Monday, August 20, 2007

The Audacity of OPS

I have intended for some time to write a post or a series of posts discussing all of the various means of combining OBA and SLG into a more complete stat that are floating around out there. This is not that piece; I have no intentions of discussing all the various OBA/SLG formulas or discussing the technical implications of the ones I do discuss. This is more of a rant, to get this off of my chest.

The title is a little misleading; OPS isn’t really audacious, although perhaps some of its supporters do fall into “recklessness” which is one definition my dictionary gives. I was just too impressed with myself for coming up with the clever phrase (do you have to be a political junkie to get it? More likely, it’s bad and even if you do get it, it’s more likely to elicit a groan then a chuckle).

I should also make it clear before I start: OPS is not a bad statistic. It certainly beats the pants off of looking at the triple crown stats, and there is absolutely nothing wrong with using OPS for quick comparisons or for studies involving large groups of players, or any such thing. But I do believe it is important to keep in mind what OPS is and is not--it is a decent, quick way to evaluate a hitter. But it is not a stat denoted in any sort of useful unit or estimated unit; it is not a stat that was constructed based on a theory about how runs are scored; and it is not a stat that you should go out of your way to use if you have other alternatives available.

First, let’s talk about the components of OPS themselves. On Base Average is a fundamental baseball measurement, because it is essentially the rate of avoiding batting outs. You don’t need me to explain to you why avoiding outs is so important, and that is the point. OBA is a statistic that we would want to invent if we did not already happen to have it sitting around.

Slugging Average is not a fundamental baseball measurement. SLG may be fairly intuitive, and it certainly is venerable, but it is not something that obviously is an important measurement to have on its own. After all, slugging average doesn’t really measure power, because it includes singles. So then what does it measure? It is bases gained on hits by the batter per at bat. But what is the greater significance of bases gained by the batter per at bat?

It really has none. Certainly it is good for batters to gain bases on hits; but that, in and of itself, is not a meaningful measurement. You can even look at the game in such a way that the goal is to gain bases--but in that case, the goal is not for the batter to gain bases, it is for the team to gain bases. And a team doesn’t gain one base for each single on average, nor four bases for each homer, nor do the ratios between one base for a single, two for a double, etc. hold when talking about the bases gained by the team.

The point is not that Slugging Average is meaningless or stupid; the point is that it just is. It is one way of attempting to quantify the value of hits other then counting them all equally as batting average does. It is a crude way of doing so, but it does have a fairly strong correlation with runs and it is a nice thing to know.

But if we didn’t already have SLG, would somebody have to invent it? I think not. There are ways to use the same inputs that would be more useful and would better reflect the run creation value of those inputs.

My message in all of that is that it is not as if OBA and SLG are both (again, my claim is that OBA is, SLG is not) obvious, fundamental things that you would want to know about a team or player’s hitting. They just happen to be two statistics that are the most telling of the widely-available stats.

And it just so happens that when you add them together, you get a measure that is very highly correlated with runs scored, easy to explain computationally, and widely accessible due to the proliferation of OBA and SLG data.

But if you did not have OBA and SLG available to you, would you think of going about creating them so that you could add them together into some uberstat? I would certainly hope not. And how simple is OPS, really? It is simple to compute, in a way, and it is simple to explain, but is it simple to explain why those two things should be added together other then that “it works”? If somebody asks you, “How do you know that just adding them together weights them properly?”, how do you respond?

I said above that OPS is simple to compute, in a way. What I meant by this is that OPS is simple to compute, if you alrseady have OBA and SLG computed for you. Then it is just a simple addition. What if somebody has not already computed them for you? Well now you have (H+W)/(AB+W) + TB/AB, which is not nearly that simple, and not a whole lot simpler then (TB+.8H+W-.3AB)*.32/(AB-H), which gives you a much better rate stat (runs created per out). I guess it can be said that it avoids multiplication--if somebody has already figured total bases for you. If you have to do that yourself, now you have (H+W)/(AB+W) + (H+D+2T+3HR)/AB, which is not that much more simple then (1.8H+D+2T+3HR+W-.3AB)*.32/(AB-H). I guess it can be said that it only includes whole coefficients, if you want to argue on its behalf.

What if we think about what OPS looks like if you write it with a common denominator? Now we have:
OPS = ((H+W)*AB + TB*(AB+W))/(AB*(AB+W))

Not so simple anymore, and can anyone possibly explain the logic behind multiplying those things together like that, other then that “it works”?

