I'm not exactly a fan of OPS+, but if you interpret a 118 OPS+ as "18% more productive than a league average hitter" rather than "18% higher OPS than a league average hitter", it is a correct statement (at least to the extent that OPS+ is a predictor of team runs scored). The negative values are an unavoidable consequence of a linear run estimator applied at extremes of offensive ineptitude, although I certainly understand why one might find them obnoxious.
But is that even true? I could agree that OPS/(league average OPS) works to use with a true percentage. The idea of adding one average to another and subtracting one is just weird and mathematically illogical. It might give answers that are ballpark-ish “correct” but that doesn’t make the process correct.
I concur that it is weird and that the process is not correct. But if forced to use OPS, some kind of OPS/LgOPS, or OPS+, I'd personally take the latter because:
1. I think it actually makes more sense to add OBA/LgOBA and SLG/LgSLG than it does to add OBA and SLG in the first place.
2. If you accept the constraint (although I certainly don't think anyone should) of a linear equation using OBA and SLG relative to the league average (I'll call then aOBA and a SLG) to estimate team runs (per game or per out, which I'll call aR), and that they must be weighted equally:
aR = m*(aOBA + aSLG) + b
you will find the best fit from coefficients very close to m = 1 and b = -1. If you do the same with OPS:
aR = m*aOPS + b
you will find the best fit coefficients very close to m = 2 and b = -1. OPS+ has a 1:1 relationship with runs; OPS/LgOPS has a 2:1 relationship
3. OPS+ inherently weights OBA more heavily than OPS because in live ball baseball LgSLG > LgOBA. The ratio of LgSLG/LgOBA is usually something around 1.2 so it functions as weighting OBA around 1.2x SLG, although if you really wanted a best fit with runs it would be something like 1.8. But it's closer than OPS' 1x.
All that being said, I would be perfectly pleased to send all forms of OPS to the landfill (I don't think they are recyclable).
Thanks for the detailed explanation. I too much prefer wOBA to OPS and wRC+ to OPS+. Playing around with Retrosheet data, it seems like the relationship was that wRC+ was close to the square of wOBA (perhaps like the Pythagorean Wins, the exponent might be something other than exactly two). Using that assumption, the m=2 and b=-1 is a close linear fit to a square function. For example, 0.8^2 is 0.64 and 2*0.8-1 is 0.6. Similarly 1.3^2 is 1.69, and 2*1.3-1 is 1.6. So basically the weird calculation is a linear approximation of a square function that is close for values near 1. It obviously fails for values close to zero or greater getting close to two or higher.
While OPS is bad enough, I cringe most at the definition of OPS+ which is OBP/(leave average OBP) plus SLG/(league average SLG) minus one. How did that originate? People erroneously talk about percentages (e.g., an OPS+of 118 they say is 18% above average). This obviously breaks down for very low OPS+ which can theoretically bottom out at -100. There are pitchers with a negative career OPS+ like Sandy Koufax with a -39 OPS+. What percentage worse is he than average? 139% worse?
I'm not exactly a fan of OPS+, but if you interpret a 118 OPS+ as "18% more productive than a league average hitter" rather than "18% higher OPS than a league average hitter", it is a correct statement (at least to the extent that OPS+ is a predictor of team runs scored). The negative values are an unavoidable consequence of a linear run estimator applied at extremes of offensive ineptitude, although I certainly understand why one might find them obnoxious.
I wrote a little bit about the interpretation of OPS+ in response to Bill James' comments in his 2023 Handbook (RIP) last year: https://walksaber.substack.com/p/rehashing-runs-created-and-ops
But is that even true? I could agree that OPS/(league average OPS) works to use with a true percentage. The idea of adding one average to another and subtracting one is just weird and mathematically illogical. It might give answers that are ballpark-ish “correct” but that doesn’t make the process correct.
I concur that it is weird and that the process is not correct. But if forced to use OPS, some kind of OPS/LgOPS, or OPS+, I'd personally take the latter because:
1. I think it actually makes more sense to add OBA/LgOBA and SLG/LgSLG than it does to add OBA and SLG in the first place.
2. If you accept the constraint (although I certainly don't think anyone should) of a linear equation using OBA and SLG relative to the league average (I'll call then aOBA and a SLG) to estimate team runs (per game or per out, which I'll call aR), and that they must be weighted equally:
aR = m*(aOBA + aSLG) + b
you will find the best fit from coefficients very close to m = 1 and b = -1. If you do the same with OPS:
aR = m*aOPS + b
you will find the best fit coefficients very close to m = 2 and b = -1. OPS+ has a 1:1 relationship with runs; OPS/LgOPS has a 2:1 relationship
3. OPS+ inherently weights OBA more heavily than OPS because in live ball baseball LgSLG > LgOBA. The ratio of LgSLG/LgOBA is usually something around 1.2 so it functions as weighting OBA around 1.2x SLG, although if you really wanted a best fit with runs it would be something like 1.8. But it's closer than OPS' 1x.
All that being said, I would be perfectly pleased to send all forms of OPS to the landfill (I don't think they are recyclable).
Thanks for the detailed explanation. I too much prefer wOBA to OPS and wRC+ to OPS+. Playing around with Retrosheet data, it seems like the relationship was that wRC+ was close to the square of wOBA (perhaps like the Pythagorean Wins, the exponent might be something other than exactly two). Using that assumption, the m=2 and b=-1 is a close linear fit to a square function. For example, 0.8^2 is 0.64 and 2*0.8-1 is 0.6. Similarly 1.3^2 is 1.69, and 2*1.3-1 is 1.6. So basically the weird calculation is a linear approximation of a square function that is close for values near 1. It obviously fails for values close to zero or greater getting close to two or higher.
Using mathematical terminology, 2x-1 is the first two terms of the Taylor expansion of x^2.
While OPS is bad enough, I cringe most at the definition of OPS+ which is OBP/(leave average OBP) plus SLG/(league average SLG) minus one. How did that originate? People erroneously talk about percentages (e.g., an OPS+of 118 they say is 18% above average). This obviously breaks down for very low OPS+ which can theoretically bottom out at -100. There are pitchers with a negative career OPS+ like Sandy Koufax with a -39 OPS+. What percentage worse is he than average? 139% worse?