When a pitch begins its flight towards home plate, the radar gun registers a specific velocity-one that correlates quite strongly to the start speed component of PITCHf/x-which unfortunately becomes the gospel as to how hard the pitch was thrown. Various factors, like the natural loss of velocity as the pitch reaches home plate, the true distance of the release, the actual flight time, the location, when the batter picks the ball up, and what pitch the batter initially anticipated all work together to alter a hitter’s perception of velocity.

While the differences between starting and ending velocity shifts nothing more than the equilibrium, these other factors either add or subtract perceived velocity, modifying a batter’s reaction time as he decides whether or not to swing, and then tries to get good wood on the ball. We have discussed the impact of location and how distance and flight time work, discovering that the PadresChris Young releases the ball closer to home than most, adding about 3.2 miles per hour of perception to his fastball. Incorporating the idea of location-based velocity deltas as we recently did, if this theoretical Young pitch were to be thrown up and in, the hitter would need to swing sooner and reduce his reaction time to make solid contact, adding another four miles per hour based on the distance out in front the bat would need to connect with the ball to achieve perfect contact. Young threw it at 85 mph and, without even delving into deception quite yet, the hitter saw a 92.2 mph pitch.

Everything comes back to time, and how the actions of a pitcher as well as the corresponding reactions of the hitter, relative to increasing or decreasing the time to pick up a pitch, decide how to react, and then react, work in tandem to make pitches appear faster or slower. Unlike Young, Ian Snell was found to be releasing the ball further from home and therefore overstating his radar gun velocity, while sequencing in a poor fashion that rarely added perceived miles per hour. As the breakdown of his battle with Carlos Guillen showed, Snell routinely registered 91-92 mph on the gun and in PITCHf/x, but his seeming refusal to come inside as well as his innate disadvantage of throwing further from home resulted in a perceived fastball velocity of closer to what Young initially registered. So, that’s two pitchers-Snell and Young-with a vast discrepancy in the radar gun reports, and yet they are opposites in perceived fastball velocity.

The interesting aspect of both of the areas in perceived velocity we have discussed so far is that one could be changed quite easily at the major league level, while the other would run the risk of screwing up a pitcher’s mechanics if you attempted to alter them. For instance, teaching a pitcher to go fastball-up-and-in/changeup-down-and-away, as opposed to the other way around, should not take much effort save for convincing the pitcher as to the correctness of the new sequence; on the other hand, teaching him to stride longer and release his pitch closer to home after utilizing an older set of mechanics for years is a much trickier proposition. In spite of this, however, the sequencing and location-based deltas are extremely important, as they can potentially lead into what is known as the crossover effect, resulting in at-risk pitches being thrown.

This ‘crossover effect’ is summed up by the inverse of that fastball/changeup sequence. Moving a pitch closer in on the hands and raising the eye level of the hitter increases the perceived velocity of the changeup, while the opposite is true of that down-and-away fastball. If the pitcher’s changeup registers at 84 mph while his fastball is at 92 mph, both pitches appeared to be the exact same velocity to the hitter if sequenced in that fashion. In other words, the crossover effect can help explain how a pitcher will execute his game plan flawlessly-raising the batter’s eye level, moving in and out and throwing different pitches-yet fail miserably. His idea of mixing speeds itself was flawed, since the goal needs to be mixing up the batter’s perceptions of what’s being thrown, where, and how fast. Because of the location deltas, a pitcher can throw two fastballs in a row, but in different locations, and still mix speeds. The crossover effect, from a more mathematical standpoint, refers to when a pitch falls within four perceived miles per hour of its predecessor.

This is another reason why it makes little sense when announcers declare that a pitcher needs to throw something off-speed in a certain situation before professing their disgust at the pitcher’s refusal to execute-an outside fastball is an off-speed pitch. In fact, if the pitcher executes a sequence of a breaking ball up and in followed by a fastball down and away, he should have satisfied this expectation from most color commentators, in spite of the fact that he really did not throw anything off-speed in a traditional sense. Both pitches were of the same perceived velocity, and that down-and-away fastball is considered to be an at-risk pitch based on its similarity to the preceding offering. Because hitters tend to struggle with identifying the characteristics of the pitch they just saw, throwing at essentially the same velocity affords them the opportunity to hit multiple pitches with one swing, as opposed to swinging for a fastball and completely whiffing at a breaking ball or changeup. As evidence, throughout his research and using the Inside Edge scouting database, Perry Husband was able to find that batter performance declined dramatically on pitches deemed to be ‘not at risk,’ as compared to their counterparts with closer perceived velocities.

Consider the performance. During the 2004-05 seasons, at-risk pitches generated whiffs 19 percent of the time, against the 23 percent of pitches not at risk. In that same stretch of time, home runs were hit three percent of the time on at-risk offerings, compared to 2.4 percent for those that weren’t. The percentage of well-hit balls dropped from 25.9 percent to 19 percent, an extremely telling statistic. Since the well-hit average does not differentiate between hits and outs, instead reporting just how hard the ball was hit period, it is hard to chalk up that discrepancy as marginal or meaningless. In short, when pitches cross over one another and become at-risk pitches, they are much more likely to get hit, and get hit hard. Further studies found that around 80 percent of all hard hits were the result of at-risk pitches.