Then there is the matter of OPS+. Some people are really shocked to learn that OPS+ is calculated as OBA/LgOBA + SLG/LgSLG - 1. “This is not a true relative OPS!”, they exclaim. “It doesn’t really mean that a 100 OPS+ batter was 20% better in OPS then an 80 OPS+ batter!” While these statements are true, and there is a legitimate complaint to be lodged about the naming of the statistic, the horror at the sacred construction of OPS being violated is somewhat audacious.

When somebody tells you that a stat is adjusted, or has a “+” suffix on the end of it, you expect it to be the ratio of the player’s stat to the league average, perhaps with a park adjustment thrown in. You don’t expect it to be a similar but different statistic. So the measurement that is labeled OPS+ does mislead. Give Pete Palmer a slap on the wrist for this, and move on.

Then when you do move on, give Pete Palmer a pat on the back. Why? Simply for the fact that the measure he has given you is more telling then the measure that you were expecting. I’m not going to get into the math here, since I plan on covering that in my later series, and I will ask you to take this on faith (at least with regards to what is presented here; this is not new information and it has been shown by other sabermetricians in other places). Let’s call OPS/LgOPS “SOPS+” for “straight OPS” plus. People think that OPS+ is SOPS+, and it is not.

The real effect of OPS+, other then adjusting for the league average, is to give more weight to the OBA portion of OPS. Not sufficiently enough weight, but around 1.2 times as much as it is given under OPS or SOPS+. The other thing it does, in addition to correlating better with run scoring, is to express itself in a meaningful estimated baseball unit. OPS+ can be viewed as an approximation, an estimate, of runs per out relative to the league average, which is what you really want to know (or at least is a lot closer to what you really want to know then the ratio of OPS to lgOPS is). Since OPS is unitless, SOPS+ is unitless as well. You can of course use SOPS+ to approximate relative runs/out as well. However, in order to do it, you have to take two times SOPS+, minus one.

So when people complain that OPS+ distorts the ratio between player’s OPS, they are right. But this distortion is a good thing, since it puts it in terms of a meaningful standard instead of a ratio of a contrived, not theoretically-based statistic (OPS). SOPS+ wouldn’t tell these folks what they think it would. A 120 SOPS+ hitter would be 20% above the league average in OPS. That does not in any way, shape, or form mean anything other then that. It does not mean that they created 20% more runs per plate appearance then an average player. It does not mean that they created 20% more runs per out then an average player. It does not mean that they were 20% better then an average player. It does not mean that they are 20% more talented then an average player.

To me, it is a parody of sabermetrics when people complain about OPS+ not being SOPS+, for any reason other then the confusion caused by its name. We sabermetricians have used OPS, and now we will complain about something that is no longer pure OPS, even though it is a more meaningful statistic with clearer units that correlates better with wining baseball games. What is inherently superior about adding OBA to SLG and then comparing to the league average versus comparing OBA to the average, SLG to the average, and adding the results? Considering that OPS doesn’t have any units to begin with and doesn’t correlate better with runs scored, nothing that I can see.

I apologize for the rambling nature of this, but I warned you when I started that it was a rant. OPS is a fine, quick way to measure a hitter. That does not mean that its units are meaningful, that does not mean that it is has meaningful units when it is divided by the league average, or that it is a statistic that has any inherent logic behind it other then adding together two things because it works, or that another metric that combines OBA and SLG in a different way is necessarily inferior or incorrect. As long as you keep those things in mind, there’s not really anything audacious about OPS.


  1. One problem with OPS+ is that the negative numbers it generates at times for very bad hitters (and NL pitchers) aren't intuitive when one sees them for the first time.

    If 50% of league average for OBA and SLG were replacement level, then we could think of negative numbers as reflecting below replacement performance, but that's not quite right, so we end up with a scale that doesn't work quite the same as the others and takes practice to get used to because it doesn't have an intuitive logic of its own.

    I think that's going to create more trouble than it's worth for a stat which isn't nearly as good as something like RC/RC+ (or wOBA which is similar but normalized differently).

  2. I can't disagree with your observation that the negative numbers are unseemly. And of course I agree that RC or wOBA would be better then OPS+.

    However, if you figure any kind of linear RC method, it will break down and start spitting out negative runs created at around the same point that OPS+ breaks out the negatives. EQR, for one, does at exactly 50% of the league average "RAW". EQR is (2*RAW/LgRAW-1)*PA*LgR/LgPA, so you can see that if RAW/LgRAW = .5, then the parenthetical is 0 and anything less then that is negative runs.

