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August 17, 2011
Why are Batters Hit by Pitches?
Every season major league pitchers throw tens of thousands of pitches inside off the plate, yet they hit batters “only” about 1500-1800 times in a season. Why do some inside pitches hit the batter, while others do not?
Albert Lyu’s graphs of hit-by-pitch locations in an article about Javier Vazquez hitting three consecutive Rays batters on September 23, 2010, spurred my investigation of this question. I was initially curious about using hit-by-pitch locations and rates as a way to identify how close each batter stands to the plate. The data has some utility for that purpose, as discussed previously, but I also became fascinated by the question of why pitches hit batters.
It would seem to me that the two main factors that determine whether a pitch hits a batter are the direction it's thrown in (more toward the batter = more likely to hit him) its velocity (faster = less time to get out of the way). If we assume that HBPs are predominantly unintentional events, and that pitchers do not intend to throw AT the batter (near, sure), then my first glance impression would be that, as overall talent/skill levels rose over time due to an expanding field of talent from which to draw players, HBP rates fell, reaching their nadir around integration, which marked a significant expansion in the talent pool.
What are the main factors that determine whether a pitch hits a batter? Location is obviously important, as an outside pitch cannot hit a batter, and pitches over the plate should not hit a batter unless he is leaning out over the plate, which according to rule should result in a strike call rather than a free base. It is plausible that pitch speed and pitch type also play a role.
In fact, pitcher and batter handedness play a big role in all of these factors. Pitchers hit same-handed batters about twice as frequently as they hit opposite-handed batters. The fact that pitchers throw different pitch types to same-handed and opposite-handed batters contributes to this difference.
Data in the following graph is from 2008-2011 and uses pitch classifications supplied by MLB Advanced Media.
Because sinkers and changeups break toward the pitcher’s throwing-arm side, pitchers tend to throw them toward that side of the plate to take advantage of the movement out of the hitting zone and away from the sweet spot of the bat. Thus, these pitch types are often thrown on the outside edge to opposite-handed hitters and on the inside edge to same-handed hitters. Four-seam fastballs also follow this trend, though to a lesser extent.
Similarly, since the slider and cutter break toward the pitcher’s glove side (at least relative to the fastball), pitchers tend to throw them on the outside edge to same-handed hitters and on the inside edge to opposite-handed hitters. Naturally, pitches that are thrown inside more often are more likely to hit batters.
In fact, opposite-handed and same-handed HBP rates by pitch type follow a nicely inverse relationship, with two small exceptions. The knuckleball is more likely to hit batters of either hand than would be predicted by this relationship, presumably because of its unpredictable movement. On the other hand, the changeup is less likely to hit batters of either hand than would be predicted by this simple relationship. It is not surprising that pitchers prefer not to pitch inside with a slow pitch.
We can define an area inside off the plate where a batter is most likely to be hit by a pitch. We will get to the geometry of that region in a moment, but first let’s look at which pitch types tend to be thrown inside toward the batter with the most frequency.
Unsurprisingly, this bears some similarity to the previous graph of HBP rates by pitch type.
We can gain more insight if we look at the locations of the pitches that hit batters.
You can get an idea from this chart roughly where batters stand relative to home plate. Pitches to same-handed batters tend hit them in the torso, regardless of pitch type. This makes sense if you think about the geometry of the pitch trajectory. Pitchers release the ball around six or seven feet off the ground and a couple feet to the left or right of center, and they are presumably aiming roughly toward the strike zone. Same-handed pitchers release the ball on the same side of the plate that the batter is standing. If they release the ball a little too early, the pitch tends to go up and in, where it has a chance of hitting the batter in the torso. If they release the ball a little too late, it tends to go down and away, where it misses the batter completely. To hit a same-handed batter in the lower legs requires a very badly aimed delivery.
The geometry works the other way around when pitcher and batter are of opposite handedness. In that case, however, pitch type matters.
