ABSO vs. OPS
I originally formulated "absolute average" (or ABSO, the Average of Batting, Slugging, and On-base) in "Better than OPS?? ABSO-lutely!!" but most of the reaction has taken place on another blog, starting with the comments to this post, and continuing with "Why do I keep Using OPS?"
Justin tested three years' worth of team stats (2005-2007) and found that "It is true that [ABSO] did a tad better than OPS in this analysis at predicting runs scored." I don't think he was very impressed by the difference, however. I decided to take a look, not at team stats, but at individual stats, and not for a three-year period, but for the entire modern history of major league baseball, 1901-2007. (But don't worry; I'm not going to be comparing modern players to old-timers.)
If we are going to try to compare OPS to ABSO in terms of individual contributions to scoring runs, we are going to require an impartial third stat to compare them to, since team runs are no help without a means of breaking them down into individual contributions. It occurred to me that only six stats are required to calculate both ABSO and OPS: AB, H, TB, BB, HBP, and SF. We don't want a run estimator with stat categories that neither ABSO nor OPS knows anything about, such as GIDP, SB, CS, or SH. Those stats would only cloud the issue. Can we construct a run estimator with all and only the six stat categories used by ABSO and OPS? Why of course.
The basic version of Bill James' "Runs Created" stat uses only four of the six: (( H + BB ) * TB ) / ( AB + BB ). It is easy enough, however, to include the other two stat categories: (( H + BB + HBP ) * TB ) / ( AB + BB + HBP + SF ). Since Runs Created is a cumulative stat, we need to convert it to a rate, e.g. Runs Created per Game, where a "Game" is defined as a certain number of "outs". I used AB - H + SF for "outs", and 27 "outs" per "Game". The result is a form of RC/G or RC27 which uses all and only the stat categories used by ABSO and OPS, thus reducing the extraneous-stat "noise" generated by more complicated versions of the formula.
For every year 1901 through 2007, I determined an OPS Champion, an Absolute Champion, and an RC/G Champion for both the National and the American Leagues. Of the 214 league-years, ABSO and OPS agreed 183 times, or 86% of the time, but ABSO and RC/G agreed an astonishing 207 times, or 97%. Of the 31 times OPS and ABSO disagreed, RC/G sided with OPS only four times.
The main criticism I have seen of Runs Created is that it tends to inflate the numbers of players with both high OBP and high SLG. But presumably that would include most if not all of the OPS and ABSO champions, and in any cases where it did not, RC/G would presumably favor the OPS champ. Besides, we are not really concerned here with "How many?" but only with "Who had more?" So RC/G need only correctly determine which combinations of hits, walks, total bases etc. lead to the most runs scored, and not exactly how many. Whether you are impressed by my results will depend, I suppose, on whether you think it does that.
Oh, and in case anyone is interested, the complete list of Absolute Champions is here.
Interesting stuff. A few quick points:
1. Your study is essentially looking only at the upper extremes of performances, which might call into question its generalizability to more ordinary players. Of course, coupled with my study (which focuses only on the middle-range of the spectrum and ignores the extremes), it does lend more support for your ABSO statistic over OPS.
That said, I'm still not convinced that it makes that big of a difference. In those cases of disagreement, how many times was the #1 OPS guy in the top 5 (or even top 3) your ABSO or RC/G statistics? I'm guessing a lot.
2. I don't really see why you'd use RC/G, as it is a problematic statistic. The issue with inflating the value of high OBP, high SLG players (which will almost always be the sorts of players you're working with in your study) is one problem. It also doesn't properly weight home runs vs. other offensive events. Tango did a nice study on this in a three part series that starts here: http://www.tangotiger.net/runscreated.html
RC works pretty well for teams, but it isn't a very good stat for players. I sound like a broken record, but why not use linear weights?
FWIW, using linear weights, I have Jerry Hairston as having essentially equal rate production as Adam Dunn this season, despite the fact that Dunn has better OBP and SLG (and OPS). Why? I think it probably has to do with Dunn's walk-heavy OBP, and the fact that Hairston's getting his SLG with lots of singles and doubles rather than homers (two doubles are worth more than one homer). I don't think Hairston could keep up that pace over a full season, but it makes for an interesting comparison of differences between these statistics. Your ABSO actually values Hairston over Dunn (on a per-rate basis), but I think that's an over-correction.
