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Tuesday, May 24, 2011
K minus BB differential or ratio?
I’m having a discussion with Bill James on the virtue of the K minus BB differential, compared to the ratio. Bill took the challenge (sub only). There are 3 things he did there that would cause bias, because he looked at all data from 1947-2010:
1. Because K rates have been on a steady rise, and there’s been a shift in batting average on balls in play between 1992 and 1994 (.280 pre-1992, .300 post-1994), that the groupings that Bill has done may have an era bias. This is why I find it helpful to look at the data from 1993-present, because there’s been a pretty strong line drawn there, in terms of looking at unadjusted data.
2. I had said it should be K minus BB per PA, not per IP. It’s not that big a deal, but it still has some bias to it.
3. And of course, HR exploded at the same time BABIP jumped (between 1992-1994). And so, if you have more guys in the high K minus BB per PA group, you’d also have higher HR rates as well.
***
I did my own study. I looked only at 1993-2010. I grouped all data by player, so we have 2513 pitching lines (no PA limit). I calculated a “walk” as BB-IBB+HB. I calculated each pitcher’s strikeout minus walk and divided by plate appearances.
I then grouped them into 5 categories:
Group 4: differential of at least .14 per PA
Group 3: differential of .10 to .14 per PA
Group 2: differential of .06 to .10 per PA
Group 1: differential of .03 to .06 per PA
Group 0: differential of less than .03 per PA
I also calculated their runs allowed per 27 outs (i.e., per 9 IP):
Grp IPouts diff/PA R/27 6-14*diff/PA
4 206352 0.169 3.66 3.63
3 436797 0.116 4.33 4.37
2 866050 0.079 4.80 4.90
1 530103 0.047 5.26 5.34
0 208194 0.009 5.94 5.88
Grp is the groups I noted above.
IPouts is IP*3.
diff/PA is the strikeout minus walk differential per PA
R/27 is runs allowed per 27 outs (or per 9IP)
6 - 14*diff/PA is simply six minus 14 times the diff/PA in the previous column
As you can see, a very strong relationship.
Bill however upped the ante, and looked at within each differential group at the K/BB ratio.
So, what I did was flag every pitcher with at least a 3 K/BB ratio as “high ratio”, anyone with under a 1.25 K/BB ratio as “low ratio”, and the rest as “average ratio”.
First up is for Group 4:
Ratio IPouts diff/PA R/27 6-14*diff/PA
Aver. 70668 0.157 3.76 3.80
High 135684 0.176 3.61 3.54
As we can see, the high ratio pitchers do indeed get a better value than their differential would suggest, but the difference is pretty small.
Group 3:
Ratio IPouts diff/PA R/27 6-14*diff/PA
Aver. 372113 0.115 4.36 4.40
High 64684 0.126 4.16 4.24
In this case, both of them are pretty much off by the same amount relative to expectations of using differentials only.
Group 2:
Ratio IPouts diff/PA R/27 6-14*diff/PA
Aver. 862868 0.079 4.80 4.90
High 3182 0.078 4.90 4.91
In this case, the lower ratio pitchers are actually the better pitchers.
Group 1:
Ratio IPouts diff/PA R/27 6-14*diff/PA
Low 8204 0.033 5.46 5.54
Aver. 521899 0.047 5.25 5.34
Here, both groups, the Low and the Average ratios, are off by a similar amount from expectations using differentials only.
Group 0:
Ratio IPouts diff/PA R/27 6-14*diff/PA
Low 166582 0.004 6.09 5.94
Aver. 41612 0.027 5.31 5.62
The biggest gap is here, with the differentials suggesting that the Low Ratio and Average Ratio pitchers should be off by only 0.32 runs, but are instead off by 0.78 runs. The worse performing group is the low K/BB ratio pitchers.
Overall, we see that while the ratio may have some additional information for us, a simple and straight strikeout minus walk differential per PA is a great indicator of performance.
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