The velocity recorded by the radar gun and what the batter perceives do not always match. As discussed previously, several factors can cause a pitch to appear faster or slower to hitters. One such factor is the flight time from the point of release to when the ball crosses home plate relative to the flight time the PITCHf/x system projects at 55 feet away. Pitches released any closer than this predetermined distance result in a higher perceived velocity with the inverse true of pitches let go from distances greater than the default. During our initial look it was observed that a few pitchers generated perceived velocities dissimilar to their recorded velocity, a proof of concept that was much more important than the velocity discrepancies themselves. Johnny Cueto, for example, averaged 92.9 mph with a perceived 90.8 mph, while Ian Snell found himself perceived to throw just 87.6 mph in spite of the reported 91.7 mph. But where Snell threw these pitches must also enter the equation, since the location of a pitch works in conjunction to the flight time to add or subtract perceived miles per hour.

Intuitively, the idea of lateral location affecting perception is not entirely new, as scouts and commentators have often remarked that an inside pitch will seem faster than one on the outside, that higher pitches will appear to have more giddyup than those on the lower half, and that the spread of these two pitches can create a relative velocity that helps pitchers maximize effectiveness. Determining the appropriate quantification techniques is what has eluded analysts, leaving unanswered the question of how to measure this qualitative information. It is valuable to learn that pitchers can add or subtract velocity based on location, and that the velocity differential between a fastball and a changeup might be much greater or lesser than it appears to be if the pitches are sequenced in a fashion that subtracts from the fastball and adds to the changeup.

The idea of location-based perception comes from a man named Perry Husband, who has a series of books on what he calls “effective velocity,” a concept similar to what we are discussing here but different enough that a marriage of our methods will help produce truly optimal results. Husband’s studies on hitting led him to quantify the various perceived velocities based on different spots in the zone, and a summary of his work in this area is in order before moving onto the nitty-gritty. In its simplest form, his calculations are based on the idea that for every location only one point exists at which a batter can achieve perfect contact, meaning the lead arm is fully extended and the sweet spot on the barrel of the bat meets the ball.

As the locations change throughout the strike zone, hitters either need to speed up or slow down their mechanics in order to achieve this type of contact. As pitches get closer to the hands, the perceived velocity increases because the hitters need to adjust the swinging mechanism in order to connect the ball with the sweet spot. On the flip side, pitches located further from the hands afford more reaction time, decreasing the perception of velocity to the hitter. Combine these increases and decreases with what was experienced when measuring the flight time perceived velocity and the net is a more advanced representation of the velocity hitters are actually experiencing. Via Nick Piecoro, a writer for The Arizona Republic, catcher Miguel Montero relayed to me his thoughts on the matter:

It’s harder to react to it, to be quick enough to turn on it. If it was a fastball outside, you can just throw your hands at it. But when it’s a fastball inside, it’s too tough to just throw your hands at it. That’s why a fastball inside is one of the hardest pitches to hit if you can locate it.

These reactionary changes-or as Montero put it, whether or not a hitter has time to throw his hands at a pitch as a means of reacting-suggest that the hitter experiences a shift in his abilities to see the pitch, to decide whether or not to swing, and to execute a swing capable of making the optimal form of contact. A pitch thrown directly down the middle will have a location-based perceived velocity equivalent to that which was measured from the flight time, so if Chris Young threw a pitch down the middle and belt-high with a perceived velocity of 88.7 mph, the location would not affect the perception in any form. Move that pitch six inches in on the hitter from the original spot, and according to Husband’s studies the hitter needs to hit the pitch 18 inches further out in front by comparison. The diagram below can offer an even better explanation of how the changes in locations-or lanes in the strike zone-affect the timing of a hitter’s swing relative to where perfect contact can be made:

Eye in the Sky

The pitch in lane three is belt-high and right down the middle, and its position corresponds to where the batter needs to meet the ball in order to perfectly sync up his timing, getting the barrel ready to wreak havoc. The pitch in lane two is middle in and belt-high, six inches closer to the hitter horizontally like we just discussed. In this case, the batter cannot simply move his swing over six inches horizontally because of the curving nature of the swing itself. To adjust for the curving nature of the swing he has to hit the ball 18 inches further out in front, which will add anywhere from 2-2.5 mph in perceived velocity, depending on the initial velocity. For this very reason the deltas for breaking pitches will tend to result in less dramatic changes, as a 75 mph curveball will gain or lose closer to two miles per hour of velocity.

