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# What is More Important for a Fastball: Velocity, Location, or Movement?

Velocity, location, and movement are all unquestionably important when we try and compare ‘good’ pitches to ‘bad’ pitches. My particular interest lies in how important each are. I’ve often wondered if a 98 mph cutting fastball can be thrown right down the middle and still have little chance of being hit for a home run? Or conversely, is an 88 mph fastball that’s straight as an arrow still likely to get a swinging strike if it paints the bottom outside corner of the zone?

The approach I decided to take to try and begin answering the question of relative importance between velocity, location, and movement, was to look at the pitchFX data for all pitches thrown during the 2011 MLB season. As a start, I decided to look only at fastballs thrown by right handed pitchers to right handed batters in an attempt to get as homogenous a data set as possible. I included all pitches from the 2011 season that MLB gameday classified as either: fastball, four-seam fastball, two-seam fastball, cut fastball, or split finger fastball. I then narrowed the data set to include only pitches that were either swinging strikes (good) or hit for a home run (bad). I decided to use swinging strikes and home run as the good/bad pitch criteria because ultimately those are the best and worst possible outcomes for any given pitch.

For righty vs. righty matchups in 2011, I found that 1,134 fastballs were hit for home runs, and 11,790 were swinging strikes. This means that approximately 10x more fastballs were swung on and missed than hit for home runs.

Next, I wanted to get a general sense of the location of the pitches for each outcome. I created two separate plots of pitch location, one for swinging strikes (SS) and one for home runs (HR). Figure 1 shows those plots. From the plots I could see that batters swing and miss at fastballs pitched in pretty much any location, so that wasn’t helpful. But, I also noticed that fastballs down and away were not often hit for home runs, and fastballs middle in look more likely to be hit for home runs than fastballs away. Although not particularly useful in answering my question, since these two figures agreed very well with conventional baseball wisdom, I was able to proceed with a more thorough investigation knowing at last my data set was good.

Figure 1 – Location of fastballs pitched by right handed pitchers to right handed batters during the 2011 MLB Season. Red dots represent pitches swung on and missed, blue dots represent pitches hit for a home run. All units are in feet. The rectangle between -0.83 to 0.83 in the horizontal and 1.6 to 3.5 in the vertical represents an approximate strike zone. Figures are from the catchers perspective, therefore negative horizontal numbers represent inside on a right handed batter.

The next thing I decided to do was run a series of independent t-tests to determine if there were any statistically significant differences in the average velocity, location, or movement of the HR group compared to the SS group. Table 1 shows the results of these tests.

Table 1 – Summary for independent t-tests for velocity, horizontal location (px), vertical location (pz), horizontal movement (pfx_x), and vertical movement (pfx_z)

 HR Avg HR Stdev SS Avg SS Stdev p Velocity 90.85 2.94 91.27 3.59 <0.05 px (ft) -0.21 0.46 0.06 0.71 <0.05 pz (ft) 2.66 0.49 2.63 0.83 0.228 pfx_x (inch) -4.49 3.46 -3.99 3.85 <0.05 pfx_z (inch) 7.76 3.00 7.08 3.78 <0.05

I found the average velocity difference between HR and SS was statistically significant. However, the difference between the averages was less than half a mile per hour, and the range of velocities for each group (as indicated by the standard deviations) were quite high. What I interpreted from this was, most MLB fastballs are probably between 88 to 94 mph, and in this range, velocity probably doesn’t matter that much.

In terms of location, in the horizontal direction I found the average location difference between HR and SS was statistically significant. Practically, I’m not sure how meaningful the difference really is. The average SS fastball was pretty much right down the middle, and the average HR fastball was only .21 ft (approx. 2.5 inch) from the middle on the inside half. In other words, it looks like hitters swing and miss at pitches everywhere, and hit home runs on pitches near the middle of the plate or middle in. No big surprises here. In the vertical direction, average location was not significantly different between groups. This may be a little bit misleading, because even though the distribution is normal for both HR and SS, the distribution is much wider for SS compared to HR. More on this in a bit.

Statistically, movement in both the horizontal and vertical direction were significantly different. Pitches that are hit for a home run appear to run in on right-handed hitters about half an inch more than pitches swung on and missed. Again, the range in movement was quite high within each group that, practically speaking, I’m not so sure how much that difference in average matters. A similar trend was found with vertical movement in that pitches swung on and missed moved downward about ¾ of an inch more than those hit for home runs. Although this was again statistically significant, I doubt it is practically significant because of the range in movement.

SS to HR ratios

After I decided that the independent t-tests didn’t really help me answer my original question of relative importance between velocity, location, and movement, I decided to take a completely different approach. Instead of looking at the differences in the averages between SS and HR groups, I instead looked within velocity, location, and movement to see what changes within each affected the outcome of each pitch.