-j
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1. I don't think it makes that big a difference overall, but it makes a big difference in the relative rankings of certain types of offensive player. For instance, Dave Kingman (relatively low average, but very high power) was the NL OPS champ in 1979, while Keith Hernandez (very high average, relatively low power) was fifth. With ABSO and RC/G, Hernandez is ranked first and Kingman fourth. (Incidentally, wOBA agrees with ABSO and my version of RC/G in this case, ranking Hernandez first and Kingman fifth. I haven't run wOBA and R/G for all years, but if you'll remind me of the R/G formula I'll be glad to do so.) You are correct, though; the OPS champ is almost always in the top three ABSO, and vice versa. I would expect this to be the case, however, since as I pointed out, ABSO and OPS agree on the #1 hitter 86% of the time.
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R/G as I use it is just linear weights divided by outs and then multiplied by 26.25 (the average number of outs per game). Some people use /27 outs, but 26.25 is a little closer to the mark, so I prefer that figure. It really doesn't matter as long as you're consistent, because it's just a constant.
You can get linear weights from my site in the player value series (see the run estimators article). Or, Patriot just posted a nice article on them at his site that gives you a choice of formulas to work from, depending on your needs:
http://walksaber.blogspot.com/2008/06/run-estimation-stuff-pt-1.html
Also, while not directly relevant, Tom Tango is trying to get Bill James to adopt Base Runs as a technical version of runs created. Base Runs performs much better than runs created, is what I use to evaluate pitchers, and is what I used to calculate the custom linear weights that I use to evaluate hitters: http://www.insidethebook.com/ee/index.php/site/article/deprecate_runs_created_in_favor_of_baseruns/
There's no good reason for him not to do it, except maybe stubbornness.
-j
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Ah, so R/G is basically like wOBA, except it is on a "per out" basis rather than "per plate appearance". I find it interesting that the linear weights for hits that Tango et. al. end up using in order to put wOBA on the same scale as OBP (1B=0.90, 2B=1.24, 3B=1.56, HR=1.95) look very similar to the weights generated by ABSO (1B=1.00, 2B=1.33, 3B=1.67, HR=2.00). How do I know these are the weights ABSO generates? Consider a player coming to bat for the very first time. If he gets a single, his batting, slugging and on-base averages will all be 1.000, so his ABSO will also be 1.000. If he gets a double, his batting and on-base averages are both 1.000, but his slugging average is 2.000, and the average of the three (ABSO) is 1.333. A triple gives him an ABSO of 1.667, and a home run is a perfect 2.000. If they had adjusted wOBA to be on the same scale as ABSO, rather than the same scale as OBP, the weights would be very similar indeed. OPS, on the other hand, adjusted to the ABSO scale, yields weights that are power-heavy (1B=1.00, 2B=1.50, 3B=2.00, HR=2.50). This may help to explain why ABSO works better than OPS.
I am a little less clear about the value of a walk or a hit-by-pitch. If either of these happens in a player's first plate appearance, his on-base average is 1.000, but he really doesn't have a batting average or a slugging average, since he hasn't yet had an at-bat. I'm not sure what his ABSO is at that point. It is certainly no lower than .333, and no higher than 1.000, however, and the correct value for BB and HBP is almost certainly somewhere in this range. Notice that I say "the correct value is" rather than "the correct values are". I can come up with no a priori reason there should be two different values for BB and HBP. Also, if I were going to do a fair comparison of ABSO and OPS using wOBA or R/G instead of RC/G, I would need a single value for BB rather than one value for unintentional BB and one for IBB, since neither OPS nor ABSO can distinguish between the two. (Recall my methodology in constructing the hybrid version of RC/G I used.) I would also need to leave out SB, CS, GIDP, etc. as before, and I am not sure that doing this would not alter some of the values that I would be using. I'm just not sure how to proceed from this point.
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