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Tuesday, September 02, 2008
Fixing BaseRuns and RARP
I’ve had a very interesting email discussion with Clay, which I will reproduce here. The quoted parts are him. I also have to say it was very pleasant, as are all my discussions with him. He certainly seems willing to make corrections where needed, and offer alternate solutions.
On the discussion here, noted in post #10: http://www.insidethebook.com/ee/index.php/site/comments/rarp_v_vorp/
Basically, I think you have an issue with RARP with pitchers, and I think it relates to the issue of EqR at the low-end. I talked about this a year or two ago, and EqR breaks down at the low-end, and the result with your pitchers-as-hitters RARP may be the result.
No, it relates to a problem in calculating replacement level at the low end.
I have defined replacement level as a .230 eqa for the league, with .260 the average value of the league. For a 100% full-time player, that’s a 22-run difference.
Other positions were defined as (230/260)*(position average). In other words, replacement eqa was always a fixed .885 ratio of the average, which equates to a .736 run ratio and a .350 offensive winning percentage. For positions with eqas from .245 to .285, the difference between average and replacement varies between 18.4 and 27.8 runs.
For a pitcher, with an eqa of .100, the replacement eqa would .0885. The difference between average and replacement is only 2 runs, which is essentially the same as average pitcher, which is why they clustered around 0. I’ll probably re-write it to force all positions into a 22-run difference, which will tend to improve rarps of catchers and shortstops, and hurt ratings of first basemen and corner outfielders. I’ll have to think about that. That would make Zambrano a 14.5 if he were a pure pitcher, and Lohse a -1.1, for a 15.6 run spread between them. Zambrano’s RARP is being held down by appearing as a pinch-hitter in six games, so his position value is higher than a pure pitcher. The program is giving too much weight to those games.
I disagree about the breakdown in EQR at low values. Keep in mind that eqa/eqr are designed to reflect the change in runs from adding this player to an average team. Properly speaking, it should not be used as team/game estimator, although as long as you’re close to the league average it works well. If you were to calculate BaseR for the entire league, subtract Lohse’s stats from the league, and recalculate based on the league minus Lohse totals, you should get a close match for the EqR, and that will be a negative run value.
Speaking of baseR, is there a reason why CS and DP are in the “B” component, but not in the A or C components where it seems they belong?
Also, it appears to me be that it could be formulated as
HR + (average number of baserunners when a HR is hit) + (remaining baserunners)*(score fraction)
The average number of baserunners is - at least, should be - calculable from the obp, and should presumed to be equal to just the average number of baserunners at any give time, with a correction for the chance that the batter is leading off an inning. The last bit should depend, essentially, on the ratio of remaining bases to outs. Of course the “obp” would need to be adjusted for HR, CS, and other non-batter outs.
Ooooh… I like that HR idea. You are right that we should be able to come up with a function, based on OBP and HR rates, actually. A team that never hits a HR will have more runners on base than a team that often hits a HR, even if they both have a .333 OBP. I like your insight, and will get my readers to offer their ideas on it.
We have the discussion about whether to put DP and CS in the “A” or “B” term all the time. Either way is “right”. It depends on the perspective. I gravitate on “initial baserunners”, others on “known baserunners”. You can extend that further by even removing SF from the A and adding it in the D term (with HR). I’m not a fan of treating SF as anything other than an out, since we don’t call it a “run-driving-in single”.
It’s possible that the “rate” way of doing replacement level is better, but I prefer the fixed set. You use 22 runs, I use 19.8 runs for hitting and 2.7 runs for fielding (total of 22.5), so essentially we agree. (The replacement PLAYER is a very below average hitter and a slightly below average fielder.)
I’ll toss in another piece - given an OBP which accounts for outs on base and reached on errors, the probability of N batters coming to the plate should be
P(N) = [ (N-1)! / ( 2! * (N-3)! ) ] * ( 1 - OBP)^2 * OBP^(N-3)
Calculate over all N for a given OBP, and you get a vaguely logarithmic plot. This relates directly to the likelihood that a given HR will occur from a leadoff hitter and to the average number of baserunners.
Agreed on SF; I tend to force it to ride with SH, otherwise you get unreasonably large values associated with it.
The trouble with not putting CS in the A/C components is that it is possible to create a line where BaseR produces more runs than (baserunners - caught stealing) would permit, at admittedly very extreme conditions.
I’ll probably make the change on the RARP on Thursday.