This finding makes intuitive sense, as major league hitters got to this far in life for a reason, and throwing similar pitches in succession-though not a guarantee for producing a sequencing kill screen-carry a much greater chance at getting hit with perfect contact, with the barrel of the bat squarely on the ball, and the lead arm extended.

Originally, I had intended to spend a few days self-joining PITCHf/x data from 2008-09-well over a million rows-in order to find the guys with high rates of at-risk pitches and correlating those rates with value-based metrics, but it dawned on me that velocity is not the only aspect affected by this crossover effect. Throwing the same pitch in the same spot or crossing over is not always bad, especially if the hitter has shown a clear inability to time the pitch. Consider a scenario wherein Cliff Lee throws an inside fastball to a right-handed hitter, who fouls the ball off after being incredibly late. Were Lee to throw the same pitch on four straight deliveries, the fastball would be at risk, but throwing it one more time might not be as costly given how late and fooled the hitter appeared to be by it. If Lee throws a two-seamer or a cutter in the same spot, the movement differential also needs to be factored in somehow. Perhaps that second pitch is fouled off again, but shows Lee that the hitter has a better sense of how to time it. He would have thrown essentially the same pitch on two consecutive deliveries, a seeming violation of the crossover effect, but this wouldn’t truly be a violation given that the process of his decision was based on gauging the hitter’s attention and what he could conceivably handle. At that point, after two of the same, Lee likely needs to throw something else, either the same pitch in a different location or a different pitch in a similar location.

The underlying point is that each pitch can be thrown at a multitude of speeds, and that changing speeds does not always mean changing the actual pitch. Throwing another inside fastball after these two would be at risk based on what Lee observed from the hitter, but you can see how this is not as linear as finding the percentages of sequences in which the second pitch fell within a fixed range (in mph) of its predecessor, especially without the important aspect of movement factored into the equation, and without the inclusion of what the hitter was expecting to see-which we will get into in a bit-as it can certainly be quantified, based on the results of some interesting studies. This is before even discussing how a difference exists between at-risk pitches and at-risk pitches in the zone. Throwing within four miles per hour of the prior pitch is not going to be as costly when the second pitch falls within a particular area in or around the strike zone at which the hitter is unlikely to offer.

How can we use this to our benefit? Perhaps we can start to answer that by asking how an understanding of at-risk pitches and the crossover effect can help a team make decisions. This unfortunately hinges upon how you define success. For instance, if Cliff Lee throws 100 pitches in a game, 95 of which were sequenced perfectly in terms of the hitter’s attention and what he could handle, mixing perceived velocities and not actual velocities, and he gets lucky on two of the remaining five pitches, but gets hit around on those three remaining “mistake” pitches, surrendering two two-run homers, his overall pitching line is not going to be very aesthetically pleasing. Nevertheless, he threw 95 percent of his pitches practically perfectly, and a pitching coach may swear that he had a fantastic game on this very basis, since the process of his pitcher’s pitch sequencing was top-notch.

Whenever discussing these kinds of processes, I automatically revert to what Paul DePodesta said about blackjack-if you have an 18 and hit, even if you magically get to 20 or 21, it was a terrible process. A poor decision that yielded positive results is still a poor decision. This translates seamlessly to the idea of at-risk pitches and sequencing, because a pitcher who fails to maximize his perceived velocity spread but succeeds is not someone acting with a solid process in place. Ian Snell may register 91-92 mph on the gun, but because he stays on the outside part of the plate so frequently and releases the ball further from home, his perceived fastball velocity will be on average much slower than reported. The pitchers utilizing their pitches in what is considered to be the right way will have a perceived velocity that barely strays from the reported velocity on average, because unless they threw an alarmingly high amount of pitches down the middle, they mixed locations effectively, and didn’t skew anything to one particular side of the zone.

This piece was intended to introduce the concepts of at-risk pitches and the crossover effect, and how they tie into the areas of perceived velocity we have explored in this space already. Moving forward, we are going to discuss the hitter’s attention zone-the small span of a few miles per hour that a hitter is led to be able to handle by the pitcher-and break down specific sequences and identify pitchers who would benefit from slight alterations. We also still have the ideas of deception, how the hitter sees the ball, and how hiding the ball through release can increase or decrease perceived velocity, based on how soon the hitter can determine what the pitch is, its intended location, and how he will react. Before exploring those remaining areas, however, it is very important to remember a few basics-that fastballs can be off-speed pitches, breaking balls can be thrown at a perceived speed similar to that of fastballs, and that bad sequencing by making a slider seem faster and a fastball seem slower can increase the likelihood that a hitter will make solid contact.

Thank you for reading

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This article, and several other recent articles, revolve around various aspects of physics in baseball. There is an excellent site with baseball physics here:

Lots of good stuff
Alan Nathan is a friend of mine and he has been extremely helpful with regards to my research on perceived velocity thus far. So yes, double recommendation to go to his site.
This article seems to be claiming that it's always a good idea to change speeds (so long as the batter isn't way off the previous one).