    ERP will start giving negative runs at some point too (for example, Greg Maddux last year was -19 OPS+, -.06 ERP) . It is true that wOBA would never encounter this problem.

    I can certainly except that criticism of OPS+, and I agree wholeheartedly that other relative stats are more useful. Personally, though, I'm willing to accept negative numbers in exchange for a stat that is denominated in a meaningful estimated unit and better correlates with runs scored (when compared to "SOPS+").

  3. For what it's worth, "It works!" isn't all that bad of an explanation. I have no idea how my father was cured of an "incurable" disease, yet I'm happy with "it works!" It dodges the question on my part, but then again, I'm not all that interested in immunology.

    OPS is basically "He doesn't make outs and he makes the kind of hits that make people run around the bases a lot." That's a pretty good definition of the point of baseball. Your point that there are better stats is very well taken (and as you convincingly show, just as easily calculated), but remember for the ESPNers out there, baby food first, then solids.

    And the title did make me chuckle. It was a cheap laugh, but a cheap laugh is the best laugh of all!

  4. Why not 2OPS (=OBA+OBA+SLG)? It's almost as easy to calculate, and is very close to the 'correct' weighting of 1.8 OBA. Further, it sort of emphasizes the importance of OBA, which is not well enough understood by the general public. How has OPS become somewhat popular with sportswriters, etc.? The same mechanisms could also be used with 2OPS, with the result that popular analyses would be much closer to the truth.

  5. You really should learn how to use the words "then" and "than" properly. I guess that would be my rant.

    And David Smyth, OPS as it is is slightly easier to compute rather than adding OBA twice to get a value. And, another of the chance results of OPS is that, for a team playing 162 games, OPS actually does a fairly good job of estimating team runs scored.

    Guys, as much as you don't like it's ubiquitousness, it's just too damn easy, and so will continue to be used.

  6. ----"And David Smyth, OPS as it is is slightly easier to compute rather than adding OBA twice to get a value."

    Well, duh, yeah. But what's the worthwhile difference you are so eager to point out, between my "almost as easy to calculate" for 2OPS, and your "slightly easier to compute" for OPS? Obviously you are ignoring (or simply incapable of understanding) my essential point that it's the tradeoff between simplicity and accuracy that matters.

    If you are going to be the language critic for us posters ("then" vs "than"), you should at least have something worthwhile to say about Base Ball...

  7. I agree with David, and with regards to this:

    "Guys, as much as you don't like it's ubiquitousness, it's just too damn easy, and so will continue to be used."

    If you came away with wanting to see OPS abolished as the point of my post or any of the comments, than I suggest that you work on your reading comprehension skills.

  8. haha, nathaniel criticized the than/then mix-up, and then proceeds to use "it's" instead of "its."


    To the point, now. I really like this article because it's about units. Too often sabermetrics is concerned with predictability and correlation, maybe because regression analysis is geekier and more exclusive. I don't know. But the discussion of units brings numbers back to the level of meaning. What does this statistic mean? That's what Bill James is always on about, what with his number-words, or word-numbers, or whatever he says. I feel like this is a core principle of sabermetrics.

    But then, the anti-sabermetrics camp attacks the stat geeks on this very point, that all these acronyms are just masturbatory material for irrelevant basement-dwelling troglodytes; they lack baseball meaning.

    It is ironic, then, that one of the few statistics to come out of the sabermetric community to be accepted by the mainstream baseball community, is OPS, which has no value in relation to anything except to itself, despite its correlation with run-scoring.

    Excuse that last rambling sentence. Exceptional article.

  9. I like your last rambling sentence. I've never thought of it that way before.

    If one is a little more cynical, rather then seeing it is ironic, the embrace of the "meaningless" OPS over other sabermetric measures could be seen as an admission that it is the (percieved) complexity that really bothers the mainstreamers.

  10. does anyone know where i can find some mlb hitting statistics that actually list any of these crazy formula?

  11. Here is a link to a new site that includes statistics from the wOBA family:

  12. This is an old post but...
    A case needs to be made for why all of these combined batting statistics inflate the importance of power hitting and deflate the importance of speed and base running skill. First, any comprehensive measure of offensive performance should include SB-CS. Second, but more difficult, would be including something that measures the total bases advanced by the runner after getting on base. If Ichiro and Prince Fielder get to second base, I think its important to know who is more likely to advance or score when a ball is put in play? Without these, OPS is just another word for power hitter. Folks love to talk about OBA and OPS, but how many of the top performers in these categories can barely run or steal a base?


I reserve the right to reject any comment for any reason.