OPS Is Real And It’s Spectacular

When measuring how closely related two things are, we typically look at the correlation (R) or the coefficient of determination (R²). A high R² implies a very strong relationship. Let’s see how strong the wOBA to OPS relationship is season to season:

Season	R²
2008	.985
2009	.985
2010	.987
2011	.990
2012	.990
2013	.992
2014	.991
2015	.992
2016	.987
2017	.985
2018	.988
2019	.987
2020	.982
2021	.987
2022	.991
2023	.985

Those are really strong correlations. It’s actually quite rare that you get such strong correlations for two variables. It’s also remarkably consistent, with the lowest R² being the short 2020 season at 0.982.

OPS By Player Season

At the player-season level going back to 2008, we get a very robust R² of 0.982, indicating the relationship is almost perfectly linear.

OPS to wOBA Prediction Error

Another way to look at how well things relate to each other is to see how much error there is when you use one to predict the other. First, here’s how close OPS is to predicting wOBA, split by points of wOBA.

We can also make these into larger buckets:

This means that if we use OPS to predict wOBA, 62% of the time we’ll be within five points of wOBA, and almost 92% of the time we’ll be within 10 points. For reference, the difference between the No. 10 batter (.381 wOBA) and the No. 30 batter (.353 wOBA) is about 28 points. From No. 30 to No. 60 is about 13 points.

The Secret To Why OPS Works So Well

Now that we’ve established that OPS works extremely well, let’s explain why, with a little bit of math. It turns out, if we force OPS to use Plate Appearances for both On Base and Slugging, we uncover an interaction between BB%+HBP% (BB+HBP per plate appearance) and Slugging/PA (total bases / plate appearance). Let’s go through this step by step.

Step 1

Slugging, as you’ll see on player pages, is Slugging/PA (Total Bases per Plate Appearance) multiplied by PA/AB.

Step 2: PA/AB Is Mostly BB%+HBP%

This is where the magic happens. A plate appearance that is a non-at-bat is one that ends in a walk, hit by pitch, error or sacrifice. These two metrics correlate very strongly, with a robust R² of 0.934, with the outliers being batters who get a lot of sacrifices, or reach on error. If you have a high PA/AB ratio, it’s almost for sure due to lots of free passes by BBs and HBPs. Here’s how that relationship looks visually, with sacrifices indicated for some batters.

Step 3: Replace PA/AB With BB%+HBP%

I created a simple linear regression between these two variables and it spit out something very interesting:

PA/AB = 1 + 1.22 * (BB% + HBP%)

If we scroll up to the formula above, we can replace the PA/AB piece with 1 + 1.22 * (BB% + HBP%), giving us this formula:

We can then simplify it to this:

Let’s see how these two correlate:

That’s a 0.998 R², which is extremely strong. For reference, Slugging/AB and Slugging/PA clock in at 0.96 R².

You’ll notice that all the metrics now have the same denominator, and magically, we’ve uncovered that OPS is OBP + Slugging/PA + (1.22 * BBHBP% * Slugging/PA), representing a small interaction between the two variables. For the purists who demand all variables be of the same denominator, here’s how you can restate OPS to all be on the same scale:

OPS = OB/PA + SLG/PA + 1.22 * SLG/PA*(BB+HBP)/PA

This will correlate almost perfectly to classical OPS. It turns out that the different scales between OBP and SLG create a non-linear interaction. In other words, the “abomination of math,” as some have mis-characterized the formula, is in fact, a feature, not a bug. This is because At-Bats and Plate Appearances have a clearly defined relationship, mostly driven by free passes. OPS leverages this (albeit accidentally), and it is the reason it works so well.

Too Much Math; Didn’t Read

If you glossed over the previous parts, I don’t blame you. The TL;DR is as follows:

Slugging Percentage, when combined with OBP, is secretly including BB+HBP. When we convert slugging to Plate Appearances instead of At-Bats, we uncover this. There is a mathematical relationship between Plate Appearances and At-Bats. The more walks you get, the more PAs you’ll have per AB.

Why I Like OPS

I think OPS is a great metric since it uses two ingredients that we’ll always see when we describe a batter. These metrics do a great job individually, and when simply added together, do a spectacular job of measuring performance. I know that if I see OBP and Slugging, I can just add the two numbers together and I’ll get a near-perfect approximation for how valuable that batter is. There is tremendous utility in simplicity.

Putting It All Together

When something works really well, it’s usually a good idea to investigate why it works so well, rather than dismiss it outright. For OPS, the key to its performance may just be that it is non-linear, given that it includes a small interaction between Total Bases and BBs+HBPs. It turns out that the two components being on slightly different scales forces a non-linear equation, which in turn produces tremendous predictions.