Stat to the Future: Defending and dissecting Defensive Runs Saved

In a recent installment, I wrote about what WAR is and the way it works; essentially, by assigning run values to plays and crediting players for creating these runs.

Offensively, it’s intuitive: a single is worth so many runs, a double is worth so many more runs and so forth. Defensively, it’s a completely different story.

In this edition of Stat to the Future, we’ll look at Defensive Runs Saved: the backbone of the defensive component of rWAR’s calculation.

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The error of errors

DRS exists to solve flawed traditional statistics used to evaluate defense, specifically errors and fielding percentage.

Exhibit A: Matt Kemp and Kevin Kiermaier.

Last season, Kiermaier had six errors and a .976 fielding percentage, and Kemp committed only one error and ran a .993 fielding percentage. Clearly, something is wrong here: the eye test can tell you that Kiermaier is a better fielder than Kemp.

The answer lies in range: Kemp might not be able to make a play on a ball hit 20 feet away from him, but he can easily make plays on balls five feet away from him. Kiermaier has far better range, so he can make plays on balls that are much further. Errors are only charged to players who can make a play and flub it, not to players who are unable to make a play.

Of course, those balls 20-plus feet away from Kiermaier are more difficult to make a play on than the balls five-plus feet away from Kemp. While Kiermaier is responsible for more outs, he still is penalized for being unable to make tough plays, and hence his fielding percentage is lower than Kemp's by virtue of attempting to make more difficult plays.

DRS attempts to solve the problem of not giving players credit for making difficult plays when they can and harshly punishing them when they can’t.

Take a look at the leaders in DRS against the winners of the Gold Glove awards and the Fielding Bible Awards from last year.

With the exception of Eric Hosmer (-7 DRS), Dallas Keuchel and Tyler Chatwood (9 DRS each), everyone who was the consensus best defender at their position also graded out as a great defender by DRS.

Calculating DRS

As Run-DMC once said, "it's tricky." Or was that Defensive-Runs-Saved-DMC? I digress.

DRS is calculated by an organization called The Fielding Bible, which compiles and publishes defensive statistics for players season by season. The Fielding Bible also publishes books of the same name, describing their methodology for calculating their metrics, though much of their information is available on their website.

DRS principally relies on batted ball data from Baseball Info Solutions — a huge dataset that is usually used by professional sports teams for analytic scouting. Batted balls by BIS are graded based on the direction that the ball is hit, the distance of the ball, the speed of the ball off the bat and the type of the batted ball (line drive, fly ball and so forth).

Batted balls can be grouped based on similarity, and then the frequency at which players turn those batted balls into outs can be evaluated as a percent. DRS gives credit for players based on how they perform on based on that percentage.

Now, a hypothetical: a screaming line drive hit just over the shortstop’s head.

Let’s say that a shortstop makes a play on that ball about 25 percent of the time. If Andrelton Simmons can’t make a play on that ball, he receives -.25 credit. If he makes the play, he receives .75 — essentially, the credit for making the play versus missing the play, leaving out the expectation that a player would make the play.

DRS then looks at how many bases batters go for on the play. If Simmons misplays it and allows the runner to go to second, then Simmons is charged with -.25 times two bases, or -.50 bases allowed on the play. If he made the play, and on those types of batted balls runners received 1.25 bases on average, Simmons receives credit for .75 times 1.25, or .9375 bases saved.

Finally, DRS uses run expectancy to determine how many runs a saved base at a position is worth: for a shortstop, this factor is around .76. To convert from bases saved to runs saved or bases allowed to runs allowed, multiply bases saved or bases allowed by that factor. In this example, Simmons is responsible for .9375 times .76 or .71 runs saved if he makes the play, or -.50 times .76 or -.38 runs if he can’t make the play, and allows the runner advance to second.

If we take all of those runs saved and lost over the course of a season, we would find their Plus/Minus score: the runs saved or lost because of a player’s defense over the course of a season. A perfectly average defender will have a Plus/Minus score of zero. Above average defenders will have a score above zero, and below average will have a score below zero.

The rest of DRS

Plus/Minus score is the core component of DRS and is representative of the general philosophy behind it: assigning runs to players based on making plays compared to an average defender. But DRS is not wholly Plus/Minus runs saved, it consists of the following components:

• The aforementioned Plus/Minus runs saved
• GDP runs saved: runs saved by turning a double play
• Bunt runs saved: runs saved by fielding bunts and getting outs
• Catcher Stolen Base runs saved: runs saved by a catcher throwing out a runner
• Pitcher Stolen Base runs saved: runs saved by a pitcher controlling runners
• Adjusted Earned runs saved: runs saved by a catcher calling pitches and framing pitches
• OF arm runs saved: runs saved by outfielders throwing out runners
• Good plays and misplays runs saved: runs saved by heads-up-plays

Except for catchers, Plus/Minus represents the majority of a player’s DRS. In the sense that DRS assigns run values to defensive plays, they can then be placed side-by-side with offensive-run-valuations to create WAR.

Of course, DRS isn’t the only way to assign run values to defense.

Don't you love cliffhangers?