The Relative Importance of Velocity

Velocity is much more important for some pitchs. (via Arturo Pardavila III)

Velocity is much more important for some pitchs. (via Arturo Pardavila III)

Editor’s Note: This piece was initially given as a presentation at the marvelous 2016 Saberseminar.

Many pitchers over the course of their careers, from Little League to the majors, get asked the question, “So how fast do you throw?” For most casual baseball fans, pitch velocity is looked at as the gold standard for how good a pitcher really is.

However, is pitching velocity actually the most important factor in determining how well a pitcher will pitch? Other factors such as movement and placement also play a role, but is their importance the same, greater, or less than that of pure velocity? Are these effects the same for all types of pitches? After considering these questions, we set out to design a research model that would allow us to begin investigating the relative importance of velocity versus movement and location of a pitch.

To begin, we considered our previous knowledge of baseball and pitching and predicted that pitch velocity does in fact play a large role in determining how good a pitcher is for most types of pitches. However, we think that role is smaller than what is traditionally thought.

While many casual baseball fans tend to only think of velocity, we believe placement and movement are more important. Obviously, this will vary by pitch type. Our hypothesis is that velocity will have the highest relative importance for fastballs. In addition, we believe the importance of pitch velocity to be reduced to the point of almost irrelevance in regard to knuckleballs.

We began by looking at PITCHf/x from 2014 and 2015. The PITCHf/x database covers every pitch thrown in the majors in a given year. We inspected two years worth of data, which meant 1,337,079 pitches. The fact that we had such a large data set with only two years of games played was extremely helpful, not only to limit bias, but also to prevent the amount of time the “scrape” function in R was needed to collect the pitch data into a data frame.

An important aspect of creating an initial correlation of pitch value to the “goodness” of a pitch was having an actual statistic with which to quantify the value of a pitch. To determine pitch value, we used the pitch linear weight values of all of the 24 base/out states as created by Tom Tango, including pitch count. The pitch value is the difference a single pitch makes for the expected runs in the rest of the half inning before and after the pitch was thrown. A large pitch value means that single pitch decreased the runs the opposing team was statistically expected to score for the rest of its half inning at-bat.

We used this as the metric against which to test the initial correlation of pitch velocity because it is a simple and straightforward metric that displays the value a single pitch has to the entire game. Therefore, to begin our analysis, we created a scatter plot of pitch start speed versus pitch value:

Figure 1: Initial plot of all pitches: start speed vs. pitch value.

Figure 1: Initial plot of all pitches: start speed vs. pitch value.

Unfortunately, due to the extremely high number of pitches being analyzed, the graph is not very helpful and gave us almost no information. The large quantity of pitches formed an indeterminate mass of points on the scatter plot, making the graph largely useless. We needed to further separate the data in order to get real results.

The first separation we did of the data was by the type of pitch. PITCHf/x gives many different classifications of pitch type. From those classifications, we created six pitch types we predicted would give us different and interesting results: fastball, curveball, slider, change-up, knuckleball, and eephus. Some of these pitch categories that we created are combinations of multiple PITCHf/x classifications. For example, we combined two-seam and four-seam fastballs into a singular fastball category.

We chose to leave out some less common pitch types such as cutters or splitters because we we wanted to simplify the data enough to see real differences between the pitch types. In addition, we still wanted to have large sample sizes of each pitch type, and not every pitch type is common enough for this. However, we chose to include both knuckleballs and eephus pitches despite their small sample size because we predicted the unique nature of these pitch types would yield interesting results.

To produce meaningful results, we used the gradient-boosted model in R and its predict function to build a prediction model using gradient-boosted trees for all fastballs. This model works by using decision trees that break up data into trees by either a range of a quantitative characteristic of the data or a qualitative characteristic. The model used to create the tree stops when there is a minimum amount of data points in each branch. Cost complexity pruning is applied to the main tree to create the ideal sequence of subtrees within the large tree. Lastly, k-fold cross validation is used to minimize mean squared prediction error, and the ideal tree is created that minimizes error.

A Hardball Times Update
Goodbye for now.

This decision tree closely mirrors human decision making more than regression and classification approaches, and it can handle qualitative data without dummy variables. Decision trees also can be displayed graphically and are easily interpreted. However, decision trees do not have the same level of predictive accuracy as regression and classification approaches. They are also non-robust, so small changes in the data set may lead to large final estimate changes. However, the gradient-boosted method of decision trees attempts to account for these disadvantages by pruning out sub-trees that have large mean squared error values. In this way, we can be certain the model we create will be the best possible way to divide the data.

For each of the six pitch types, we created a scatter plot and a decision tree. The scatter plots show a distribution of a pitch type over the course of the two seasons, with extremely wide or high/low pitches filtered out of the results. This step screened for wild pitches with low run values to optimize our results for “standard” pitches. The bar graphs show the output of the decision trees. The gradient-boosted model creates a graph that shows the values of different aspects of a pitch relative to each other. The five aspects of a pitch we analyzed are as follows:

  • Starting velocity (start_speed)
  • Px (horizontal distance from the center of the plate)
  • Pz (vertical distance from the center of the plate)
  • Pfx_x (horizontal distance change from pitcher’s release to home plate)
  • Pfx_z (vertical distance change from pitcher’s release to home plate)

To evaluate the contribution of certain aspects of the pitch to the overall pitch value, we looked at the relative importance value given by the boosted model we used in R.

