Stuff+, Location+, and Pitching+ Primer

Introduction

Pitching+ is one of three models that, along with Stuff+ and Location+, attempts to look at the process underlying a pitcher’s performance in order to remove some of the noise that can be present when looking at on-field results. Eno Sarris and Max Bay created Pitching+, with inspiration from work by Ethan Moore, Harry Pavlidis, and Jeremy Greenhouse, among others. Sarris and Owen McGrattan currently maintain and work to improve the model, with engineering support from Matt Dennewitz.

Stuff+

Stuff+ looks only at the physical characteristics of a pitch. Important features include, but are not limited to, release point, velocity, vertical and horizontal movement, and spin rate. A pitcher’s secondary pitches are defined based on their primary fastball — with “primary” defined by usage in an outing — and so are judged by velocity and movement differentials along with raw velocity and movement numbers. The model also includes “axis differential,” a statistic that attempts to describe the difference between the movement expected by spin alone and the observed movement affected by the phenomenon described as seam-shifted wake.

Stuff+ was trained against run values, so even if the research community is divided about how much a pitcher can control weak contact, the model includes an inherent nod to the possibility that they do possess some of that ability. The importance of release point in the model also suggests that Stuff+ includes some deception — you’ll find some pitchers with unique release point and movement combinations score very well despite lower velocities, at least. Vertical attack angle is not explicitly in the model, but it is captured by the interaction between release points and movement.

Generally, the model aims to capture the “nastiest” pitches in baseball, using a decision tree-based model to capture the nonlinear relationships that exist across release points, velocities, pitch movement, and more.

Here’s a look at how velocity and vertical movement combine to make a slider good, with Jacob deGrom’s slider shown in black, the league average slider shown in green, and the league’s performance in each bucket shown by the colors (red = good for the pitcher):

Location+

Location+ is a count- and pitch type-adjusted judge of a pitcher’s ability to put pitches in the right place. No velocity, movement, or any other physical characteristics are included in the statistic. A breaking ball should go to different parts of the strike zone in 2-0 and 1-2 counts, and Location+ captures that phenomenon. Stringer-based command statistics that attempt to judge what a pitcher was intending to do with each pitch do not add predictive value to those models, so Location+ only looks at actual locations and implicitly assumes the intent is generally the same across the league in certain counts with certain pitches.

Here’s a look at how Location+ values change around the zone, specifically for a right-handed pitcher throwing a sinker to a right-handed batter in a 3-2 and 3-1 count, as seen from the batter’s side:

Pitching+

The overall model, Pitching+, is not just a weighted average of Stuff+ and Location+ across a pitcher’s arsenal. Rather, it is a third model that uses the physical characteristics, location, and count of each pitch to try to judge the overall quality of the pitcher’s process. Batter handedness is also included in Pitching+, capturing platoon splits on pitch movements and locations.

The model is designed so that 10 points of Stuff+, Location+ and Pitching+ is a standard deviation on the pitch level. Once those numbers are summed up, the spread changes.

Fittingly, a reliever going to a starting role should see his Stuff+ drop around 5.5 points, which makes sense because relief pitchers usually don’t throw as hard once they move into starting.

On the individual pitch level, it may be unsurprising that breaking and offspeed pitches are received more favorably by Stuff+ than fastballs, but the distributions tighten a bit when you look at Pitching+, which takes location into account. Changeups see some of the widest spread in Pitching+ largely due to the fact that they’re heavily reliant on velocity and movement differences compared to the primary fastball. Splitters see the largest spread because of the pitch’s sensitivity to differences in fastball characteristics, as well as how difficult the pitch is to locate in general. (There’s no table for Location+ values since they are centered at 100 for each pitch type.)

The reason to use a model like this is simple: it’s predictively powerful. Before the season begins, Pitching+ out-predicts any current projection system for relievers when judged by the size of the Root Mean Square Error, as seen below by the bottom blue line. Once the season gets going (curved line), it takes about 250 pitches before in-season Pitching+ beats preseason projections for relievers. Here the horizontal lines represent pre-season ERA projections for the different projection systems as well as the previous year’s actual ERA, FIP, and xFIP. A linear transformation was performed to bring the previous year’s Pitching+ to an ERA scale. For the line plot, the RMSE is measured between the in-season Pitching+ up to that pitch number and the end-of-year ERA. So for all pitchers who threw at least 50 pitches, the RMSE in the first point is between the transformed Pitching+ at the 50th pitch and the end-of-year ERA.

Starters are a little more complicated, as they have more robust on-field result samples and deeper arsenals, but the story is similar. Before the season, starting pitcher Pitching+ has a lower RMSE when compared to on-field results (ERA) than most projection systems. In season, Pitching+ begins to beat pre-season projections by around the 400th pitch, or four or five starts in.

The power of this model really shines during any given season. Strikeout minus walk rate is powerful as a rest-of-season predictor, and Pitching+ becomes strongly reliable (it predicts itself rest-of-season) faster than K-BB% as judged by Cronbach’s Alpha. Similar to the graphs above, here we’re measuring Cronbach’s Alpha between the metric at the given PA number and the measure at the end of the year:

Pitching+ also predicts rest-of-season results better than K-BB% in smaller samples:

If Pitching+ is so powerful, why split the model into Stuff+ and Location+? That has to do with how quickly each becomes reliable — Stuff+ becomes reliable 80 pitches into the season and is extremely powerful relative to any other single stat in the tiniest of samples, while Location+ takes something more like 400 pitches to reach a similar level of stability (a high barrier, Chronbach’s Alpha ~0.9) — but also with how sticky each component is year to year. Below, you can see how sticky Stuff+, Location+, and Pitching+ are year to year, and how Stuff+ drives most of the season-to-season stickiness of the overall model:

On any given pitch, the location is hugely important, more than the stuff. But stuff is stickier season to season and start to start, so it’s a safer bet; as noted here, the free agent market has also been paying more for stuff than location recently.

The longer a pitcher is in the big leagues, the more their actual results matter when weighed against their Pitching+ numbers. But being able to judge a pitchers’ ability to throw good shapes and velocities to the right locations should also have separate value to those trying to evaluate hurlers because of how quickly those shapes, velocities, and locations become meaningful.