Opposite-handed pitchers release the ball on the opposite side of the plate from the batter. If they release the ball a little too early, the pitch tends to go up and away, where it misses the batter. If they release the ball a little too late, it tends to go down and in, where it has a chance of hitting the batter in the feet. However, if the batter is leaning in toward the plate, his torso can come very near the strike zone, in which case an opposite-handed pitcher can hit him with a pitch up and in.
The chart above shows that opposite-handed pitchers hitting a batter in the torso mostly happens with fastballs, and hitting a batter in the legs mostly happens with breaking balls.
You can also get an idea from the two preceding charts of where batters typically stand. You can see that left-handed batters stand a little closer to the plate than right-handed batters. It is probably no accident that the strike zone that umpires call for left-handed batters is shifted a couple inches farther outside than the zone for righties. Figuring out the chain of causation for that effect is a bit complicated, though, and something we discussed in a previous article on the strike zone. We will come back to this briefly when we compare Chase Utley and Raul Ibanez later in the article.
We can draw boxes that encompass the vast majority of HBP locations. For right-handed batters, we draw a box around the torso area from -1 to -3.2 feet horizontally and 3 to 5 feet vertically. We draw a box around the legs from -1.8 to -3.2 feet horizontally and 0 to 3 feet vertically. For left-handed batters, we draw a box around the torso area from 1 to 3 feet horizontally and 2.8 to 4.8 feet vertically. We draw a box around the legs from -1.4 to -3 feet horizontally and 0 to 2.8 feet vertically. These boxes encompass about 94 percent of HBP locations.
How often do different pitch types come inside within these boxes and how often do they hit the batter in the torso or the legs? The pitch classifications here are from MLB Advanced Media from 2008-2011. They count some sinkers in with the fastballs, but for purposes of comparing HBP rates, these classifications should be sufficient.
You may have noticed on the HBP location graphs that a few of the pitches that hit batters were located over home plate. The most egregious two examples over the very middle of the plate may be due to data errors. Video for those two pitches is no longer available on the MLB website for confirmation, and game descriptions make no mention of either pitch. The pitch marked at 4.1 feet high and -0.3 feet horizontal hit Jeff Francoeur on May 18, 2008, and the pitch marked at 3.2 feet and -0.2 feet horizontal hit Grady Sizemore on September 21, 2008. Video is available in the MLB archives from 2010 to the present, but no pitch over the middle of the plate has hit a batter during that period—or least no umpire has awarded a batter first base for being hit by a pitch over the middle of the plate during that time. But on May 17, 2011, umpire Alfonso Marquez called a ball, in accordance with rule 6.08(b), when Astros batter Matt Downs stuck out his elbow in the path of a pitch up and in from Braves reliever Cory Gearrin.
6.08 The batter becomes a runner and is entitled to first base without liability to be put out (provided he advances to and touches first base) when—
(b) He is touched by a pitched ball which he is not attempting to hit unless (1) The ball is in the strike zone when it touches the batter, or (2) The batter makes no attempt to avoid being touched by the ball;
If the ball is in the strike zone when it touches the batter, it shall be called a strike, whether or not the batter tries to avoid the ball. If the ball is outside the strike zone when it touches the batter, it shall be called a ball if he makes no attempt to avoid being touched.
APPROVED RULING: When the batter is touched by a pitched ball which does not entitle him to first base, the ball is dead and no runner may advance.
Somewhat more common is a borderline strike that hits the batter, particularly a left-handed one. For example, on May 20, 2011, a curveball from Dave Bush hit Jimmy Rollins on the foot. Rollins squared to bunt, and the ball bounced in the dirt just in front of his left foot, ricocheted up, and appeared to hit his foot. Rollins’ foot was out of the batter’s box but not over the plate, though the PITCHf/x system indicated that the pitch nicked the corner of the plate.
Another example is the cutter from Mariano Rivera that hit Dan Johnson on the forearm on September 20, 2010. The PITCH/x system indicated that this pitch was located at height of 4.1 feet and nine inches from the center of the plate. This pitch was not a strike, but it was one of the three closest pitches to the plate to hit a batter in the last two seasons.
