from Amazon
Monday, May 19, 2008
Deconstructing Equivalent Runs (EqR)
I would quote the entire post, as Patriot did a fantastic job in showing the glaring holes in EqR. However, let me highlight a few important passages for those who don’t have the time or inclination to understand the nuances that lead to absurdity:
The most important to thing to understand about the structure of Equivalent Runs is that it is essentially a linear weights formula. It is difficult for some people to recognize this from just taking a glance at the formula. However, if one really takes a look at the formula, you’ll see that the only source of non-linearity is the treatment of stolen bases and caught stealing. The denominator of RAW is PA + SB + CS. If SB and CS are both zero, then the RAW denominator cancels with the multiplication by PA, and the formula is 100% linear.
Thus, for all of the window dressing, EqR may as well be Estimated Runs Produced, Batting Runs, or any number of other linear weight estimators. In fact, if you apply the above formula to the teams in the aforementioned sample, and compare it to the “actual” EqR figure (using the long-term averages for L and X), the largest difference for any team is four runs--the 1991 Expos and the 1992 Angels.
You need to take a look at the chart that accompanies this statement…
When looking at the other SB/CS combinations, the EqR stays within a 1.5 run range for all of the combinations. However, the weights for the various hit types move pretty wildly, even for the home run, which should be fairly stable. The out is also bizarrely affected.
... as it shows the HR value to be between 1.21 runs per HR to 1.46 runs per HR, while making a change ONLY to the SB/CS of the player. This is beyond a ridiculous proposition to accept. At the same time, it goes to show how you can come up with virtually anything half-cocked, and still come out with something reasonable.
(Note: see posts 2 and 3.) Note that adding 130 SB with 42 CS added just 1.3 runs. In that case, you might as well not even consider SB/CS at all, if the formula is balanced in such a way that it devalues the effect of the SB by having the run value of the HR depressed like that.
You may also appreciate my post from a year and a half ago where I looked into EqA and compared it to other run estimators.
To me, the only reasonable conclusion from all of the tortuous (and torturous) moves involved in EqR/EqA is that Davenport simply wanted a run estimator of his own. To do that, he had to make sure it looked much different than RC or a linear estimator.