Using usage rates to find great pitches

One of the aspects of any baseball game that never fails to interest me is the strategy of each individual at-bat. The pitcher and batter are constantly adjusting to the tendencies of the other and trying to predict and counter their opponent's adjustments while disguising their own. From an analytical perspective, it can be a little annoying, for lack of a better word, since it makes it really hard to discern what's a basic characteristic of the pitcher or batter and what's an adjustment.

As an example, consider the linear pitch weights published by FanGraphs. They're calculated by looking at the change in average run expectancy after every pitch. If Corey Kluber throws a fastball for a strike as the first pitch of an at bat, his fastball is credited with the decrease in run expectancy from a 0-0 to a 0-1 count. If he throws a changeup for a ball the next pitch, the changeup is credited with the increase in run expectancy from a 0-1 to a 1-1 count. If a curveball is hit for a home run the next pitch, the curveball is credited with the increase in run expectancy from a 1-1 count to a home run. Fairly intuitive, and usually fairly small, but over the course of the season, they allow for some real distinctions between pitches -- by this measure, Kluber's curveball was worth 21.6 runs in 2014, compared to -10.4 runs for his sinker.

That said, there are a couple limitations to this method that keep it from clearly identifying the "best" pitches. First, it ignores the interrelated nature of pitching. A pitcher might have a curveball that almost always is in the dirt and rarely is swung at, and so looks bad by linear weights, but is used to change the hitter's eye level and increases the number of swings-and-misses on high fastballs thrown the next pitch. The fastball gets all the credit, but some of it is because of the previous pitch, and linear weights aren't able to pick out that strategic interaction.

Second, linear weights tell us about what happened to those pitches and not their underlying characteristics. Consider another hypothetical pitcher who throws a fastball and a slider. It could be that his slider is very good and his fastball is very bad. A "normal" rate of pitch use for a pitcher like that might be 30 percent sliders and 70 percent fastballs, but because the difference between his pitches is so great, this pitcher increases the number of sliders he throws. Batters begin to expect sliders, and his results on the slider start to look worse. His fastball is still really bad, so he keeps increasing the number of sliders he throws until it's no better than the fastball, which has improved somewhat because hitters are now surprised to see a fastball. By linear weights, his fastball and slider look equally valuable in this situation, despite the fact that his slider is much, much better as a pitch, and it's his extreme use of it that makes its results worse (but the pitcher's overall results better).

Is there a way to identify pitches like this, those that are excellent but "overused" and therefore missed by linear weights? The biggest clue lies in usage patterns. Going back to this hypothetical situation, I said a "normal" rate of sliders for a pitcher with this repertoire was 30 percent, but this hypothetical pitcher is throwing much more than that. The 2015 season is about 20 percent done; there's a substantial sample of pitchers who have thrown enough pitches to draw some conclusions about their usage rates, so I set out to find some of these pitches.

Pulling data from FanGraphs, I looked at the 127 pitchers who had thrown 30 or more innings as of Sunday's games and the rates at which they threw seven different pitch types: fastballs, sliders, cutters, curveballs, changeups, splitters, and knuckleballs. I wanted to compare pitchers to their peers, in terms of repertoire, since 30 percent might not be a high rate of curveballs for the whole sample. For a pitcher who also throws a fastball, slider, and changeup, it may be, and that's the kind of pitch I wanted to catch. Each pitcher was therefore categorized based on which pitches they threw more than 4 percent of the time. Arbitrary? Absolutely! But this hopefully keeps pitchers with their actual peers as opposed to comparing someone who truly throws a slider to someone who has messed around with one or has had some pitches misclassified by PITCHf/x.

For each pitch thrown more than 4 percent of the time, I calculated the z-score of its usage rate by comparing it to the average usage rate of that pitch among pitchers in that category. There are some things this method can't identify; if a pitcher is the only one to throw a certain mix of pitches, like fastball/knuckleball (R.A. Dickey) or fastball/slider/splitter (Jason Marquis), none of those pitches will show up. This is definitely a rough measure and is by no means a definitive ranking, but it should hopefully provide some useful information. I'm going to go through the top 5 pitches to see if this is picking up something real.

Rank	Name	Pitch	Repertoire	Usage Rate	Z-Score	LW
1	Collin McHugh	Slider	Fastball/Slider/Curveball/Changeup	43.7%	3.01	-0.56

Immediately, there's a disagreement between linear weights (LW) and this method, which is the point, so that's good. (The value in the LW column is the value per 100 pitches rather than the total value to allow pitches to be compared to each other without adjusting for usage.) Joe Vasile wrote about McHugh's slider here at BtBS less than two weeks ago and pointed out that his usage rates are incredible when compared to all pitchers, not just those with a similar repertoire to him.

For McHugh this season, it's been his curveball and fastball that have been particularly effective; per Brooks Baseball, more than half of his strikeouts have come on those two pitches, and hitters have a .280 SLG/.233 BABIP against his curve and a .346 SLG/.211 BABIP against his fastball, compared to a .500 SLG/.380 BABIP on the slider. That said, some of those good results are likely due to his high slider usage, and just being able to throw his slider so frequently while still getting good results overall is a sign that it is probably still a good pitch, despite the underwhelming results on it. This is a good pitch to start with, both because McHugh's usage is so extreme and it's an example of a pitch that doesn't look good in isolation but is likely providing lots of value to his other pitches.