By far the subset with the largest quantity of pitch data, fastballs were the first group of pitches we analyzed, with the results of our relative importance test as follows:


As we can tell, speed is not the aspect with the highest relative importance. This contradicts our hypothesis but conforms with our earlier results. Interestingly, the gradient model shows placement is by far the most important aspect of a fastball, with movement being clearly the least important. This relative importance make sense for fastballs because the pitch itself has little movement compared to the other pitch types we tested. Fastballs do not generally break like curveballs or sliders, and the relative importance of movement should be especially low in our analysis because we did not include cut fastballs in our fastball category.

After we ran this analysis on fastballs, we turned to the next largest subset of pitches, curveballs:


Curveballs have speed as the most important aspect of the pitch. It is interesting to note that the importance of placement versus movement is not consistent and depends on which direction of movement/placement is being analyzed. While slightly surprising that speed is the most important aspect of a curveball, one explanation behind the high relative importance of velocity is that the combination of a breaking ball that is also traveling more than 80 miles per hour can be deadly for hitters. In addition, the high relative importance of vertical movement of a curveball was expected because this is the entire point behind the pitch.

After curveballs, we analyzed sliders. For sliders, we were expecting a low relative importance of speed and a high relative importance of movement due to the pitch’s nature as a breaking ball. Also, while sliders had a decreased sample size, it was still large enough to run relatively conclusive results, seen below:


Based on the graph, velocity is, as suspected, the least important aspect of a slider. Sliders are designed to fool batters through their movement, particularly the way they drop away from the hitter. Therefore, the vertical placement of a slider in the strike zone will play a large part in determining if the batter is able to make contact with the ball, or if he swings and misses because he perceived the ball to be higher than it actually was.

While generally faster than curveballs, sliders still do not rely upon their speed. This makes it an interesting result that sliders have velocity at extremely low relative importance, while curveballs had velocity as the more important aspect of the pitch. While we were unable to determine a reason for this incongruity between the different pitch types, it is certainly an interesting result.

Following sliders, we analyzed change-ups, the last grouping of pitches we used that still had a relatively large sample size. As with sliders, we expected low relative importance of velocity and high relative importance of movement. The results are as follows:


Unsurprisingly, speed has very small relative importance for a change-up. Being pitched up to 15 mph slower than a pitcher’s fastball, a change-up is designed to fool a batter into thinking he sees a fastball, with a grip on the ball that induces friction between the pitcher’s finger and the ball that reduces the velocity of the pitch. The combination of unexpected movement and slower velocity can make a very effective pitch.

The high relative importance of vertical placement–as well as, to a lesser extent, horizontal placement–leads us to believe, in line with general baseball intuition, change-ups that are thrown low and away from the batter are very effective. The ability of a pitcher to place a change-up away from a batter leads to many swings and misses, creating a high relative importance determined from the pitch linear weight value.

After having tested four categories of regularly thrown pitches, we decided to see if any interesting results would arise from looking at types of pitches that are very different from a traditional pitch. While we knew these results would be less reliable because of the small sample size, we were intrigued to see if these two types of pitches were significantly different from the other four traditional categories of pitches that we analyzed. The first type of pitch in this vein that we analyzed was the knuckleball, with our results below:


Completely against our original hypothesis, speed was the aspect of a knuckleball with the highest relative importance. This is surprising given the general slow speed of knuckleballs, but, as with curveballs, this could be due to the combination of movement and higher velocity creating an even better pitch.

However, a major flaw in this analysis is that most of these pitches all came from the same pitcher: R.A. Dickey. Steven Wright is the only other active major league pitcher who regularly throws a knuckleball, and he threw significantly fewer pitches than Dickey throughout our sampling of the 2014 and 2015 seasons. Also, while Wright by no means underperforms with his knuckleball, Dickey’s knuckleball is clearly better than Wright’s, having won him a Cy Young award, creating a large divide in the overall pitch quality of the data that led to results that should be analyzed without a high level of confidence.

Finally, we were intrigued with what results this model would give for an eephus, a bizarre type of pitch that is rarely thrown. An eephus essentially is just an abnormally slow pitch, ranging from close to 60 mph down into the 40 mph range, that is essentially lobbed by the pitcher and tends to stun the batter. We were unsure of what to expect for the relative importance of eephi because of the strangeness of the pitch. Even with an extremely small sample size, we ran the model and gathered the following results:


These results are interesting but less reliable because there were so few (approximately 600) thrown in the past two years. It is surprising to see how low the relative importance of horizontal movement is compared to the other aspects of the pitch, but no real conclusions can be drawn from this test because of the small sample size.