We have seen how location and pitch type affect the chances that a pitch will hit the batter. Does pitch speed matter?
If we separate fastballs into above-average and below-average speed groups, pitchers are more willing to come inside with faster fastballs. Pitchers threw 2.7% of fastballs faster than 91 mph inside in the high-HBP-rate boxes we defined earlier, as compared to 2.6% of fastballs slower than 91 mph. Since slower inside fastballs are more likely to be hit hard, it is not surprising that faster fastballs are thrown inside a little more often.
However, given that a fastball is located inside, batters are slightly less likely to be hit by a faster fastball. 5.9% of faster-than-average inside fastballs hit the batter, whereas 6.2% of slower-than-average inside fastballs hit the batter. Perhaps the batters are more attuned to the possibility of being hit by a blazing 95-mph pitch and more ready or more motivated to jump out of the way, whereas when an 81-mph offering from Jamie Moyer heads their way, they are slightly more willing to take one for the team. In any case, the two competing effects almost balance out such that fastball speed makes very little difference in HBP rate.
Fastballs of above-average speed hit batters 0.24% of the time, and fastballs of below-average speed hit batters 0.25% of the time. Similarly, HBP rates for sliders and curveballs are nearly the same for above-average and below-average speeds.
Which pitchers throw inside the most and the least often in the areas where batters are likely to be hit?
Whose inside pitches hit batters the most often (minimum 200 inside pitches)?
Rivera throws inside the most of any pitcher, but with his pinpoint control, he hits batters at only an average rate. Marmol has a nasty fastball-slider combo and questionable control, and batters should beware when standing in the box against him. Otherwise, I do not notice a particular pattern with the groups of pitchers at each end of this spectrum.
Which batters see the most inside pitches (minimum 6000 pitches)?
The percentage of inside pitches seen by a batter has a relationship to his HBP rate, but it is weaker for batters than for pitchers. Batters control how close they stand to the plate, and that choice has a strong effect on how often they are hit by pitches.
Which batters are hit the most often by the inside pitches they see (minimum 200 inside pitches)?
Chipper Jones stands much farther from the plate than Quentin, but Jones is a switch-hitter, which also reduces his chances of being hit—he is always an opposite-handed batter. Let’s compare two players of the same handedness and on the same team but with very different HBP rates.
Chase Utley does not even meet the minimum for the list above, with only 126 inside pitches, yet somehow 79 pitches hit him. Raul Ibanez, on the other hand, saw 2.2 percent of inside pitches and was hit by only 3.8 percent of those.
If you compare Utley’s stance to that of Ibanez, you can see that Utley stands closer to the plate and dips his front shoulder in toward the plate. (Worthy of note, though a subject for a different time, is how the umpire positions himself differently for the two batters.)
Here is what happens because Utley stands so near the plate. (Note that the perspective in the following charts is flipped to the catcher’s viewpoint).
This chart also shows the boxes we defined earlier for inside pitches. Utley stands so close to the plate that he is hit by pitches even closer to the plate than those in our defined boxes.
Here is the same chart for Ibanez.
So, we see that in addition to pitch type and the handedness of the pitcher and batter, the stance of the batter contributes to how often he is hit by pitches.
Because of the geometry of pitch trajectories, pitchers hit same-handed batters at about twice the rate that they hit opposite-handed batters. Four-seam fastballs and sinking fastballs tend to hit same-handed batters in the torso, while breaking balls tend to hit opposite-handed batters in the legs. Pitch speed, on the other hand, whether for fastballs or breaking balls, did not seem to have much effect on the rate of hit batters.
It is unclear to what extent the conclusions from modern HBP data apply to all of baseball history. However, it would appear that changes in pitch type usage and lefty-righty matchups across history, as well as changes in batter stances and the tendency of pitchers to throw inside, could have contributed to the long-term changes in HBP rates that Dan Fox observed.