**PITCHf/x: A Primer**

When Sportvision released PITCHf/x in 2006, they revolutionized the way that MLB pitchers are evaluated. Two cameras were mounted in every stadium to track the speed, vertical and horizontal movement of every pitch thrown. This data is then compiled and released daily by MLB Advanced Media for public access.

With the introduction of PITCHf/x, analysts no longer had to rely solely on radar gun speeds and scouts’ opinions to determine a pitcher’s skills. Based on the speed and movement of each pitch, it is classified either by an algorithm or manually as a certain pitch type. We can then evaluate pitches based on the results they are generating – for example, we can say that Player A has a good fastball because batters swing and miss on it XX% of the time.

One note, which will come up very frequently in the study, is how vertical movement is quantified. On most changeups, vertical movement will be positive, meaning that the changeup has some amount of “rise” on it. These pitches, of course, don’t actually rise; they just drop less compared to a hypothetical, spineless pitch. So, when thinking about the drop on a changeup, remember that the lower the vertical movement measurement, the more the pitch drops.

**Evaluating Changeups**

This article originally stems from the science fair project that Mark Rosenberg (of The Rosenblog), Jack Lang and I worked on during this past winter. In that project, we regressed pitch components from multiple types of pitches against many different result stats.

In this study, we’ll focus primarily on changeups. Because there are many grip variations and different arms slots used to throw the pitch, there are many different “shapes”, or horizontal and vertical movement combinations. For a point of reference, the league average changeup has roughly five inches of horizontal movement, and 7.5 inches of vertical movement (rise).

Indians pitcher Carlos Carrasco’s changeup, for example, has only 5.37 inches of horizontal movement, but features an incredible -0.21 inches of vertical movement.

White Sox starter Chris Sale, on the other hand, throws his changeup with 12.58 inches of horizontal movement, and 3.24 inches of vertical movement.

Orioles starter Chris Tillman’s changeup has 4.73 inches of horizontal movement, and 8.34 inches of vertical movement.

*Blue arrows are the PITCHf/x measurements, and the red arrow is the resultant vector

Remember: a greater vertical movement value means it “drops” less. While Carrasco’s vertical movement is the smallest from a visual standpoint, it actually represents the most vertical movement, because it has the least “rise”.

Generally, changeups generate groundballs at a high rate relative to other pitch types. As I explained in an article at DRaysBay about Rays pitcher Jake Odorizzi, pitchers prefer some batted ball types more than others:

“Each batted ball type has a certain average BABIP—or probability of falling in play for a hit. These rates are illustrated in the table below.

Remember: a greater vertical movement value means it “drops” less. While Carrasco’s vertical movement is the smallest from a visual standpoint, it actually represents the most vertical movement, because it has the least “rise”.

Generally, changeups generate groundballs at a high rate relative to other pitch types. As I explained in an article at DRaysBay about Rays pitcher Jake Odorizzi, pitchers prefer some batted ball types more than others:

“Each batted ball type has a certain average BABIP—or probability of falling in play for a hit. These rates are illustrated in the table below.

Looking at this table, it may seem like a pitcher should try to generate as many fly balls as possible, because they fall for hits least often. However, this frequency only involves hits that are in play, and since home runs aren't technically in play, they are not counted by this metric.

In essence, fly balls are risky. When they stay in the park, they rarely fall for hits, but studies by John Burnson (

Groundballs, on the other hand, result in hits more often than fly balls. However, ground balls are never a threat to leave the park, so they are a safer bet than fly balls in this regard.

This isn't to say that one is better than the other. Both fly ball pitchers and ground ball pitchers can be successful in the major leagues, and more factors than their batted ball profile go into their performance.”

Because changeups can be used to induce groundballs, they often serve as a staple in most pitchers’ arsenals. But what aspects of changeups are actually influential in generating groundballs, and which are not as important?

Two years ago, Harry Pavlidis conducted a similar experiment in an effort to find what components make an effective changeup. My test is similar, however the data used and some of the mechanics are different.

First, I compiled all seven years of PITCHf/x data from Baseball Prospectus. After organizing the data into a spreadsheet, I was able to run regressions comparing the physical components of the changeup to the groundball rate. The physical components were the independent variables, and were vertical movement, horizontal movement, velocity of the changeup, and the difference in velocity between the pitcher’s fastest pitch and their changeup.

From my first basic regression, I found that vertical movement, velocity and velocity difference were all significant on the 99% level, and my model had an r-squared value of .444. Vertical movement and velocity difference were negatively correlated, while velocity was positively correlated.

