## Catchin' Those Balls

Defensive efficiency is a quality stat. A defense's job is to catch as many balls in play as possible, and that's exactly what defensive efficiency measures. For the most part, more balls caught equals better than. However, the stat does have some flaws. Some defenses face easier to field balls than others, and defensive efficiency, or DER, does nothing to account for that.

Since my mind tends to wander onto these subjects, and I had no real desire to study for my midterm, I came up with the creatively named stat "Advanced Defensive Efficiency" designed to fix some of the flaws present in defensive efficiency. The logic behind this stat is as follows:

Every type of batted ball in play has an average chance of being caught. For example, a line drive that stays in the park gets turned into an out 26.92 percent of the time. If you look at every ball in play that a defense faces, multiply it by the chance of it being turned into an out, then divide the sum of all those balls by the total number of balls in play, you get a number I call "Expected Defensive Efficiency" or eDER. This number represents the defensive efficiency a team would have if they caught each batted ball type an average amount of times. From here, advanced defensive efficiency is calculated by subtracting a team's DER by their eDER.

Before I present the numbers that I generated, I should warn you that this data is not entirely accurate. The exact amount of each batted ball type a team allows isn't available, just a percentage. Because of this, the final advanced defensive efficiency (aDER) numbers can be off by as much as half of a percent, and that's huge in a stat where the best and worst teams are separated by three percent. With that in mind, here are the aDER numbers for the 2006 season.

 Rank Old Rank Team DER eDER aDER 1 1 SDN 71.80% 70.16% 1.64% 2 2 DET 71.20% 69.70% 1.50% 3 6 CHN 70.50% 69.26% 1.24% 4 5 HOU 70.60% 69.49% 1.11% 5 9 SLN 70.40% 69.33% 1.07% 6 8 TOR 70.50% 69.67% 0.83% 7 13 SEA 69.80% 69.18% 0.62% 8 3 NYN 70.80% 70.30% 0.50% 9 18 ATL 69.20% 68.70% 0.50% 10 17 ARI 69.30% 68.81% 0.49% 11 4 NYA 70.60% 70.64% -0.04% 12 14 MIL 69.40% 69.45% -0.05% 13 21 CIN 69.10% 69.27% -0.17% 14 10 ANA 70.30% 70.61% -0.31% 15 25 CLE 68.60% 69.01% -0.41% 16 7 SFN 70.50% 70.93% -0.43% 17 26 BAL 68.50% 69.07% -0.57% 18 22 COL 69.00% 69.60% -0.60% 19 11 CHA 70.00% 70.67% -0.67% 20 19 MIN 69.20% 69.98% -0.78% 21 29 TBA 68.00% 69.21% -1.21% 22 16 FLO 69.30% 70.55% -1.25% 23 23 PHI 68.80% 70.12% -1.32% 24 30 PIT 67.60% 68.95% -1.35% 25 20 LAN 69.10% 70.51% -1.41% 26 12 WAS 69.80% 71.24% -1.44% 27 24 TEX 68.80% 70.26% -1.46% 28 15 OAK 69.40% 71.11% -1.71% 29 27 BOS 68.30% 70.33% -2.03% 30 28 KCA 68.20% 70.36% -2.16%

Abbreviations used:
Old Rank - The team's rank in defensive efficiency
DER - Defensive efficiency
eDER-Expected Defensive Efficiency

In 2006 The Dodger pitching staff allowed less line drives than any other pitching staff in baseball, which should have resulted in a high DER for the Dodgers. Instead, they finished 20th in baseball in DER which resulted in them tumbling further down the list in aDER. The big surprise here is Oakland, a team celebrated for its defense. They had the second highest eDER in baseball, yet finished only 15th in defensive efficiency, making them the third worst defense in baseball, and no where near the fourth to last. This conclusion seems to agree with the unremarkable rate2s Oakland put up at every position but third base and center field.

I like where this research is heading and I'd like to expand on it some more. There's two ways I can do this. First is getting actual numbers for batted balls instead of percentages. That will let me make actual conclusions from this data instead of saying "yeah, the Dodgers probably weren't very good defensively, but the data could also be flawed". The second is to introduce park factors into the equation. I think with Dodger Stadium's small power alleys line drives and fly balls get turned into outs more often, but I can't draw any real conclusions.

While individual defensive metrics are far from perfect, I think that team defensive metrics can be pretty well nailed down, and that aDER could be the best way to go about it.

Some other notes:

Percentage of time each type of batted ball in play is turned into an out:
Line Drives: 26.92%
Ground Balls: 74.8%
Outfield Fly Balls: 86.13%
Infield Fly Balls: 98.8%

Batted ball values from "What's A Batted Ball Worth?" by Dave Studenmund in the 2006 Hardball Times Annual.

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