May 23, 2009

Prospectus Idol Entry

Joe Maddon's New Math

by Jeff Euston

Last year, before his team's magical 2008 season began, Tampa Bay Rays manager Joe Maddon gave his players t-shirts featuring an unlikely mathematical message: "9 = 8." Nine players, playing hard for nine innings each game, could make the Rays one of the eight clubs to reach the post-season, he told the team.

After Tampa Bay's fast start, Maddon revealed another explanation for his fuzzy math. He figured the Rays needed to improve by 27 games to win the American League East. And they could do it, he believed, if they could improve by nine victories in each of three different areas: the offense, the bullpen and the defense.

The Rays exceeded their manager's expectations, winning 97 games, a remarkable 31-victory improvement over their last-place season in 2007. For someone who orchestrated that sort of historic turnaround, it might seem that nothing is impossible. After all, in the process of directing his club to the American League pennant, Maddon also apparently cracked the code for measuring team defense.

Origins

Since baseball's earliest days, evaluation of defense has traditionally been based on five standard statistics: total chances, assists, putouts, errors and fielding percentage. But that has changed.

The statistical movement that transformed the way clubs evaluate offense and pitching has moved to the last frontier of objective analysis: defense. A variety of tools for measuring defensive performance are now available: Clay Davenport's Translations, John Dewan's Plus/Minus system, Dan Fox's Simple Fielding Runs, Mitchel Lichtman's Ultimate Zone Rating and David Pinto's Probabilistic Model of Range, to name just a few. Many clubs have their own proprietary systems for evaluating and valuing defense, and general managers are acquiring and paying players accordingly.

The spark ushering in this new era of analysis was lit in the Eighties, thanks in no small part to the work of Bill James, who proposed a novel idea: Much of what is perceived as being pitching is, in fact, defense. More specifically, James developed what he called a defensive efficiency record (DER), "a team statistic intended to estimate the percentage of all balls in play that a team has turned into outs."

James' theory, now known as simply Defensive Efficiency, leapt into the popular consciousness in 2008, when Maddon's Rays improved from worst to first in Def Eff and in the standings, en route to the World Series. Year-over-year defensive rankings for the last 10 World Series clubs are listed below. All but one club showed significant improvement in Defensive Efficiency for the year they reached the World Series. The exception was the 2006 Cardinals, who experienced a slight drop from sixth in Def Eff in 2005 to seventh in their championship season.

A new perspective

James' analysis was a departure from traditional fielding statistics in two distinct ways. First, he began the process by evaluating defense as a whole rather than using individual fielding statistics as a baseline. Second, he removed the subjectivity inherent in the traditional scoring model by evaluating each ball in play, regardless of how it was judged by the official scorer.

James began by calculating the number of Plays Made by a team's defense. He did so by making two estimates.

The first estimate:

PO - K - DP - 2(TP) - OCS - A (of)

James assumed a batted ball was turned into an out every time a putout was recorded, unless 1) the putout was a strikeout, 2) two or three putouts were recorded on the same play (a double play or triple play), or 3) a runner was thrown out on the bases, either as an opponent caught stealing or via an assist from an outfielder.

The second estimate:

BFP - K - H - W - HBP - .71 errors

James assumed a batted ball was turned into an out every time a batter faced a pitcher, unless 1) the batter struck out, 2) the batter hit safely, 3) the batter walked, 4) the batter was hit by a pitch, or 5) the batter reached on an error.

James averaged his two estimates, giving him a reliable figure for Plays Made.

That done, James divided Plays Made by Plays Made plus Plays Not Made, and the Defensive Efficiency Record was born.

PM
PM + H - HR + .71 Errors

Plays Not Made included hits, plus .71 errors, less home runs, the vast majority of which were balls defenders had no chance to field.

James found an average defensive efficiency record to be about .695, with most successful teams ranking above average. In fact, James found that his DER calculation correlated well with a club's winning percentage. This was a marked contrast from a traditional metric, like fielding percentage, which yielded no clear pattern when compared to winning percentage.

He also reached another conclusion: Although differences in DER "might look small, they are anything but," James wrote in his 1984 Baseball Abstract. "The effect of having a DER which is .020 below the league average would be very similar to the effect of having a team batting average which is .017 to .018 below league, which is to say that it would wipe you out of a pennant race 99% of the time."

Def Eff and PADE

As calculated for Baseball Prospectus analysis today, Defensive Efficiency (Def Eff) is:

1 - ((H + ROE - HR) / (PA - BB - SO - HBP - HR))

Balls in play (hits and errors, less home runs) are divided by plate appearances, less walks, strikeouts, hit-by-pitches and home runs. The result is subtracted from one, yielding a percentage of balls in play converted into outs. Defensive Efficiency also may be approximated using the formula:

1 - BABIP

where BABIP represents batting average on balls put into play.

The best teams actually convert balls in play into outs about 73 percent of the time, a Def Eff figure of .730. The worst teams do so about 69 percent of the time (.690). James' point on the importance of small variations in defensive efficiency still holds true.

In 2003, analyst James Click created the Park Adjusted Defensive Efficiency metric, accounting for the park factors that affect the DER calculation in each specific ballpark. Click accounted for a variety of factors that might affect a club's defensive efficiency figure: park factor, number of balls in play allowed by the pitching staff, ground ball to fly ball ratio, lefty-righty balance of the pitching staff, and opportunities for double plays. His resulting PADE figure illustrates how much better or worse than average a team ranks in converting balls in play into outs. Click's research has shown that a one percent difference in PADE is worth 13 runs, or 1.3 wins, over the course of a season.

According to the 2008 PADE figures, the Rays were 1.26 percent above average in turning balls in play into outs, adjusted for park figures. Only a year before, Tampa Bay had been 5.64 percent below average. Using Click's method, the 6.9 percent defensive improvement resulted in an increase of 8.97 wins for the Rays, almost exactly what Joe Maddon wanted from his fielders.

Maddon's new math worked, at least where defense was concerned.

Defensive Rankings for World Series teams, 2004-08 MLB rankings in parentheses. Team Defensive Efficiency statistics are available at http://www.baseballprospectus.com/statistics/sortable/index.php?cid=204024

Tampa Bay  Def Eff      PADE
  2007     .656 (30)   -5.64 (30)
  2008     .710 (1)     1.26 (3)

Philadelphia  Def Eff       PADE
  2007        .686 (17t)    0.15 (11)
  2008        .696 (9t)     0.58 (6)
       
Colorado     Def Eff     PADE
    2006     .684 (20)    0.94 (7)   
    2007     .701 (5t)    3.07 (2)

Boston     Def Eff       PADE   
    2006   .680 (25t)   -1.11 (19)   
    2007   .705 (1t)     3.22 (1)

Detroit     Def Eff      PADE   
    2005    .698 (14t)  -0.25 (15)   
    2006    .702 (3)     2.01 (4)   

St. Louis   Def Eff     PADE
    2005    .704 (6)    1.02 (9)   
    2006    .697 (7)    0.85 (9)   

Houston     Def Eff     PADE
    2004    .686 (24)    - 1.64 (26)   
    2005    .706 (4)      0.32 (13)

Chicago AL  Def Eff     PADE   
    2004    .695 (10)   0.06 (10)   
    2005    .713 (2)    2.67 (1)   

St. Louis   Def Eff      PADE
    2003    .700 (10)   -0.70 (17)
    2004    .711 (2)     1.58 (2)

Boston     Def Eff      PADE
    2003   .685 (23t)  -0.80 (18)       
    2004   .693 (14t)   0.95 (4)

Jeff Euston is an author of Baseball Prospectus. Follow @JeffEuston
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