The vertical movement correlation makes logical sense. Less “rise”, or more drop, would increase the probability that the hitter makes contact on the top half of the ball and drives it into the ground.

Furthermore, velocity being identified as significant suggests that faster changeups get more ground balls. Pavlidis’ study takes this a step further, and reports that pitchers with a larger velocity differences get more whiffs. So, if we combine these last two conclusions, we see that pitchers that throw hard while still maintaining a sizeable velocity difference generally have the most success.

Having identified the significant variables, we can plug the data back into the regression model to see which pitchers’ changeup’s components indicate that they have elite pitches. If you are interested in using the formula to generate expected groundball rates for other pitchers, you can find the formula here. Here’s a table of the starting pitchers' changeups that are best at generating groundballs, according to their pitch components:

In essence, fly balls are risky. When they stay in the park, they rarely fall for hits, but studies by John Burnson (

**2015 Baseball Forecaster**) have shown that a pitcher has very little control over how far the fly balls that they allow travel. Being a "fly ball pitcher" makes the pitcher more susceptible to home runs, which can be costly.Groundballs, on the other hand, result in hits more often than fly balls. However, ground balls are never a threat to leave the park, so they are a safer bet than fly balls in this regard.

This isn't to say that one is better than the other. Both fly ball pitchers and ground ball pitchers can be successful in the major leagues, and more factors than their batted ball profile go into their performance.”

Because changeups can be used to induce groundballs, they often serve as a staple in most pitchers’ arsenals. But what aspects of changeups are actually influential in generating groundballs, and which are not as important?

Two years ago, Harry Pavlidis conducted a similar experiment in an effort to find what components make an effective changeup. My test is similar, however the data used and some of the mechanics are different.

First, I compiled all seven years of PITCHf/x data from Baseball Prospectus. After organizing the data into a spreadsheet, I was able to run regressions comparing the physical components of the changeup to the groundball rate. The physical components were the independent variables, and were vertical movement, horizontal movement, velocity of the changeup, and the difference in velocity between the pitcher’s fastest pitch and their changeup.

From my first basic regression, I found that vertical movement, velocity and velocity difference were all significant on the 99% level, and my model had an r-squared value of .444. Vertical movement and velocity difference were negatively correlated, while velocity was positively correlated.

The vertical movement correlation makes logical sense. Less “rise”, or more drop, would increase the probability that the hitter makes contact on the top half of the ball and drives it into the ground.

Furthermore, velocity being identified as significant suggests that faster changeups get more ground balls. Pavlidis’ study takes this a step further, and reports that pitchers with a larger velocity differences get more whiffs. So, if we combine these last two conclusions, we see that pitchers that throw hard while still maintaining a sizeable velocity difference generally have the most success.

Having identified the significant variables, we can plug the data back into the regression model to see which pitchers’ changeup’s components indicate that they have elite pitches. If you are interested in using the formula to generate expected groundball rates for other pitchers, you can find the formula here. Here’s a table of the starting pitchers' changeups that are best at generating groundballs, according to their pitch components:

Generally, the expected groundball rate matches up pretty well with the actual groundball rates. Yohan Flande was the only major outlier. It makes sense, because 2014 was his rookie season, and he is most likely still adjusting to the majors. Now, let’s look at the worst changeups.

Odrisamer Despaigne is the major outlier in this table, but, as Jeff Sullivan of FanGraphs points out, Despaigne has a very unique, and borderline incomparable changeup. Sullivan explains that he has a strange grip, and uses multiple arm angles. Because of this, there’s a strong chance that Despaigne “beats the formula”, and his groundball rates won’t be accurately projected using this model.

In addition to identifying good and bad changeups of major league players, it can also be used as an evaluation tool for minor league pitchers. There isn’t PITCHf/x data available for minor leaguers during the regular season, but prospects often pitch the Arizona Fall League, where PITCHf/x cameras are set up. Pitch shapes stabilize in as little as three pitches, so we can evaluate changeups even if there’s a small sample size.

A great example of this is with Rays prospect Colton Reavis. Reavis was a 30th round selection by the Rays in 2013, and hasn’t been featured atop any prospect lists. But, if we look at the PITCHf/x data from the Arizona Fall League, which DRaysBay author Ian Malinowski did in his article about Reavis, we see that his changeup could be incredible.

In addition to identifying good and bad changeups of major league players, it can also be used as an evaluation tool for minor league pitchers. There isn’t PITCHf/x data available for minor leaguers during the regular season, but prospects often pitch the Arizona Fall League, where PITCHf/x cameras are set up. Pitch shapes stabilize in as little as three pitches, so we can evaluate changeups even if there’s a small sample size.