Rank	Name	Pitch	Repertoire	Usage Rate	Z-Score	LW
2	Jesse Chavez	Cutter	Fastball/Cutter/Curveball/Changeup	43.0%	2.73	2.90

Chavez's cutter comes in at #2 and provides an interesting contrast to McHugh's slider. Again, Chavez uses his cutter heavily, but unlike McHugh's slider it's also his most valuable pitch by a substantial margin according to linear weights. Thus far in 2015, both his fastball and curveball have a negative value, and his changeup is basically zero.

Eno Sarris has a fantastic interview with Chavez, found here, in which Chavez talks a lot about his pitch mix and usage. While Chavez had always known how to throw a cutter, it has a reputation as an arm-killer, and he didn't begin using it in games until he got to the Athletics. He's used it fairly heavily each of the last three years, and Chavez is very unique in that respect; of pitchers with the same repertoire, the next highest cutter rate is 29.5 percent, for one Corey Kluber. It's only this year that Chavez's cutter is really getting identified as a great pitch by linear weights, and the 43.0 percent usage rate through Sunday would represent a new high. It will be interesting to see if batters begin to predict the cutter more often as the season goes on and if it will lose some effectiveness as a result.

Rank	Name	Pitch	Repertoire	Usage Rate	Z-Score	LW
3	Bartolo Colon	Fastball	Fastball/Slider/Changeup	84.4%	2.65	0.00

Colon's fastball(s) have been thoroughly covered, so I won't spend too much time here. Suffice to say that he actually has a few varieties of his fastball, and that variation along with excellent command makes it less valuable for hitters to sit fastball against Colon than you would expect by just looking at his usage rate. As a result, he can throw a fastball incredibly frequently without seeing poor results, and that high frequency in turn means that his other pitches are more unexpected and more valuable as a result. Colon has basically always pitched like this; may he pitch like this forevermore.

Rank	Name	Pitch	Repertoire	Usage Rate	Z-Score	LW
4	Drew Pomeranz	Curveball	Fastball/Curveball/Changeup	31.9%	2.31	-1.18

Pomeranz's curveball is another example of exactly the sort of pitch I was hoping this would pick up, as it looks fairly unexciting by linear weights (-1.18 runs per 100 this year, -0.49 runs per 100 career) but has a reputation as an excellent pitch and is used extremely frequently because of that. Baseball Prospect Report said of Pomeranz in 2010 that

"His curveball looks exactly the same way coming out of his hand [as his fastball] and then drops on you. He likes to come back with high fastballs after the curveball, again with the same release point. You have to be ready for his curveball because he will throw it any time in the count."

Given that, you'd expect Pomeranz's heavy curveball usage to make his fastball more surprising and more effective, and indeed, he's currently 13th in whiff rate among pitchers having thrown at least 100 fastballs, at 9.6 percent, per Baseball Savant. This is a good indication that Pomeranz's curveball is much more valuable than linear weights would seem to suggest and another point in favor of this method.

Rank	Name	Pitch	Repertoire	Usage Rate	Z-Score	LW
5	Felix Hernandez	Changeup	Fastball/Slider/Curveball/Changeup	27.1%	2.29	3.22

This should come as a surprise to no one. Felix's changeup is basically one-of-a-kind and a pitch he leans on extremely heavily. His usage rate has actually undergone two big jumps in his career, into 2011 (7.3 points) and into 2014 (9.7 points), but each time the effectiveness of the pitch per linear weights has remained basically unchanged. So far in 2015, he's backed off a little bit from his 2014 levels but is still well above 2013 and every prior year.

A changeup is traditionally thought of as a surprise pitch (hence the name), relying on a similar look to the fastball but different speed. Felix uses his changeup extremely frequently, and its velocity is much closer to his fastball's than most changeups, meaning it relies much less on his fastball for its success. I really, really want Felix to take this to the extreme and keep increasing his changeup percentage, if only to see what happens to the pitch's effectiveness as a result. The following are the highest changeup use rates among qualified starters from 2008 through 2014:

Rank	Season	Name	CH%
1	2014	Alex Cobb	38.1%
2	2014	Felix Hernandez	32.2%
3	2008	Edinson Volquez	31.9%
4	2011	Jeremy Hellickson	31.8%
5	2008	Cole Hamels	31.5%

Holy Alex Cobb! I think if anyone can break 40%, it's Felix. I won't hold my breath, but a boy can dream.

Based just on these top five results, this method seems to be a good alternative way of finding excellent pitches. There are obvious blind spots and shortcomings, but it provides a way to use data to evaluate something that traditionally has been the domain of scouting only: the underlying quality of the stuff. Linear weights are still a fantastic tool, and they pick up a lot that this method doesn't. But they have their blind spots as well, and looking at them in conjunction with the deviations from standard usage patterns should provide a more complete view of what pitches are really the best.

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Henry Druschel is a Contributor at Beyond the Box Score. You can follow him on Twitter at @henrydruschel.