Run Projections Using Stuff+ Metrics
The last times gave birth innovative metric that measure pitcher quality, independent of traditional results like K% or BB%. Probably the most important of these are Pitching+, Stuff+, Location+ and Command+, all published by Max Bay and Eno Sarris at The Athletic (I want to thank Eno for his encouragement on this article, although any errors and unwise methodological choices are 100% mine).
Pitching+ is an overall 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 marble. Additionally, Command+ measures the location of a pitcher’s throws relative to their intended location. You can find these measurements for 200 starting pitchers in Eno’s recently released ranks for 2022 (see also more on Eno’s methodology here and here).
This article incorporates Stuff+ and Command+ into a more traditional pitching projection and highlights some resulting movers and shakers for fantasy managers to target (sufficient historical data on Location+ and Pitching+ is not yet available to incorporate into a projection) .
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How Stuff+ works
First, the graph below establishes the predictive validity of Pitching+. It shows that Pitching+ is 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 theoretical construct related to Pitching+, and Command+. Table 1 shows the correlation between the first half of 2021 Stuff+ and Command+ and various results in the second half of 2021 (data is limited, so the “first half” extends from the start of the season to July 19and; the “second half” takes place from July 23rd until the end of the season).
Table one. Correlation matrix between first half metrics and second half metrics.
Stuff+ of the first half has a strong correlation with K% of the second half – almost as strong as K% has with itself. Impressively, Stuff+ also correlates more strongly with K%-BB%, ERA-, and FIP- in the second half than the metrics do with their first-half counterparts. The first half’s +order correlates with the second half’s BB% in the expected direction, but the strength of the correlation significantly lags the BB% correlation with itself. Following, Table 2 shows the root mean squared error (RMSE, a measure of typical error when predicting a metric, lower is better) when various first-half metrics are used to predict second-half ERA- and xFIP- semester.
Table Two. Root mean square error using various first half metrics to predict second half ERA and xFIP.
Table note: RMSEs are on an ERA- scale. An RMSE of 36 is a typical prediction error of about 1.5 earned runs per nine innings. An RMSE of 17 is a typical prediction error of about 0.7 earned runs per nine innings.
The Stuff+ and Command+ model in the first half fare well against the other models in terms of predictive power, slightly outperforming each model except xFIP, which slightly outperforms it. Equally impressive, Stuff+ and Command+ from the first half together predict xFIP from the second half almost as well as xFIP from the first half.
Having established the predictive validity of Stuff+, and to a lesser extent Command+, this article now turns to their integration into traditional pitch projections. Since Stuff+ is highly correlated with K% and uncorrelated with BB%, it makes sense to incorporate Stuff+ into a projection model for K%. By the same logic, it makes sense 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 15 rounds of regression to the mean, a traditional forecasting approach), while model two also adds Stuff+ to show improvement. Model three captures only regressed BB% (first half BB% plus 30 IP regression to mean), while model four also adds Command+. One could also build models to predict ERA, but this may provide more information to model more reliable metrics like K% and BB% rather than a high variance metric like ERA.
The results in Table 3 show that incorporating Stuff+ into a projection model for K% leads to substantial predictive gains. The adjusted R-squared jumps seven percentage points in model two relative to model one. A four unit increase in Stuff+, for example from 100 to 104, is associated with a one percentage point increase in future K%, for example from 25% K to 26% K (in these regressions, Stuff+, Command+, K%+ , and BB%+ are each scaled so that one equals the league average, which can make it difficult to interpret the regression coefficients in the table). A one percentage point increase in K% is associated with a 0.65 percentage point increase in future K%. A 1% increase in Command+, on the other hand, doesn’t add much to what BB% provides on its own.
This could perhaps be explained by the fact that they are two related parameters which, in a certain sense, measure a pitcher’s ability to reach his points. If the predictive validity of Pitching+ is any indication (Figure 1), Location+ would likely be a big improvement over Command+ in BB% modeling, and incorporating Pitching+ into outcome models will likely bring additional gains – both are areas for future research.
Close, Table 4 shows the pitchers whose throws change the most (in terms of K% thrown minus BB% thrown, an important measure of pitcher skill) when incorporating Stuff+ and Command+ into their throw. For comparison, it also shows a traditional K% minus BB% projection that doesn’t incorporate Stuff+ and Command+.
Table Four. Some projections for 2022 K%-BB%
These projections are based on 2021 data only and add only a little regression to the average (30 PI for BB%, 15 PI for K%). Additionally, the team at The Athletic have hinted that they will likely release their own projections at some point; be sure to follow their important work.
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