A great example of this is with Rays prospect Colton Reavis. Reavis was a 30th round selection by the Rays in 2013, and hasn’t been featured atop any prospect lists. But, if we look at the PITCHf/x data from the Arizona Fall League, which DRaysBay author Ian Malinowski did in his article about Reavis, we see that his changeup could be incredible.

Plugging the data into the formula, we see that we would expect Reavis to have a 55% groundball rate on his changeup, which is above league average. Paired with a 94 mph fastball and a lively slider, Reavis looks to have a great arsenal.

While this model is a decent estimator of changeup performance, there are certain aspects that it doesn’t address. Is more movement always good? Can a changeup be thrown too hard? If the changeup has a lot of movement, does velocity matter as much?

To try and answer these questions, I constructed a “total movement” value for each player in my data pool. The process of this was pretty simple – I found the value of the resultant vector shown in the images above through vector addition (Pythagorean theorem).

Now, I had an estimate of the pitches total movement, and could run regressions using only a certain band of players that had similar total changeup movement. This isn’t a perfect measure, because many different shapes could achieve a total movement of 9.0 inches, for example. However, it did serve as a viable way of grouping similar pitches.

After many attempts to find groups that would yield the highest r-squared values, I settled on the following buckets, which worked out to be nice numbers:

· Under 8 inches

· 8-9 inches

· 9-10 inches*

· 10-11 inches

· 11+ inches

All of the groupings were moderately successful, as they featured larger or similar r-squared values when compared to the original model. The 11+ inch bucket's r-squared was lower, at .494, but had higher accuracy in projecting these players than with the general model.

The 9-10 inch bucket, however, was the major outlier. No combination seemed to include this group without major sacrifices in the r-squared value, so I made it their own group, which has a .381 r-squared. I’m not sure if it was just by chance that this section had such low correlation, or if there is some underlying factor. It may be because the league average changeup has a total movement value of 9.05, and with a changeup this nondescript other parts of the arsenal play a bigger role in determining its success.

We can look at the differences in significant statistics to begin to understand how pitch components affect the different styles of changeups.

Here’s a table showing which statistics were significant on the 95% level in each of the buckets:

While this model is a decent estimator of changeup performance, there are certain aspects that it doesn’t address. Is more movement always good? Can a changeup be thrown too hard? If the changeup has a lot of movement, does velocity matter as much?

To try and answer these questions, I constructed a “total movement” value for each player in my data pool. The process of this was pretty simple – I found the value of the resultant vector shown in the images above through vector addition (Pythagorean theorem).

Now, I had an estimate of the pitches total movement, and could run regressions using only a certain band of players that had similar total changeup movement. This isn’t a perfect measure, because many different shapes could achieve a total movement of 9.0 inches, for example. However, it did serve as a viable way of grouping similar pitches.

After many attempts to find groups that would yield the highest r-squared values, I settled on the following buckets, which worked out to be nice numbers:

· Under 8 inches

· 8-9 inches

· 9-10 inches*

· 10-11 inches

· 11+ inches

All of the groupings were moderately successful, as they featured larger or similar r-squared values when compared to the original model. The 11+ inch bucket's r-squared was lower, at .494, but had higher accuracy in projecting these players than with the general model.

The 9-10 inch bucket, however, was the major outlier. No combination seemed to include this group without major sacrifices in the r-squared value, so I made it their own group, which has a .381 r-squared. I’m not sure if it was just by chance that this section had such low correlation, or if there is some underlying factor. It may be because the league average changeup has a total movement value of 9.05, and with a changeup this nondescript other parts of the arsenal play a bigger role in determining its success.

We can look at the differences in significant statistics to begin to understand how pitch components affect the different styles of changeups.

Here’s a table showing which statistics were significant on the 95% level in each of the buckets:

While we can’t know for sure, we can theorize why some statistics were significant in some regressions and not others.

Horizontal movement was only significant for pitches with less than eight inches of total movement. With a total movement so small, I think that a pitcher needs to maximize movement in all directions to avoid having their changeup look like a batting practice fastball. If they didn’t maximize movement, hitters could wait for the slow, straight pitch and drive it.

