Incorporating Stuff+ Into Traditional Pitching Projections

Recent times have birthed innovative metrics that measure pitcher quality, independent of traditional results like K% or BB%. The most prominent of these are probably Pitching+, Stuff+, Location+, and Command+, all published by Max Bay and Eno Sarris at The Athletic (I want to thank Eno for providing encouragement on this article, though all mistakes and unwise methodological choices are 100% my own).

Pitching+ is an all-encompassing metric derived from a combination of Stuff+, which measures the quality of a pitcher’s stuff based on the physical characteristics of their pitches, and Location+, which measures the value of a pitch based on its location at the plate. Additionally, Command+ measures the location of a pitcher’s pitches relative to their intended location. You can find these metrics for 200 starting pitchers in Eno's recently released ranks for 2022 (also see more on the methodology from Eno here and here).

This article incorporates Stuff+ and Command+ into a more traditional pitching projection and highlights a few resultant movers and shakers for fantasy managers to target (sufficient historical data on Location+ and Pitching+ is not yet available for incorporating into a projection).

How Stuff+ Works

First, the graph below establishes the predictive validity of Pitching+. It shows Pitching+ as on par with the Big Three projection systems in predicting ERA one season into the future, and superior to SIERA and xFIP.

Figure 1. Pitching+ has strong predictive power.

Before preparing a projection model, and because a little external validation never hurt anyone, this article first examines the predictive validity of Stuff+, a key related theoretical construct to Pitching+, and Command+. Table 1 shows the correlation between the first half of 2021 Stuff+ and Command+ and various outcomes in the second half of 2021 (data is limited so the “first half” runs from season start to July 19^th; the “second half” runs from July 23^rd until season end).

Table One. Correlation matrix between first half metrics and second half metrics.

First-half Stuff+ has a strong correlation with second-half K%--almost strong as K% has with itself. Impressively, Stuff+ is also more strongly correlated with second-half K%-BB%, ERA-, and FIP- than the metrics are with their first-half counterparts. First-half Command+ is correlated with second-half BB% in the expected direction, but the strength of the correlation considerably lags the correlation of BB% with itself. Next, Table 2 shows the root mean square error (RMSE, a measure of the typical error when predicting a metric, lower is better) when various first half metrics are used to predict second-half ERA- and xFIP-.

Table Two. Root mean square error using various first half metrics to predict second-half ERA- and xFIP-.

Table note: the RMSEs are on an ERA- scale. A 36 RMSE is a typical prediction error of about 1.5 earned runs per nine innings. A 17 RMSE is a typical prediction error of about .7 earned runs per nine innings.

The first half Stuff+ and Command+ model hangs tough with the other models in terms of predictive power, slightly outperforming each model except for xFIP, which slightly edges it out. Also impressively, first half Stuff+ and Command+ together predict second half xFIP almost as well as first-half xFIP does.

Having established the predictive validity of Stuff+, and to a lesser extent, Command+, this article now turns to incorporate them into traditional pitching projections. As Stuff+ is highly correlated with K% and not correlated with BB%, it is logical to incorporate Stuff+ into a projection model for K%. By the same logic, it is sensible to incorporate Command+ into a projection model for BB%. Table 3 shows the results of various models of K% and BB%.

Model One only captures regressed K% (first half 2021 K% adding in 15 innings pitched of regression to the mean, a traditional forecasting approach), while Model Two adds in Stuff+ as well to show the improvement. Model Three only captures regressed BB% (first half BB% plus 30 IP of regression to the mean), while Model Four adds in Command+ as well. One could build models to predict ERA as well but it may provide more insight to model more reliable metrics like K% and BB% rather than a high variance metric like ERA.

The results in Table 3 show incorporating Stuff+ in a projection model for K% results in substantial predictive gains. The adjusted R-squared jumps seven percentage points in Model Two compared to in Model One.  A four-unit increase in Stuff+, e.g., from 100 to 104, is associated with a one percentage point increase in future K%, e.g., from 25% K to 26% K  (in these regressions, Stuff+, Command+, K%+, and BB%+ are each scaled so one equals league average, which may make interpreting the regression coefficients in the table confusing). A one percentage point increase in K% is associated with a .65 percentage point increase in future K%. Command+, on the other hand, does not add much in explained variance over what BB% provides by itself.

This could perhaps be explained by the fact that they are both related metrics that, in some sense, measure a pitcher’s ability to hit their spots. If the predictive validity of Pitching+ is any indication (Figure 1), Location+ would likely be a big improvement on Command+ in modeling BB%, and incorporating Pitching+ in outcome models will likely provide further gains--both are areas for future research.

Conclusion

To close, Table 4 shows the pitchers whose projections change the most (in terms of projected K% minus projected BB%, an important measure of pitcher talent) when incorporating Stuff+ and Command+ in their projection. For comparison, it also shows a traditional K% minus BB% projection that does not incorporate Stuff+ and Command+.

Table Four. A few 2022 K%-BB% projections.

These projections are based on 2021 data alone and add only a bit of regression to the mean (30 IP for BB%, 15 IP for K%). Further, the team at The Athletic has hinted that they will probably publish their own projections at some point; be sure to follow along with their important work.

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