The quantification of location based perceived velocity gets a little hairy since nobody, not even Greg Maddux himself, can hit spots 100 percent of the time, and because the original perceived velocity affects the amount of additional miles per hour to tack on or off. However, the idea that certain zones can add or subtract perceived miles per hour remains valid even if this lack of extreme precision precludes us from adding a category to the leaderboards. It also does not invalidate the idea in any way if we simply think of the location deltas in perceived velocity as ranges, so if middle-in equates to +2 mph for a perceived 90 mph pitch, we can say that it appeared 2 to 2.5 mph faster.

Before delving into an actual plate appearance to combine these two aspects of perception, let it be known that a slight change was made to the original location deltas, based on my skepticism that every major league hitter is capable of achieving perfect contact on every pitch. While it makes sense that many would act with this as a goal, I am hard-pressed to find any photos in which a hitter has fully extended his arms, making perfect contact with the ball on an up-and-in pitch. Hitters like this surely exist-they’re called ‘Albert Pujols‘-but that sort of skill is unlikely to be observed across the majority of major leaguers. Whereas the original deltas suggested that an up and in pitch could add five miles per hour the more likely scenario involves an addition of 3.5 to 4 mph of perceived velocity given the probability that a hitter will cheat and compromise his mechanics, resulting in sub-optimal contact, but some form of contact nevertheless. In cheating this way, the hitters still perceive the pitches to be faster, but not nearly as fast as if they were to contact the ball perfectly since the reaction times are not tinkered with as much.

When determining the perceived velocity based on both of these factors, we have to compare the new figure to what was calculated based on flight time, which is what I was referring to earlier by marrying these methods. With the aforementioned Chris Young pitch that had an 85.7 mph actual velocity and an 88.7 mph perceived velocity, the location delta would be measured relative to the 88.7 mph. With that in mind, below are diagrams comparing Husband’s deltas to my discounted versions for fastballs or pitches greater than 85 mph, with the locations coming from the point of view of the catcher with a right-handed hitter at the plate.

In the following chart, the dark blue indicates the actual strike zone, while the lighter blue area constitutes what Husband termed a ‘pressure zone.’ The blank boxes constitute areas wherein pitches would either knock a batter to the ground or hit the ground to the point that even Vladimir Guerrero would lay off. I find it incredibly important to once again stress that the box on the left is Husband’s work based on where the hitter has to connect with the ball to achieve that perfect form of contact; the second box on the right is mine, and it discounts the magnitude of the reaction time and distance in an attempt to more accurately model how hitters act in reality.


Based on the data presented above-which may lend itself to some fine-tuning-Ian Snell could inch closer to that 91.7 mph mark by throwing the fastball inside. If he threw a pitch 92 mph with a perceived 88 mph, but it was located up and in on a righty (the circled area above), the pitch would appear to be 91-92 mph. However, as he starts throwing the pitch on the outer portion of the plate, his already slower perceived velocity loses even more miles per hour since the hitter has more time to react and produce optimal contact. What these figures also suggest is that every pitch can have several different perceived velocities, and that certain pitches may crossover each other. If Snell throws a perceived 88 mph fastball down and away to a righty and follows with a perceived 80 mph changeup up and in at that circled area, each pitch is going to appear 84 mph to the hitter. Sure, eye levels may have been changed and he would have gone inside to outside, but the reaction time afforded to the hitter makes the pitches appear to be velocity twins.

This may have been a concrete reason for Snell’s struggles in Pittsburgh, as several fans have noted his seeming refusal to throw inside. If that were truly the case and Snell’s relatively dramatic dropoff in perceived velocity rung true over a larger sample of pitches, then hitters were in the box observing fastballs in the 85-86 mph range and not the 90-93 that he registered on the gun, given his location and actual release point. Let’s walk through a plate appearance of Snell’s, and compare the perceived velocities based on both actual flight time and the location.

Each of the charts below showcase different pitches in a plate appearance between Ian Snell and Carlos Guillen. Guillen’s batting lefty, meaning that the diagrams above need to be reversed to factor in the location deltas-with the perceived velocity based on flight time (PV) and the perceived velocity based on flight time and location (LV) encapsulated to the right of the zone. Note that this was an 11-pitch sequence featuring nine fastballs (six four-seamers and three two-seamers), and that both of the off-speed pitches he threw ended up in the dirt, meaning their overall perceived velocities would best be estimated by the lower portion of the pressure zone, even though Guillen was unlikely to swing at all.

