# Understanding Defensive Ratings

You know, ever since coming out with my Range system, I’ve gotten many e-mails and comments from people who were confused about what the run values meant or of what magnitude they were. That’s become a problem in sabermetrics; as our metrics get more powerful, they become more confusing. That’s why, for example, I like Gross Production Average (GPA), which THT tracks. GPA puts a player’s offensive contributions onto a batting average-like scale: it’s simple, but very accurate.

So in answering an e-mail about my Manny Ramirez/Miguel Tejada article, I was trying to explain to what Ramirez’s projected defensive rating next year equated. And then it hit me: why not convert it to batting average? Simply put, I took Ramirez’s defensive run value, found its equivalent in hits and subtracted that from the average batter’s line.

Let me explain that step by step. In the 2005 American League, the average hit was worth .655 runs. The average batter had 154 hits in 575 at-bats per 150 games. So if Ramirez’s Range rating was -38 runs, his equivalent batting average would be (154 – 38/.655)/575. Those -38 runs were equal to 58 hits, so Ramirez’s equivalent batting line would be 96 hits in 575 at-bats, or a .167 batting average, which is pitiful.

So why not do this exercise for every major league player? I did, and I’m here to report the results. Before I do, I want to remind you that Range ratings are not perfect. In fact, I know to a pretty good degree which ones are off and which aren’t. I hope to be back next week with an article about the accuracy of Range ratings. I can tell you right now that the vast majority are indeed correct, so feel free to use them in any analysis you do, but remember that small caveat.

Okay, now let’s have some fun with bullet points:

• The best eqBA belonged to Kelly Johnson, who was the only .400 hitter at .414. The worst player here was Russ Adams, .156.

• In fact, there were lots of players below the Mendoza line. Twelve out of 220 players “batted” below .200, 5.5%. I think the reason so many players were so bad is that most teams have little or no idea as to how to value defense. The Cincinnati Reds, for example, probably have no idea that Ken Griffey Jr.’s defense completely negates his offensive contributions. Range also has a bit of a problem in terms of its spread (a few of the ratings are a little too high or too low), but even with UZR, 3% of all players with at least 600 innings played “batted” below the Mendoza line. Certain players that just should not be out in the field are playing defense; that almost never happens on offense because teams can better evaluate that facet of the game.

• The standard deviation of eqBA was .041, which means that 68% of all players have an eqBA between .227 and .309, and 95% are between .186 and .350. I think that might give a slightly better idea of where a player ranks; a .227 eqBA might look terrible, and it certainly isn’t good, but 16% of all players are worse.

• Because the numbers have not been adjusted for position, a .227 eqBA for a shortstop is actually like a .246 eqBA for a left fielder, for example. In fact, position-adjusted, Ramirez (.167 eqBA) would be the worst fielder in the MLB.

• If I regress eqBA to come up with a simple projection for next season, four guys end up with a projection of below .230, which is something like a threshold for playing defense at all (replacement level, if you will). Those players are Adams, Ramirez, Griffey and Michael Young. Adams and Young should be moved to easier positions; Ramirez and Griffey should DH.

I hope this idea proves useful and simplifies things for people. If you bought the THT Annual (and if you haven’t, you can still do so), a spreadsheet with eqBA for every major league player with at least 600 innings played in 2005 will be available on the Annual site.

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