I started with velocity. I broke down both the SS and HR groups into 1 mph increments. I then determined the ratio of pitches at each velocity that were swinging strikes compared to home runs. This ratio effectively tells me how much more likely a pitch is to be swung on and missed rather than hit for a home run. Remember, in general a fastball is 10x more likely to be swung on and missed than hit for a home run. A higher SS:HR ratio is better for the pitcher. What I found was that fastballs between 87 to 92 mph were actually less than 10x more likely to be swinging strikes. More interestingly, I found that fastballs 96 mph were more than 20x more likely to be swinging strikes. Ninety-eight mph fastballs are 33.5 times more likely to be swinging strikes. So looking at Figure 2, it appears as though fastballs over 95 mph are considerably less likely to be hit for home runs. Also somewhat interestingly, fastballs less than 86 mph are also less likely to be hit for home runs.

Figure 2 – Swinging strike (SS) to Home run (HR) rate broken down by velocity

As for location, Figure 3 shows the SS:HR ratio for both the horizontal and vertical directions. In the horizontal direction, it looks like most pitches in the strike zone are less than 10x more likely to be swinging strikes than home runs. The only exception is the outer six inches. Pitches about 3-4 inches from the outside edge of the plate are nearly 20x more likely to be swinging strikes, and pitches that paint the outside edge are over 40x more likely. On the other hand, if a right handed pitcher paints the inside part of the plate on a right handed batter with a fastball, he’s only 7x more likely to get a swinging strike than a home run (less than average). In the vertical direction, it looks like both high strikes and low strikes are better at getting swinging strikes than stuff right down the middle. At 1.75 ft from the ground, or typically just above the knees, the pitcher is 35x more likely to get a swinging strike. Interestingly, at 3.5 ft from the ground, or typically about the top of the strike zone, the pitcher is only about 13x more likely to get a swinging strike. This isn’t too much above the 10x average. Only when the pitch gets 3.75 ft above the ground, or out of the strike zone, does the likelihood change to 25x.

Figure 3 – Swinging strike (SS) to Home run (HR) rate broken down by horizontal and vertical location. For the horizontal direction, zero indicates the middle of home plate and negative numbers are inside to a right-handed hitter. For the vertical direction, zero is the ground.

Finally, the most interesting findings to me come from movement (Figure 4). I was very surprised to see how little horizontal movement matters with respect to SS:HR ratio. From the t-tests I found that pitches hit for home runs had slightly more horizontal movement inward than pitches swung on and missed. This finding was again seen here. From the graph, it looks like inward movement causes the SS:HR ratio to remain around 10x. However, both a straight fastball and a slightly tailing fastball have a slightly higher rate of 15x. In the vertical direction, again movement does not seem to matter for the most part. Upward movement greater than 4 inches has a consistent ratio of approximately 10x. Only when upward movement is 4 inches or less does the SS:HR ratio considerably increase. At 2 inches upward movement, the SS:HR ratio is 26x.

Figure 4 – Swinging strike (SS) to Home run (HR) rate broken down by horizontal and vertical movement. For the horizontal direction, negative numbers are inside to a right-handed hitter.

Side note: The vertical movement value given by the pitchFX system can be slightly counter-intuitive. PitchFX defines movement with respect to a pitch thrown with no spin and acted upon by gravity. Gravity pulls all pitches downward, however, spin on the ball can create a small amount of lift. Therefore, most fastballs classified by the system have upward movement. The average upward movement for an MLB fastball is between 7-10 inches.

To summarize, it appears as though velocity and location matter far more than movement when it comes to fastballs. Fastballs over 95 mph are far less likely to be hit for home runs than swung on and missed (over 20x), however, fastballs between 87 to 92 mph were no different with respects to how likely they were to be hit for home runs compared to swung on for strikes (all about 10x). Fastballs on the outer edge of the plate were over 40x more likely to be swung on and missed, and fastballs down in the zone 35x. Fastballs up in the zone were not much different than fastballs in the middle of zone. For a high fastball to be effective, it must be out of the strike zone. Tailing fastballs seem to be better than cutters.

Finally, I think the take home message here is, if a pitcher is gifted enough to have a 95+ mph fastball, it probably doesn’t matter too much where they throw it. As long as they can throw it for strikes, they will be effective. Pitchers that don’t have that 95+ mph fastball can also be effective, however, they need to locate their pitches. There are still places in the strike zone they can throw their fastball and be very effective. The idea that movement on a fastball matters appears to be totally erroneous. A pitcher probably can’t live on a fastball that is 92 mph with a lot of movement if he can’t locate it. A pitcher probably can live on an 88 mph fastball with little movement as long as he can locate it. Location is far more important than movement for fastballs.