Snell 1-0

Remember that with Guillen batting as a lefty and with these charts putting us in the perspective of the catcher, Guillen would be standing where the velocity box appears. Snell started him off with a changeup in the dirt. The perceived velocity based on the flight time registered 80.6 mph though the location subtracted another couple miles per hour. Had this been a fastball in the dirt, we could subtract another mile per hour or two, but the off-speed pitches result in less dramatic deltas due to the slower initial velocity.

Snell 1-1

Snell then followed with a four-seam fastball up and away in the zone. Though the pitch strayed from the belt-high and middle-in area that would result in no delta whatsoever, the raising of Guillen’s eye level washed away the drop in perceived velocity expected from pitches on the outer part of the zone. Guillen fouled the pitch off to even up the count.

Snell 2-1

With a 1-1 count, Snell went back to the off-speed well, and served up a dirt-grabbing slider. Just like the initial changeup, Guillen was unlikely to swing at this pitch, so the LV of 77.1 becomes somewhat arbitrary. Through three pitches, Snell has thrown two off-speed pitches in the dirt and a four-seam fastball that held true to the flight time estimated velocity.

Snell 3-1

Snell then missed badly with a four-seam fastball, the type of location Bob Uecker would proclaim was “juuuuuust a bit outside.” Just like the off-speed pitches in the dirt, this offering strayed so far from the zone that tracking the perceived velocity does not matter much, given that Guillen was very unlikely to swing. This raises an interesting point that we will likely explore in some more depth moving forward, in that these perceived velocity numbers can explain a lot when discussing pitch sequencing, but pitches this far out of the zone may work to allow hitters to train out the velocity of the pitch they just saw, which could theoretically reduce the ramifications of velocity spreads and differentials between pitches. For those keeping score at home, Ian Snell has thrown three of the first four pitches way out of the zone, with the only solid pitch producing identical perceived velocities between flight time and location.

Snell 3-2

Needing a strike, Snell located a four-seamer down the middle and down in the zone, catching the majority of the location that subtracts two miles per hour. Guillen fouled the pitch off to bring the count full, which would set off a rather odd series of four pitches in which Snell stayed outside, continuously losing perceived miles per hour and affording more reaction time to make perfect contact:

Snell 3-2 F1

Locating down and away subtracts approximately four miles per hour, even though one could make a valid argument that this particular location, towards the very top edge of that box, should result in a lesser negative delta.

Snell 3-2 F2

This one was out of the zone, past the outside corner, the type of pitch that Montero likely had in mind when explaining that hitters have more time to throw their hands at the ball; again, Guillen fouled it off. It’s interesting to note that Snell added three miles per hour of perception between these two pitches despite staying on the outside corner or out of the zone, since he raised Guillen’s eye level.

Snell F3

This two-seamer missed down and away, and if you haven’t noticed the pattern yet, let me blatantly point it out. Aside from the very first fastball that Snell threw, every pitch in this plate appearance, each of which appeared slower on flight time compared to the start speed reported by the system, lost even more velocity based on the location. This would seem to be the perfect time to come in on Guillen, given that he has now grown accustomed to seeing a slower speed. Even an off-speed pitch on the inside part of the plate is going to gain velocity and appear much faster than the prior pitches. On top of that, even though these three fastballs have ranged in perceived velocity from 81-87 mph, the horizontal location did not change much, altering only the eye level.

Snell F4

Snell once again went for the outside corner, this time missing the down-and-away portion of the zone. While this location might be solid in an isolated setting, Guillen had plenty of time to spoil it off. He has to come inside now, right? Right?!?

Snell F5

OK, so this was not inside per se, but this marks the only example in this plate appearance in which Snell actually gained perceived velocity based on the location. Had he located it approximately six inches closer to Guillen at the same height, the pitch would have appeared close to 92 mph, slightly exceeding the start speed reported by PITCHf/x as if the ball was released 55 feet away. After drastically raising Guillen’s eye level and jumping from a 79.6 PV to a 90.0 PV, one could reason that going back to the outside corner makes sense as a means of really messing with his perception.

Snell Boom

Instead, Snell threw a two-seamer very close to belt-high and down the middle, catching just enough of the bottom part of the zone to lose velocity. Essentially, he threw a fastball as close to the middle of the plate as possible wherein he could still lose perceived velocity to the hitter. Guillen jumped on it, finally ending the epic battle by launching a solo home run. This would be the lone run surrendered by Snell on the day, and it might have been prevented had he implemented the perceived velocity and location delta idea. That isn’t to say that every pitcher needs to utilize this strategy to succeed, but this plate appearance suggested that those calling the pitches did not fully take advantage of setting Guillen’s attention at a specific point-the four consecutive outside pitches with more substantial perceived velocity drops-and then messing with his perception by following the sequence with a pitch boasting a sharp spike in perceived velocity on the inside part of the plate.