For pitches with ten or more inches of total movement, velocity or velocity difference was significant in these regressions. I believe that this stems from the preparation of the hitter. If a hitter knows that a pitcher’s changeup has a ton of movement on it, they may be inclined to not swing, and wait for a flatter pitch. If the changeup is significantly slower than the pitcher’s other pitches, then it will be easier to identify and the hitter is less likely to make the mistake of swinging at it. But, if the pitcher’s changeup has enough velocity that it is harder to pick up, he may cause the hitter to swing and miss, or drive the ball into the ground.

Using this method of grouping and creating an “aggregate model”, we can project groundball rates with more precision, and measure the relative importance of each component.

In Pavlidis’ study on groundballs and whiffs, he makes important conclusions about the value of vertical movement, but doesn’t mention horizontal movement. My regression found it to be of little importance when focusing on groundballs. I was curious to see if horizontal movement was important in other ways.

I thought that horizontal movement may, from a logical perspective, have something to do with causing batters to chase bad pitches. The pitcher could throw the changeup on the outside or inside part of the plate, and have it break either in or away from the hitter, depending on handedness.

To measure this, I compiled swinging strike rates (whiffs/pitches) for both inside the strike zone and outside the strike zone for all pitchers who had thrown at least 250 changeups last season. (250 changeups allowed me to have a large enough sample for both in the zone and out of the zone.) But, after I ran the regressions, I found that horizontal movement had very little significance in determining these whiff rates.

This was perplexing, because it would’ve seemed to be important. It’ll require its own article, so look out for Part 2.

From this, we can identify the important components in a changeup, and tailor our analysis to those components. By evaluating a changeup based on it’s shape, and not only the results, we can reduce “noise” in the data and get a better understanding of how good the pitch is. Furthermore, we can evaluate it much faster, because shape stabilizes very quickly.

In addition to using the general model to examine shapes, we can use the movement-specific models to analyze the relative importance of these components as movement is altered. This gives us a better understanding of not only who throws good pitches, but also how and why these pitches are effective.

The horizontal movement mystery is yet to be solved, but I’m going to take another crack at it soon. Stay tuned.

Horizontal movement was only significant for pitches with less than eight inches of total movement. With a total movement so small, I think that a pitcher needs to maximize movement in all directions to avoid having their changeup look like a batting practice fastball. If they didn’t maximize movement, hitters could wait for the slow, straight pitch and drive it.

For pitches with ten or more inches of total movement, velocity or velocity difference was significant in these regressions. I believe that this stems from the preparation of the hitter. If a hitter knows that a pitcher’s changeup has a ton of movement on it, they may be inclined to not swing, and wait for a flatter pitch. If the changeup is significantly slower than the pitcher’s other pitches, then it will be easier to identify and the hitter is less likely to make the mistake of swinging at it. But, if the pitcher’s changeup has enough velocity that it is harder to pick up, he may cause the hitter to swing and miss, or drive the ball into the ground.

Using this method of grouping and creating an “aggregate model”, we can project groundball rates with more precision, and measure the relative importance of each component.

**The Horizontal Movement Mystery**In Pavlidis’ study on groundballs and whiffs, he makes important conclusions about the value of vertical movement, but doesn’t mention horizontal movement. My regression found it to be of little importance when focusing on groundballs. I was curious to see if horizontal movement was important in other ways.

I thought that horizontal movement may, from a logical perspective, have something to do with causing batters to chase bad pitches. The pitcher could throw the changeup on the outside or inside part of the plate, and have it break either in or away from the hitter, depending on handedness.

To measure this, I compiled swinging strike rates (whiffs/pitches) for both inside the strike zone and outside the strike zone for all pitchers who had thrown at least 250 changeups last season. (250 changeups allowed me to have a large enough sample for both in the zone and out of the zone.) But, after I ran the regressions, I found that horizontal movement had very little significance in determining these whiff rates.

This was perplexing, because it would’ve seemed to be important. It’ll require its own article, so look out for Part 2.

**So What Does This All Mean?**From this, we can identify the important components in a changeup, and tailor our analysis to those components. By evaluating a changeup based on it’s shape, and not only the results, we can reduce “noise” in the data and get a better understanding of how good the pitch is. Furthermore, we can evaluate it much faster, because shape stabilizes very quickly.

In addition to using the general model to examine shapes, we can use the movement-specific models to analyze the relative importance of these components as movement is altered. This gives us a better understanding of not only who throws good pitches, but also how and why these pitches are effective.

The horizontal movement mystery is yet to be solved, but I’m going to take another crack at it soon. Stay tuned.

*PITCHf/x data is from Baseball Prospectus, and in-zone/out-of-zone whiff rates are from BrooksBaseball.net.*