That seems quite counter-intuitive to me though: wouldn't pitchers have to mix over multiple pitch strategies in each situation, in order to keep the batter unsure of the coming pitch?

Perhaps the ideal mixed strategy would tend to change up the perceived speeds more often than not, but you've gotta mix in other pitches too, no?
It's not always about changing speeds on every pitch because movement is key as well. This is more of just an introduction to the ideas of crossing over and throwing at risk pitches. You want to throw all of your pitches effectively, but you want to sequence them in fashions that don't carry risk. Going fastball-changeup isn't always going to produce a velocity spread, which is really the major point.
Love the topic and always look forward to your articles, Eric. I used to pitch and find it interesting now to think about the science behind what I learned intuitively over the years.

On this topic specifically, I think this is exactly why hanging sliders are so dangerous. The sequence of low outside fastball-hanging slider would have similar perceived velocity, and of course movement on the hanging slider would be minimal. That puts the pitch squarely in the at risk category.

I think this also relates to the concept of "speeding up the bat" of a hitter, which you'll occasionally hear ex-player broadcasters refer to (I'm sure I've heard McCarver say this, which is telling given he was a catcher). That language never made sense to me, but the basic point was you don't really want to throw an offspeed pitch inside. I think this is the intuitive, player's way of describing what you're referencing in this article. "Speeding up the bat" doesn't literally mean anything, it just means the offspeed pitch loses a chunk of its perceived velocity differential when thrown inside, making it easier to hit.
Exactly. We're so caught up with the radar readings so we are trained to think that a 92 mph fastball followed by an 82 mph changeup is devastating due to the differential. But if they were sequenced in a fashion that essentially borrows from Peter to pay Paul, the pitches are of similar velocity. Much of it is intuition, but the idea that a pitcher can raise eye levels, "mix" speeds, go in and out, but throw 2 pitches with the exact same perceived velocity in a row is incredibly interesting.
I wonder if you have thoughts on something else that popped into my head a couple times as I was reading your previous articles. You discussed the effect of location on perceived velocity within the framework of the swing arc (i.e. you have more time to square up an outside pitch than an inside pitch). But I was wondering this, also. Does the location also make it more or less difficult to judge velocity and movement and react accordingly? I'm talking about perspective/angle on an object in motion. If it is coming directly at you it is much harder to judge its motion than if you have an angle on it. So an inside fastball is more difficult to judge, while an outside fastball is easier. Just to be completely clear, with the outside fastball you actually see it moving across your field of vision and getting larger within your field of vision. With a fastball straight between your eyes you can only determine velocity by judging the pace at which the ball is getting larger. The extra visual information on the outside fastball should make it easier to identify and hit. I don't think this add/subtracts perceived velocity, as you could misjudge the velocity in either direction, but it seems like it would disrupt timing in a disproportionate way, i.e. more for an inside pitch than an outside pitch.

Of course that is just fastballs where there is no/minimal break. With a breaking ball, it might be easier to judge the speed if it is thrown low and outside for the same reason as above, but the break may be more difficult to judge if thrown there because it would be occurring in the same plane as the hitter's eyes. This would give you the same poor read on the break as you have on the velocity of a fastball aimed right between your eyes. If the breaking ball is thrown inside, the velocity might be more difficult to judge, but you will have a better perspective on the break, so maybe net net it is easier to hit.

This all makes me think about why a good changeup is so effective. If you are a 2 pitch pitcher (fastball, breaking ball) and you throw a breaking ball away, the hitter can identify the speed, know it is a breaking ball, and decide when and where to swing (or not). If you also have a changeup, identifying the speed of an outside pitch no longer tells you everything you need to know about when and where to swing. You now have to read the break (or guess), which is difficult to do given your poor perspective on the break of a low outside pitch. An inside changeup would also be troublesome, but for a different reason. As mentioned above you have poor perspective on velocity on inside pitches, and while you have a good perspective on break, the break of a changeup looks similar to that of a fastball. So you really could have a difficult time identifying a good changeup no matter where it is located.

I'll stop rambling. Just curious whether you have any thoughts on this aspect of pitch location.
I don't doubt your line of thinking. This isn't an area in which I'm an expert at all, but I'm going to be speaking to some optometrists and specialists in this area to find out their thoughts. I think, too, expectations loom large. Facing Verlander you expect to see a faster pitch than when facing Moyer and so on.
The biggest influence, I think, is how the batter looks at the pitch. When doing some research on the "hopping" fastball, the was some interesting stuff there. About the time a batter is making the swing decision, they eyes go from seeing the ball a long distance away to focusing on it closer (imaging driven standing on next to the highway. When a car is far away, you see things one way. There is a point where the car seems to go faster, gets bigger, etc.) Some batters will move to their eyes to the where they believe they ball will be. Others will follow the ball until they can't keep up any more and never see the ball at the impact area.

The last one is going to be able to collect a bit more information on the pitch, the first one is going to be wrong at times (and tend to see 'hopping' fastballs).

I think that type of information is going to effect this research. There might be two very distinct groups. Might have to determine if a batter is a Type 1 or Type 2 when dealing with the pitchers, and adjust accordingly.