When comparing the velocity spread of a pitcher we cannot simply assume that if he goes fastball/fastball/changeup that the final pitch looked a set number of miles per hour slower to the hitter, because location plays a starring role in the perception of velocity and what the hitter sees. Snell’s radar-gun readings averaged 91 mph for the four-seam fastball, and 84 mph for his changeups, but if he utilizes the three-pitch sequence mentioned above, it is unlikely that the perceived velocities were 91/91/84, offering a spread of seven mph. For all we know, the perceived velocities of the sequence could have been 87/84/84 given that Snell will lose velocity by releasing the ball further than 55 feet and that his locations caused more of a crossover effect, decreasing the velocity of the fastball while enhancing that of the changeup.

Moving forward we will get into some pitch sequencing, calling on the location deltas as a means of finding which pitchers crossed over most often and what happened on those pitches as well as which pitchers, consciously or not, subscribed to the perceived velocity theory and were able to maximize their velocity spreads by using certain sequences. Additionally, I plan on exploring some sequences themselves, finding for instance the perceived velocity spreads on different fastball-changeup location and velocity combinations and comparing the differentials to actual run value results. We won’t be able to use the flight time information over the larger sample but the delta numbers are of more interest here than the actual observed velocities. Hitters are not seeing what the radar gun says they are in most cases, which is an important concept to grasp because teams should be striving for the pitchers who appear to throw 95 mph even if it only registers 92 mph instead of the reverse.

Thank you for reading

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Interesting article. One of the things that I think I noticed (though without any data, it's hard to know for sure) is that part of Barry Zito's return to average seems to be from an increased willingness to throw up and in to right handed batters. Molina *never* seemed to call this during Zito's first couple of seasons, but Pablo Sandoval did, and so did Eli Whiteside, and maybe eventually, Molina caught on. Prior to that, it just seemed like everything he threw to right handers was either on the outside corner, and it not only looked slower to batters, but they appeared to be handing over the plate waiting for it. Or it missed outside for a walk. Given his velocity, or lack thereof, you wouldn't think Zito could get away with pitching up and in to right handed batters, but perhaps perceived velocity is the reason why.
Brilliant work, Eric!
Another great piece, Eric. This shows why "fastball up and in, off-speed down and away" is so often preached by pitching coaches. I'm sure many do so simply because it's been proven a more effective strategy than the reverse, but don't actually realize *why* this is the case. If, as they say, pitching is all about upsetting the hitter's timing, then increasing the separation in perceived velocities of your pitches by location can only advance that goal.

In addition, and though it may have been intuitively obvious to some, you've provided a great illustration of the value of learning to hit to the opposite field. Letting the ball "get deeper" buys you time, and effectively makes the pitch slower (though you may sacrifice on the bat speed you're able to generate given the shorter time/distance between the start of your swing and contact with the ball). This helps explain the higher contact rates (and lower HR rates) of hitters like Tony Gwynn and Derek Jeter.

I cannot say enough good things about this series. Well done.
I am seriously considering letting my BP subscription lapse this off-season, but articles like this might convince me to renew. Great work.
This is great stuff... One question I have is this: do you know (or can you look at video to see) where the catcher was set-up for each of these pitches? In other words, how much of the location was what Snell was trying to do and how much of it was just where the pitches ended up?

As you noted not even Maddux could hit every spot every time, but it seems that you might be able to control for wildness (so to speak) by estimating where the pitcher plans to throw the pitch (obviously you can't do this for a large number of sequences)...
You really can't. Catchers don't often set up initially where they expect the pitch to go. They tend to shift mid-pitch. That would be extremely difficult to pinpoint.
Good stuff. Just wanted to pick a nit about one of your sentences.

"...I am hard-pressed to find any photos in which a hitter has fully extended his arms, making perfect contact with the ball on an up-and-in pitch. Hitters like this surely exist—they're called 'Albert Pujols'—but that sort of skill is unlikely to be observed across the majority of major leaguers."

Actually, Pujols doesn't extend his arms when he crushes the ball. This was broken-down expertly in the following post at Viva El Birdos:

Keep it up, this is great work quantifying this type of information.
Mark McGwire is the guy I think of when it comes to full extension.
Quick, somebody point Brian Bannister at this article... If anybody'd be the first pitcher to try to use this data, I'd put my money on Banny.