Rewriting OPS: A Math Experiment

You probably didn’t wake up this morning thinking, “Hmm, I’d love to think about a math concept,” but I started thinking about Lou Whitaker, and how absurd it is that he’s not in the Hall of Fame yet, and for some odd reason this led me down a math path.

Let’s see if I can retrace the steps.

Whitaker’s raw OPS is .789. That’s very good for his time — Whitaker’s OPS+ is 117. That’s basically the same OPS+ as Hall of Fame infielders Ryne Sandberg (119), Barry Larkin (116), Robbie Alomar (116), Derek Jeter (115), and Cal Ripken Jr. (112). It’s noticeably better than his Hall of Fame teammate Alan Trammell (110).

But there’s something specific about the make up of his OPS that intrigues me. As you know, OPS is on-base percentage PLUS slugging percentage.

In Whitaker’s case:

What struck me is how close Whitaker’s OBP is to his SLG.

And this led to a math concept that I’ve seen called “Arithmetic Mean-Geometric Mean Inequality.” I don’t know if that’s ACTUALLY what it’s called, but the concept as I (barely) understand it is this: For numbers with a fixed sum, the product is LARGEST when the numbers are equal.

What the heck does that mean? Well, it seems very useful for OPS specifically — because, see, not all OPS are built the same. Let’s take someone with a .900 OPS just as an example. Here are four possibilities for a .900 OPS. You take a guess: Which of these four is the most productive for scoring runs?

The answer, I believe, is A. And here’s why. Because .450 TIMES .450 is the highest possible product for a .900 OPS. Look at the products of each:

See? A is the highest. Not only that, but the more distance between on-base and slugging, the lower the product is.

Now, you may ask: How do you know that the product of on-base percentage and slugging percentage tells you anything? And that’s the fun part: We’ve known that for more than 40 years because multiplying OBP and SLG is at the very heart of Bill James’s Runs Created system!

Smarter people than me can go deeper into the math in the comments … what I think matters here is that not all OPS are alike. And even though I’m hopeless at math, I thought: Hey, could I create a True OPS that credits players for having more balanced on-base percentages and slugging percentage?

And, against all odds — thanks to a lot of searching — I think I have! Maybe! Probably not! But maybe!

Here’s my crack at it — a quick formula that adjusts OPS for balance between OBP and SLG:

The formula is: True OPS = 2 × √(OBP × SLG)*

*If this formula actually works — someone else probably invented it already. Bill James probably invented it 30 years ago, and I just missed it. I want to be clear: I’m not taking credit for this. If it doesn’t work, though, yes, it’s all on me.

So let’s put it into use! For example, how does Whitaker’s balanced .789 OPS compare with Nick Castellanos’ more extreme OPS?

That feels … interesting to me. Oh, you should know: True OPS can never be HIGHER than actual OPS. If the slugging percentage and OPS are identical, then True OPS will be exactly equal to OPS.

OK, here’s a fun one from this season — Bobby Witt Jr. vs. Pete Crow-Armstrong:

I would love to do a whole bunch of these — tell you who has the highest True OPS in baseball history, for example — but I’m going to leave it here for now and let our guy Tango and any other people who are way better at math look. See if there’s anything to it. Then they can tell me, (A) I’m dumb and wrong or (B) That there might be something to this but we need to change some stuff.

should change something.

We’ll update you on True OPS next week!

In the meantime, it’s a crime that Lou Whitaker is not in the Hall of Fame.