This week, we’re going to take a look at a controversial issue from its least controversial angle. The topic? Defense–a subject that, when we approach it statistically, tends to cause fistfights and sour feelings.

Why is defense such a problem? Because it’s hard to reconcile what’s actually happening on the field with what we see, and it’s even harder to assign responsibility for defense among the team’s fielders. The first problem is the one that draws the big emotional responses. We tend to grade fielding based on how difficult and/or graceful the plays look. So when we see Derek Jeter unleash one of his patented jump-throws in Friday’s game against the A’s, and it creates an immediate impression of elite defense. The play is spectacular, acrobatic, and it takes a single away from the batter.

Not to denigrate the accomplishment of making a difficult play deep in the hole, but it’s worth noting that we don’t place such an emphasis on aesthetics when a player is at bat. At the plate, we care much more about the end result–single or groundout, homer or fly ball–than we do about how stylish the batter looks while getting there. There’s also the issue of whether defensive stylishness actually adds anything to the quality of play. Often when players make spectacular dives or leaping grabs, it’s because they had a slow first step, or were badly positioned to make the play. Comparing this to hitting again, it’s a lot harder to hit a pitch in the dirt or way off the plate than it is to hit one that’s down the middle. A handful of times a week, you’ll see a player successfully golf a slider off his shoe tops for a home run, or slash a pitch that’s headed for the opposite batters’ box down the line for a double. Sometimes the guy with that hacktastic hitting style is Vlad Guerrero, sometimes he’s Shea Hillenbrand, and you need better tools than just a highlight reel of their most difficult hits to discern the vast difference between those two batters.

The other issue, once you get past the aesthetics, is how to break down credit for the team’s defense between the pitchers and the fielders, and among the individual fielders. Unlike offense, defensive opportunities are not doled out on a rotating basis, and those opportunities are not all created equal. Maybe that nifty throw Jeter made was on a ball that the third baseman should have made. Should the guy at the hot corner get a demerit because the shortstop fielded the ball? Do we give extra credit to a center fielder like Ichiro Suzuki, who spends most of his time bracketed by a pair of fairly immobile cornermen?

One way that we can gloss over some of the issue of assigning individual players credit is by looking at the defensive performance of a team as a unit. That way, we don’t care whether it was Ichiro’s responsibility to field a fly ball to left center or Raul Ibanez‘s, we just worry about whether the team converts that fly into an out. The most basic tool to assess defense in this manner is Defensive Efficiency Rating, also abbreviated DER or Deff-Eff. If you remember our conversation about batting average on balls in play (BABIP) a few weeks ago, DER is, loosely, the inverse of BABIP–it simply measures how often a team’s defense converts a ball in play into an out.

As a statistic, DER doesn’t possess much nuance-it doesn’t track double plays, assists, or errors. However, it’s a good, simple way to see if a team is doing its job afield. A number of reports on the stat page keep track of DER, including the Team Defensive Efficiency report, which keeps track of the overall team numbers, and the Pitcher Defensive Efficiency report, which tracks the balls in play information for each pitcher separately (however, this report is not updated during the season, so you can’t see this year’s numbers yet).

One improvement that has been made to DER is adjustment for ballpark, something BP alumnus James Click incorporated in a statistic innovatively named Park Adjusted Defensive Efficiency (PADE). PADE takes a team’s DER, compares it to the MLB average, and then applies an adjustment factor based on the team’s ballpark’s effect on batting average. This helps account for the fact that it’s much more difficult for a team to maintain a good DER in Boston, where there is next to no foul territory and the Green Monster in left field, than in a more spacious park, like you have in Oakland or San Diego. This gives us a scale where the league-average defense is the zero point, and a positive or negative number represents the percentage of balls in play converted into outs above or below the MLB average.

Sadly, we don’t have a sortable report for PADE yet, so I’ll give you a chart of the 2006 PADE rankings, with DER and Fielding Runs Above Average (FRAA) for comparison.

