Feb 29, 2008

Value of Defense in Griffey

Witnessing a great defensive play is certainly one of the true joys of watching a real baseball game; in HBD, we have to settle for a little "++" next to a line in a box score. It's tough to get excited about a "++" because it has none of the aesthetic value of a Jim Edmonds diving into the right-centerfield gap to turn a sure triple into an out, or Torii Hunter scaling the wall to rob another home run. In order to attach a little more meaning to "good plays" and "bad plays," an attempt to quantify the value of good (or bad) defense is presented below.

One nice thing about the "++" versus a real-life defensive gem is that, in HBD, there's no annoying Joe Buck to tell you how a "play like that doesn't show up in the box score" -- in this case, it actually does. Because they are tallied, taking a team's total "good plays" and subtracting out "poor plays" and passed balls is a crude way of evaluating a team's defensive prowess. Translating that into runs and wins is a bit trickier.

In starting with passed balls, two things are important to note: (1) a passed ball only occurs with guys on base and (2) the incremental number of runs allowed due to a passed ball would never be more than one, even accounting for guys moving up a base into scoring postion. With respect to (1), an easy (but almost certainly inaccurate) way of evaluating the effect of a passed ball is to assume that it occurs with equal frequency with lead runners at first, second or third. Assuming that is the case, a passed ball would cost a team, on average, around 0.33 runs. For example, when a runner on 3rd with two outs who scores due to a passed ball, that run is directly attributable to the passed ball if the man at the plate makes an out. However, if that batter gets a hit, the run would have scored anyway; therefore the passed ball is effectively inconsequential. This 0.33 is biased high since a greater percentage of runners reach 1B than 2B or 3B.

Item (2) pertains more to a situation where multiple runners are on base. For example, if the situation was first and third when the passed ball occurred, obviously a run scores and the other runner moves up to 2nd. If the next guy singles and the runner scores from second, that run would be attributable to the passed ball; however, the guy who actually scored when the passed ball occurred would have scored regardless. Consequently, only one of those runs is ever attributable to the passed ball. Taking all of this into account, the value of a passed ball is probably on the order of 0.25 runs.

Regarding a "good play," if we assume that each such event results in adding one out to the situation while leaving all runners in place as they were, we can lean heavily on the statistical work of others to quantify its value. Specifically, clicking here takes you to a run expectancy matrix which shows how many runs might be expected following any given combination of outs and base runners in MLB. Assuming that each situation occurs with equal frequency, that gives a "good play" a value of about 0.5 runs. That may be biased low because the average team OPS in HBD is much higher than in MLB, but you could also argue it is biased high because situations with fewer guys on base occur more frequently than with the sacks packed.

A "poor play" is more difficult to quantify because it is not clear whether it would only result in a one-base shift in runners or if an "out" can effectively be converted into double, etc. In any event, it seems likely that a "poor" play is likely of slightly greater detriment than the benefit received from a "good play."

Taking all of this into account, about 2/3 of a run per event feels about right for each "good play" and "poor play"

So, we are still not where we would like to be with this necessarily, but cutting the shuck-and-jive, expected net wins due to defense over 162 games are presented below. (If anyone has any additional insight here, let me know. This is fairly "back of the envelope.")

Expected Net Wins due to Defense over 162 Games by Franchise

Pittsburgh Ponies: +1.84
Cheyenne Duck Snorts: +1.71
Little Rock Razorbacks: +0.82

Pawtucket G-Maniacs: +0.74
Trenton Cage Rattlers: +0.74
Fargo Fuzznuts: +0.53
New York Yank-Mes: +0.44
Colorado Mile High Rapids: +0.37
Charlotte Wolves: +0.33
Oakland Dragons: +0.31
San Antonio fighters: +0.31
Montgomery Miracles: +0.02
Charleston Cobras: -0.06
Los Angeles Mojo: -0.13
Atlanta Ripettoes: -0.23
Albuquerque Ranchers: -0.27
Rochester Regal Beagles: -0.35
Texas Dusters: -0.38
Philadelphia Revolution: -0.44
New York Cyclones: -0.45
Cincinnati centipedes: -0.48
St. Louis Jayhawks: -0.64
Kansas City Twisters: -0.68
Salem Warlocks: -0.71
Montreal Valiants: -0.82
Syracuse Swingers: -0.89
Cleveland Rockers: -1.13
Florida Tropic: -1.13
Honolulu Beach Bums: -1.26
Anaheim Jack A$$es: -1.27
Tacoma Appleseed: -1.35
Houston Bombers: -1.57

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