Awhile back I had written about OPS and how it is a good back of the envelope calculation for correlating a player's production with run creation. After doing so I went on to discuss normalizing OPS against the league average (called NOPS or OPS+) and then contextualizing OPS for the home park of the player using the Batter Park Factor (BPF).
A couple days ago I received an email from Brandon Heipp who has done some fine work on the BaseRuns estimator that I cited in my article on the subject. He pointed out to me that the technique of dividing NOPS by the BPF is not as accurate as using the square root of BPF. I hadn't heard of doing this and was simply following the method used by Pete Palmer in The Hidden Game of Baseball. In looking back at the book, however, I notice that Palmer, after showing how to divide NOPS by BPF, says the following on page 87.
"To apply Batter Park Factor to any other average - On Base, slugging, Isolated Power, batting average-use the square root of the BPF. This is done so that run scoring for teams, which is best mirrored by On Base Average times slugging percentage, can be represented clearly."
In other words:
1. Since BPF is a measure of the impact of a ballpark on runs scored
2. and Batter Run Average (BRA calculated as OBA*SLUG) very closely correlates with run scoring
3. and BRA/BPF = (OBA/SQRT(BPF)) * (SLUG/SQRT(BPF))
Then to more accurately contextualize OBA, SLUG or other components of run scoring you should divide them by the square root of BPF.
This can also be seen in the basic runs created formula RC = ((H+BB)*TB)/(AB+BB). This formula is the equivalent of OBA*SLUG*AB. If you divide this by the BPF it is equivalent to (OBA/SQRT(BPF)) * (SLUG/SQRT(BPF)) * AB. And so once again the more accurate way to apply BPF to the components of run scoring is by using the square root.
OPS does not correlate as closely with run scoring as do either RC/G or BRA. Albert and Bennett in their book Curve Ball found that using OPS "the number of runs scored by a team per game can be predicted within about .15 Runs per Game for two-thirds of the teams." Although not as good as RC/G, BRA, Total Average (TA), or Batting Runs, it does correlate much more closely than the traditional stats such as OBA, SLUG, or AVG. As a result, it's probably not as important to use the square root with OPS as pure component statistics such as OBP or SLUG for example.
That said, I did recalculate the top leaders in OPS using the square root of BPF. Here they are:
Year OPS NOPS NOPS/PF
2002 NL Barry Bonds SFN 1381 186 195
2001 NL Barry Bonds SFN 1379 182 191
1920 AL Babe Ruth NYA 1379 189 185
1921 AL Babe Ruth NYA 1359 179 177
1923 AL Babe Ruth NYA 1309 178 176
1941 AL Ted Williams BOS 1287 177 175
1957 AL Ted Williams BOS 1257 178 173
2003 NL Barry Bonds SFN 1278 171 172
1926 AL Babe Ruth NYA 1253 170 172
1927 AL Babe Ruth NYA 1258 168 171
These are very similar to the previous list of course but Ted Williams 1957 list now makes the grade since Williams benefited from playing in Fenway Park. Babe Ruth's 1931 season falls off. Of course Bonds' 2004 season would rank right up there but given recent events I didn't feel like calculating it.