We saw in my previous post that absolute average, or ABSO (the Average of Batting, Slugging, and On-base averages) does a much better job than OPS of estimating how much the limited set of events used to calculate the two stats contribute to run-scoring, at least on the high end of the offensive spectrum. We also saw that a recent study had confirmed a slight edge for ABSO over OPS in the three most recent seasons, major league-wide.

That same study found that the most accurate stats over that time period are those based on linear weights, notably R/G and wOBA. I decided to see how closely ABSO approximates one of these two most-accurate stats. Since R/G is on a per-out basis and has a large number of defined events, while wOBA is on a per-PA basis and has a more limited set of events, it will be easier to compare ABSO to wOBA.

The weights of each event are calculated based on the run values, relative to the out, of each event. However, they are not the actual run values. For instance, the actual run value of a non-intentional base on balls is 0.62, and the value of a single is 0.77, as empirically derived from whatever finite sample the inventors of wOBA used. In order to put wOBA on the same scale as OBP, they decided to increase each of the weights proportionately.

Now, if that move is legitimate, it would be just as legitimate to proportionately increase the weights a bit more, making the value of a single 1.00, for the purpose of easier comparison to ABSO. (For reasons that will soon become clear, the single is the basic unit of absolute average.) Since RBOE is unknown to ABSO, we will discard that event. Since ABSO cannot distinguish between intentional and non-intentional bases on balls, we will replace NIBB with BB in the formula, calculating a new value based on the relative frequencies of intentional and non-intentional bases on balls. (For this purpose, I used totals for the 2007 season.) The resulting new stat I will call "wOBA-prime" (or wOBA').

When a player comes to bat for the very first time in a season, several things can happen. If he makes an out, his batting average, slugging average, on-base average and absolute average will all be zero. If he gets a single, his batting, slugging, on-base, and ABSO will all be 1.000. Thus, in ABSO, the value of a single, relative to the out, is one.

Now, if the player gets a double instead of a single, his batting and on-base will each be 1.000, his slugging will be 2.000, and his ABSO will be 1.333. If a triple, his ABSO will be 1.667, and if a homer, a perfect 2.000. But what if he gets a walk, or is hit by the pitch? Then it becomes a bit messier, due to the fact that batting and slugging use at-bats as its denominator, while on-base uses plate appearances. If ABs are still zero, it isn't clear that the player even has an ABSO, or if he does, what it is. I could argue that his ABSO is anywhere from .333 (counting batting and slugging as zero) to 1.000 (counting batting and slugging as non-existant, in which case you would only divide by one to get the average). However, if you "pin down" the hit-weights to the values calculated above, and look at actual players, it appears that, for good offensive players, the average value of a walk can range from about .6 to about .7. It does not appear to matter whether the player is one who walks a lot or one who walks very little. (Career-wise, Barry Bonds and Vlad Guerrero each have a computed walk-weight of .65.) I place the average value of the walk (and the HBP) at .67, the mid-point between the above two theoretical extremes, giving us the following weights for comparison:

Absolute average, as you can see, does a pretty good job of approximating the wOBA' weights. It appears to slightly undervalue the other events relative to the single, but remember that linear weights are only valid for the sample over which they are generated. As they say in the fine print, "Your results may vary." The empirically-derived nature of linear weights is both a strength and a weakness. It is a strength in that it leads to increased accuracy for the sample in question, but a weakness in that it provides no absolute standard against which to measure offensive performance. It is a moving target, continually shifting, and providing anomalous results like valuing bases on balls (even non-intentional bases on balls) differently from hit batsmen, when there is no a priori reason to value one over the other in terms of run-scoring.

It is worth mentioning that another proposed stat, 2OPS, generates the exact same hit-weights as ABSO, but due to the fact that OBP is counted twice, the walk and HBP weights will be inflated. Even if 2OPS turned out to be more accurate than ABSO, it would have little chance of being accepted by mainstream fans. ("Why, exactly, are we counting OBP twice? I'm confused.") GPA would have even less of a shot of fan acceptance. ("What does the 1.8 represent? Is that like pi or something? And why the heck are we dividing by four?") Show them an array of linear weights and their eyes will glaze over -- right after they roll them at you.

But tell the mainstream fan that, because a good hitter needs to hit for average, hit for power, and get on base, we are going to use the Average of Batting, Slugging, and On-base averages, and he'll say, "You know, that makes sense." Mainstream fans, the older ones anyway, resent saber-stats because saber-guys, in a fit of iconoclastic fervor, tried to take away the stat the fans grew up with: batting average. Why not give it back to them, as a component of absolute average? Joe Saberguy can view it as a correction to the under-weighting of OBP in OPS without a corresponding over-weighting of walks. Joe Fan can view it as a vindication of the stat of his youth. Everyone can be happy, gather around the campfire, and sing "Kumbaya".

Or not.