, when facing a southpaw) will reach base on errors more frequently than a slow, left-handed hitter who strikes out a lot (i.e. Adam Dunn). Does it not make sense, then, to give some credit to Pagan for reaching on an error even though it was clearly -- at least to a great extent -- Wiggington's fault (see 1:42)? The error was merely the result of Pagan's skill-set, which lends itself to frequent ROEs.
Indeed, this seems to be an area in which hitters can be undervalued. ROEs, which lower a player's triple-slash-line and OPS+, are actually a good thing. And while I don't know that it'd be practical to run a correlation study -- as it would entail going through each batter one by one, I think it's safe to say that this is a repeatable skill (based on a hitter's speed, GB/FB tendencies, and handedness).
Part of the calculation for Baseball-Reference's implementation of Wins Above Replacement is "Runs Reached on Error," and indeed, if we look at Pagan and Dunn, we can see this divide. Pagan has been worth +7 Rroe over his career (~2000 PA), whereas Dunn sits at -8 career Rroe (~6500 PA). It's not a particularly significant difference, but in this nuanced game, every little thing makes a difference. As demonstrated by the initial example -- Pagan's ROE that helped the Giants eventually win a 1-0 game -- something as seemingly meaningless as the ability to frequently reach base on errors can play a crucial role in a team's ability to win a game.
Now, this is hardly the first time this area has been explored. BtB's own Matt Klaasen had a piece on the "error of the reached on error" last year, and as Bill Petti informed me, Clubhouse Confidential did a segment on this about a month ago. Even the New York Times had a piece on this back in 2006. But I felt it was worth rehashing this. Generally, it doesn't make a significant difference in estimating a player's value, as with Pagan and Dunn; but consider that the difference between the two greatest extremes, Derek Jeter and Carl Yastrzemski -- over their whole careers in pure terms of "runs reached on error" -- is 68 runs, or roughly seven wins. I'd say that's fairly significant.
Anyway, this just serves as another example of why it's important to look beyond OPS and even wOBA, neither of which uses ROE as a positive factor in its calculations. (To be clear, this isn't to suggest that wOBA should include ROE). It's also important to understand that "errors" are not simply a function of defense.