Monday, May 12, 2008

How to Calculate Clay Davenport’s EqR and EqA (Unofficially, Of Course)

Equivalent Runs (EqR) and Equivalent Average (EqA) are measures of offensive productivity developed by Clay Davenport, and popularized through the various publications of Baseball Prospectus. EqR is a measure of runs contributed and EqA measures the rate of run production. While the presence of other websites and books have somewhat reduced the use of EqR and EqA by the sabermetric public, they still pop up from time to time. Unfortunately, a lot of people do not seem to understand how they are figured. I will attempt to explain that here.

I should note, of course, that I am in no way affiliated with Baseball Prospectus, and thus my description should be taken as that of an outsider, who may be out of the loop on changes to the methodology, or may himself misunderstand the procedure. So if anything that I say contradicts what they say, you know who to believe. Also, BP sometimes presents EqR and EqR formulas within the context of a larger evaluation system that also leads to WARP. That approach is pretty much equivalent to the older one described here; this one is more straightforward if one is only interested in understanding EqR and EqA.

Also, the issue of how to figure EqR and EqA is clouded by the fact that BP rarely publishes them in their unadjusted form. The EqA figures in their annual, for instance, have been put through the wringer of Davenport Translations to conform to an ideal league environment. I have no insight to offer on this process, and my description only attempts to cover straightforward applications of the two statistics.

Finally, I should note that I have written about this subject before, and thus there is nothing new here, even in the context of my own writing. I have seen comments that imply the article on my website on this topic is somewhat arcane, and I wanted to write a more accessible version. So as always, I milk this for all its worth by cross-posting to the blog. This installment is an attempt to be objective and just give a straightforward explanation of the formulas. The next article will give my opinions on the method, but I want to keep those two parts separate.

To figure EqR, one starts by figuring Raw EqR, or simply RAW:

RAW = (H + TB + 1.5*(W + HB + SB) + SH + SF)/(AB + W + HB + SH + SF + SB + CS)

RAW is then converted into an estimate of runs, EqR. The formula is:

EqR = (2*RAW/LgRAW - 1) * PA * Lg(R/PA)

EqR starts by taking the league average runs per PA as a given, and then changes the estimate for the team based on how their RAW compares to the league RAW. This relationship has a slope of two; if a team has a RAW 10% better than the league average, they are expected to score 20% more runs than the league average.

EqR is the estimated number of absolute runs contributed; as such, it is a similar measurement to Runs Created, Extrapolated Runs, and many other familiar methods. Equivalent Average is the rate that Davenport chose, just as Bill James uses RC/G or Offensive Winning Percentage.

EqA is designed to correspond to the scale of Batting Average, due to its familiarity to most baseball fans. Thus, the average is generally around .260 (the aforementioned translations force the average to exactly .260); figures below .200 are dreadful, figures above .300 are good, etc.

EqA is based on EqR per out, but that simple figure is first divided by five, then raised to the .4 power to produce EqA:

EqA = (EqR/Out/5) ^ (.4)

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