# First Pitch Strike and Swing and Miss Rates

### Two FanGraph Pitching Stats

In the Pitcher Leaderboard of the Fangraphs site, they have an interesting Plate Discipline tab that provides an interesting collection of contact and swing percentages for all qualifying pitchers for the 2016 season.  Let’s focus on exploring two of these statistics:

• F-Strike % — percentage of first pitches that are strikes
• SwStr % – percentage of pitches that are swing and misses

One always hears about the desirability of a first pitch strike for a pitcher.  Also it seems clearly desirable (from the pitcher’s perspective) to induce a swing and miss, so one would like SwStr % also to be high.

I downloaded this data for 2016 qualifying pitchers — here is a scatterplot of the two proportions.   It is interesting that there is little association in the graph — knowing that a pitcher is good in getting a first-pitch strike doesn’t tell you much about the proportion of swinging strikes.

### Predicting WAR from These Two Stats

A summary measure of a pitcher’s effectiveness during the season is the WAR (wins above replacement) stat.  (I know that a WAR doesn’t isolate the pitcher’s effectiveness from the contribution of his defense, but we won’t go down that road here.)  I also collected the WAR values from the FanGraphs Value page and merged this with the plate discipline stats.  I redraw the scatterplot where the size of the plotting point is proportional to the WAR value.

Since the WAR values seem higher in the upper right section of the plot, this motivates the use of the regression model

WAR = a + b1 First_Pitch_Strike_Proportion + b2 Proportion_Swinging_Strikes

that is easy to fit using the lm function:

```fit <- lm(WAR ~ F_Strike + SwStr, data=d2)
```

I display the fit on the scatterplot by showing lines where the predicted WAR is equal to 0, 2, 4, and 6.

### Looking at Residuals

For particular pitchers, this model does a great job in explaining R — here is a list of the pitchers whose absolute residual was smaller than 0.1.

```            Name F_Strike SwStr   WAR     Residual
1     Cole Hamels    0.576 0.122   3.0 -0.029145560
2    Max Scherzer    0.651 0.153   5.6  0.091603020
3   Ricky Nolasco    0.610 0.092   2.5 -0.009598109
4 Edinson Volquez    0.563 0.085   1.5  0.080470932
5     Chad Bettis    0.627 0.087   2.6 -0.022889175
6     Doug Fister    0.596 0.059   1.1  0.068429141
```

For example, Max Sherzer’s 2016 WAR value of 5.6 is accurately predicted knowing his first strike and swing and miss rates.

### The Big Residuals

Although the regression indicates that both first pitch strike and swing and miss are helpful in explaining the variation in WAR values, it is interesting to find pitchers who succeed (or failure) despite their first pitch strike and/or swing and miss proportions. Let’s first locate the residuals that are larger than 2 — these points correspond to pitchers who do much better (from a WAR perspective) than predicted from their first pitch strike and swing and miss rates. I indicate those with a + on the scatterplot.

These two pitchers, Rick Porcello and Jose Quintana, have above-average first pitch strike rates, but below-average swing and miss rates. Of course we know Porcello had a great 2016 season — finished with a 22-3 record and a Cy Young crown. Why was he successful? Here’s an interesting quote from an ESPN article:

“Porcello’s most common explanation for last season’s breakthrough is that he better understands what makes him effective. In 2015, he strayed from his signature sinker in an attempt to strike out more hitters with his relatively ordinary four-seam fastball. Last year, he got back to throwing the ant-killing sinker that induces so many weak ground balls.”

Next, we find the residuals smaller than -2 — these pitchers underperform (with respect to WAR) given their first pitch strike and swing and miss rates.

Here are the five pitchers:

```            Name F_Strike SwStr   WAR  Residual
1 Michael Pineda    0.673 0.141   3.2 -2.248726
2    Josh Tomlin    0.677 0.074   1.0 -2.019739
3   Jered Weaver    0.642 0.081  -0.2 -2.863600
4  James Shields    0.547 0.092  -0.9 -2.298488
5    R.A. Dickey    0.621 0.106   1.0 -2.225892
```

Michael Pineda was great with respect to first-pitch strikes and swing and misses, but he had an average WAR value, suggesting some problems. This article examines the locations and movements of his pitches in the 2016 season.

It is interesting that Jered Weaver had similar first-pitch strike and swing and miss rates as Rick Porcello, but Weaver’s WAR value was actually negative. A quick look at his pitching statistics suggests that he left two many pitches over the middle of the plate, allowing 37 home runs in 2016.

### Wrap-Up

This brief exploration shows that first-pitch strike and swing and miss rates are important stats to consider when one looks at a pitcher’s effectiveness. These two rates, by themselves, explain about 50 percent of the variability in WAR values. But, as the exploration of residuals indicates, there are other factors to consider. Pitchers can be effective in inducing groundballs or flyballs for outs. Or location problems can doom pitchers who look good relative to first-pitch strikes and swing and misses.

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