Wednesday, June 30, 2004

To what extent are errors hurting the Red Sox?

After making three errors last night, the Red Sox now rank near the bottom of the league in miscues (they're 27th). All these errors got me to thinking about how many wins the Sox should have given the state of their defense.

One of the first things that sticks out is that even though Boston is at the bottom of the league in errors committed, the team ERA ranks seventh best in MLB -- and this is partly responsible for their current win total. Unfortunately, they lead the league in unearned runs (58) and this definitely has an impact on how many games they have won. So while this team has thus far been able to minimize the damage by getting outs after allowing errors (this is purely conjecture -- I haven't looked into it), because of all the unearned runs, the Sox have definitely squandered some wins. So my question is, how many more losses should the Sox have if they were an 'average' defensive team (given that they are now below average)?

Using 2004 data, I quickly threw together a model for Wins. Specifically, I regressed Wins on OPS, ERA and UERA (UERA is unearned run average. There are problems with this model, but I used it primarily for parsimony and recognize there are other, more detailed models). Anyway, the data yield the following model:

Wins = -11.81 + 105.41OPS -6.92ERA - 3.67UERA

R-sq: 0.70
In English this means that each ten percentage point increase in a teams' OPS will increase their win total by roughly 1 win (over the first 75 games of the season). Decreasing a teams' ERA by one run will lead to an increase of 7 wins (over the first 75 games of the season) and decreasing a teams' UERA by one run will lead to an increase of almost 4 wins.

Obviously, there are two components to a teams' success. Scoring runs (measured in my simple model by OPS) and preventing runs (measured by ERA and UERA). A team can have low error totals but still struggle to win games if they can't score runs (see the Expos). On the other hand, a team can do well even if they give up a lot of unearned runs (see the Red Sox).

Anyway, back to my initial question: How many losses would the Red Sox have if they had an 'average' defense (where I'm using ERA + UERA to measure how effective a defense is -- at least in terms of errors resulting in runs scored. And in the spirit of full disclosure, I used ERA in the model because Errors showed no statistical relationship to Wins -- the correlation between Wins and Errors was -0.045).

As of June 29, the Red Sox have 42 wins. The above model predicts that the Red Sox should have 44 wins (OPS = 0.814, ERA = 3.94, UERA =0.78). The average UERA in MLB is 0.39. So how many wins would Boston have if they allowed roughly 0.30 fewer unearned runs per game? Doing the substitution (Wins = -11.81 + 105.41(.814) -6.92(3.94) - 3.67(0.39)) we see that the model predicts that the Sox would have five more games (49). Given that Boston is currently 6.5 games back, that means they could be as close as 1.5 games behind the Yankees (Of course, less than half the season has been played. Given the Yankees maintain their current winning pace, the Red Sox would actually be in first place by season's end).

Five games over the first half of the season may not seem like much, but over the course of 162 games, these wins add up. Nonetheless, in a division that is perennially won by the Yankees, and with Lucchino, Henry, Epstein et al. trying to slay the evil empire, every win counts. So even though (at least on the surface) the rash of errors have been somewhat minimized by timely pitching (at least anecdotally) and clutch hitting, the law of averages is lurking around the corner and is eager to rear it's head. Translation: Errors are never good -- and good pitching can only mask mistakes for so long. As of yet, the errors haven't had a profound effect on the standings, but if the Sox keep tempting fate, they can forget about the Wild Card because they could end up battling Tampa Bay for third place in the division.