Team  Year       DER       PADE    FRAA
----  -----     ------    ------  ------
SDN   2006      .7130      2.81      22
DET   2006      .7020      2.10      35
HOU   2006      .7011      1.99      22
NYN   2006      .7035      1.31       9
SFN   2006      .7009      1.19      -8
ANA   2006      .6916      1.05       9
CHN   2006      .7011      0.65     -13
ARI   2006      .6850      0.23       1
ATL   2006      .6867     -0.01      -7
COL   2006      .6838     -0.14      36
CHA   2006      .6942     -0.14      12
FLO   2006      .6858     -0.36      -8
NYA   2006      .6949     -0.64      19
OAK   2006      .6894     -0.66      -9
PHI   2006      .6817     -0.81      -3
SLN   2006      .6972     -0.91      12
LAN   2006      .6812     -0.95       6
TOR   2006      .6933     -1.00      17
MIL   2006      .6874     -1.01     -17
BOS   2006      .6801     -1.18     -17
KCA   2006      .6764     -1.39      -9
WAS   2006      .6918     -1.59     -27
CIN   2006      .6818     -1.64     -23
SEA   2006      .6895     -1.70      -6
MIN   2006      .6862     -2.13      16
TEX   2006      .6802     -2.16      17
BAL   2006      .6802     -2.57     -18
PIT   2006      .6745     -2.71     -13
CLE   2006      .6754     -2.74     -10
TBA   2006      .6716     -4.46     -55

As you can probably guess based on the chart, FRAA is the third team defensive metric I’ll introduce you to today. You might remember a brief discussion of Clay Davenport‘s Defensive Translations, in the second edition of Toolbox. Basically, FRAA is a component-based defensive measure using basic game information we have throughout the game’s history: putouts, assists, double plays, ballpark factor, and the handedness of a team’s pitchers. The DT system scores each player’s defensive performance, but some of you might not realize that it also keeps track of team totals. This information is not available as a sortable report on the Statistics page, but we can cull it out of the Davenport Card Team pages, which are maintained for every team in our database going back to the 19th Century. The easiest way to access a team page is through the team audit toggle at the top of this page-you pick your team, and the first link on the audit page will be the team’s 2007 “DT Card listing.” To get prior years, you either have to play with the URL in your browser, or navigate using the links on the individual player cards. Each player DT card carries on the left-hand side links to each team on which the player received time in the major leagues.

With a little elbow grease, by looking at the team pages you can produce a current defensive ranking of teams by FRAA:

Year   Team     DEF-EFF     FRAA
----  -----    ---------   ------
2007   NYN        .734       34
2007   COL        .696       26
2007   CHN        .721       25
2007   NYA        .711       23
2007   ANA        .709       23
2007   OAK        .719       16
2007   PHI        .692       10
2007   SDN        .714        9
2007   BAL        .713        8
2007   BOS        .710        8
2007   MIN        .699        7
2007   DET        .699        4
2007   CLE        .692        4
2007   WAS        .706        2
2007   PIT        .684        2
2007   SFN        .715        1
2007   TOR        .713        1
2007   MIL        .699       -2
2007   CHA        .701       -3
2007   KCA        .690       -3
2007   ATL        .697       -5
2007   SLN        .707       -6
2007   LAN        .697       -7
2007   HOU        .692       -9
2007   ARI        .694      -12
2007   TEX        .688      -15
2007   CIN        .681      -21
2007   SEA        .679      -22
2007   FLO        .681      -29
2007   TBA        .666      -40

So that’s what we have for this week. If you have any questions, or topics you want me to cover in this space, you can send me a message using the links at the bottom of the page.

Further Reading

Clay Davenport, “Shortstops and DFTs”: An early description of the Davenport Fielding Translation system.

Joe Sheehan, “The Daily Prospectus-Dee-fense”: A quick introduction to Defensive Efficiency.

James Click, “Getting PADE-Improving on Defensive Efficiency”: An article introducing the PADE statistic.

James Click, “Getting PADE, Redux”: A follow-up to the original PADE article, with refinements to the statistic.

James Click, “Prospectus Basics-Defense”: A slightly more technical overview of defensive metrics.

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