In conclusion, our hypothesis was proved to be mostly wrong. The importance of velocity compared to movement or location varied widely based on pitch type. In some cases, velocity did indeed turn out to be the most important factor in determining the value of a pitch. Also, while we suspected velocity would be most important for fastballs and least important for knuckleballs, the results actually were almost completely flipped, with velocity being of middle importance for fastballs and the most important for knuckleballs.

After completing our research, we were able to see some flaws in our design that could be corrected if we were to do more investigation of the subject. Most importantly, we would increase our sample size, which would be able to give us conclusive results on knuckleballs. For knuckleballs, it would be important to get a wider variety of pitchers instead of just Dickey and Wright.

When it come to the eephus, we see that the pitch is thrown so rarely it might require scraping almost all of the available years of PITCHf/x data to get conclusive results, which would require a very large amount of time for a computer to process in R. We also relied on the PITCHf/x classifications of each pitch while separating our data. It is estimated that about 10 percent of pitches in the database are identified incorrectly, which could lead to some errors. If given more time, we could investigate these and filter out the mislabeled pitches.

In addition, we would determine a better way to separate the data by range within each aspect of the pitch. We initially tried to separate the different pitch types into different pitch velocity categories. For example, we split fastballs into ranges of about five miles per hour.

While we attempted this in the presentation, this method actually oversplit the data because of how the decision trees within the gradient-boosted model already split the data by velocity range. The gradient-boosting tree model already was splitting the data by velocity when it deemed this would lower the mean square root error. By splitting the data into different velocity ranges and running gradient-boosted tree models on these, we further increased the error by limiting the impact velocity could have on pitch value. This is why for fastball, velocity was the third-most important quality, while it was least important or second-least important for most other pitch types.

References & Resources

Kevin Dorosh, Julia Prusaczyk and Sara Stokesbury are students at Tufts University. All three are members of the Baseball Analysis at Tufts club. Follow them on Twitter @KDoorman21, @JulPrusac and @sarastokes14.
Newest Most Voted
Inline Feedbacks
View all comments
7 years ago

Many, many points for finding a way to use the word “eephi”. Or inventing it.

7 years ago

This is a really interesting presentation.

With fastballs, grouping two- and four-seam fastballs together might reduce the impact of velocity and movement, because there is generally a tradeoff between movement and velocity between the two fastballs (i.e. two-seamers give up a little velocity to get more movement). Did you check if splitting two- and four-seamers into separate groups affected the results at all?

For change-ups (and possibly other off-speed pitches), it might also be helpful to include a variable for the difference in speed from that pitcher’s average fastball. Conventional wisdom would be that the speed difference is more important than the actual speed for change-ups.

Regarding the relative influence numbers: does that describe how much, for example, a 1 mph increase affects the pitch value, or how much difference the overall spread of pitch speeds affects pitch values? In other words, if you had two groups of pitches, one ranging from 70-90 mph and the the other from 85-90, and for both groups a 1 mph change had the same impact, would the model assign the same relative impact to velocity in both groups, or would the impact for the first group be larger? If it’s the latter, that might be partially why velocity is found to be less important for sliders than curveballs, since at least anecdotally I would guess sliders have a smaller range of velocities than curveballs.

Do you have any plans to extend this from determining the relative impact of each trait on individual pitches to the relative impact on pitchers? For example, location is really important for individual fastballs, but the advantage of a well-placed pitch won’t apply to every pitch from a good control pitcher since he’ll still throw some pitches in bad locations. Whereas a velocity advantage will be present on pretty much every pitch, so the relative impact of velocity might increase when you look at all pitches thrown by a pitcher together rather than individually. It would be interesting to see how this extends from individual pitches to pitchers if you do decide to go down that road.

7 years ago

Great work! I think this is an interesting problem and I like the approach you took.

I agree with several of the suggestions of Kincaid. Specifically, I question why two-seamers and four-seamers should be combined. Movement matters a lot more for two-seamers than it does for four-seamers. Also mentioned by Kincaid, speed relative to a pitcher’s fastball likely plays a much bigger role than the actual speed for off-speed pitches.

Regarding the eephus pitch, my guess is that a majority of those pitches are thrown by position players, if they were not previously filtered from the dataset (something worth doing).

Was horizontal movement and location adjusted for batter handedness? Whether or not they were changes the residuals which the subsequent boosted trees are built on.

Jetsy Extrano
7 years ago

What’s the actual fit of these models you’re building? Relative importance of dimensions wouldn’t seem to mean much if the whole model together didn’t capture what’s going on.

What do the relative numbers actually measure, for that matter?

You use RE24 values, so are you working only with balls put into play? That may not be what you want. At the least, let me channel MGL and say if you don’t handle ball/strike count you may not be measuring what you think. Like location changes in pitchers’ counts versus hitters’.

If “movement” means the x and z Magnus values, fastballs actually have a lot and sliders have very little. FYI.

Micah Daley-Harris
7 years ago

Great piece. All else being equal did faster mean better for the off-speed pitches?

Fake Yeezy
6 years ago

While Under Armour is mostly an apparel company, footwear “has been hailed as the next true leg of Under Armour’s growth” as the company faces more competition in apparel.