Were you to take a web journey to a search engine and query the terms “fastball, changeup, sequence,” a slew of sites would surface, many of which include in their brief synopses that a sequence of this sort helps keep hitters off balance. Conventional wisdom dictates that these two pitches, when thrown one after the other, can fool a hitter based on their similar movement and vast velocity gap.

As we have discussed over the last few weeks, velocity is not always as advertised, since several factors dealing predominantly with the reaction time of the hitter can either speed up or slow down the perception of pitch speed. Pitchers that utilize a cambio are usually judged on the velocity discrepancy relative to their heater, but such judgments can prove inaccurate if and when the hitters perceive the velocities to be closer in value than the radar gun suggests. It then stands to reason that the ultimate goal in evaluating fastball/changeup sequences involves measuring the perceived velocity of the off-speed offering to the perceived velocity of el numero uno, given that perception matters most.

Both Josh Kalk-now an analyst with the Tampa Bay Rays-and Dave Allen, of Baseball Analysts and FanGraphs, have already done some great work in this area. Back in February, Kalk examined the run values of each two-pitch sequence, finding that a changeup on the heels of a heater benefited hitters to the tune of 0.02 runs per 100 pitches. Hitters were not necessarily world-beaters off of this sequence, but they clearly held an advantage over those making the deliveries. One reason might be that pitchers, as a whole, were not optimizing their perceived velocity discrepancy between the two pitches. Another could be that those with higher success rates simply were not using the specific sequence as frequently as those without. In a separate study, he also found a positive correlation between the success of a changeup and the difference between the seasonal velocities for both pitches; the greater the difference, the more likely success would be observed.

Allen tackled the issue in a slightly different manner, evaluating the success of a changeup based on the speed separation from the previous fastball in each plate appearance. The results surprisingly suggested that there was little difference between success rates when the changeup ranged from 5-12 percent slower than the preceding fastball. The results were non-linear, with slight alterations within that range but rapid drop-offs on each side. They also conflicted with Kalk’s findings, as one study suggested that changeups five miles per hour slower than a pitcher’s average fastball were less successful than those 10 mph slower, while the other indicated little difference between 5-10 mph separations. One potential reason for this, mentioned in the comments of Allen’s thread, tied back to absolute velocity of pitches; a 95 mph pitch may work well with an 84 mph changeup, but the same 12 percent drop applied to an 89 mph heater would produce a 78 mph pitch that hitters might find easier to time and tame.

What happens if we apply these ideas to the world of perceived velocity? Might the picture become a bit clearer? After all, throwing a down-and-away fastball followed by an up-and-in changeup is going to increase the risk that the second, slower pitch gets hit hard, based on the crossover effect. Regardless of the gap between the velocities pitchers average according to radar gun readings, we would expect that pitchers with lower perceived deltas will afford hitters more opportunities to hit the ball hard. Harder-hit balls will translate into more bad outcomes for pitchers. In other words, for now, forget about the absolute difference between a fastball and changeup, and instead focus on the percentage of how much slower a changeup is perceived to be in relation to the perception of the immediately preceding fastball in the same at-bat.

To eliminate any potential confusion, by fastballs in this study, I am referring to four-seam fastballs. Calculating the perceived velocity percentage difference of changeups that follow fastballs and scaling the run-value results per 100 pitches, the numbers start to benefit the pitchers around 11 percent, and begin their descent after the 17 percent interval. Allen’s results saw little difference at any point along the 5-12 percent range, whereas the perceived velocity marks observe a sharp spike around the 13-14 percent mark, with 15 percent also remaining effective. Prior to that 11 percent starting point, the data hinges along the average threshold, if not outright benefiting the hitters. Additionally, due to the non-linearity, no significant correlation surfaced. With an r-value of 0.13 between the run value and the percentage gap, something faintly suggestive exists, suggesting that higher percentage differences in perceived velocity yield more beneficial results for the pitcher, but there’s nothing on which to hang our hats.

These findings confirm the conventional wisdom discussed above, as hitters struggle more when they perceive the changeup to be much slower than they perceived the fastball to be, but when the discrepancy gets too large, the pitch apparently becomes easier to time. Also interesting are the sample sizes of the various percentage points, as they really do suggest that pitchers are efficient in the aggregate as far as sequencing this combination in a fashion that borrows from the changeup to add to the fastball. Relatively few sequences involve changeups with perceived velocities lesser than seven or eight percent slower than the fastball perception, or greater than 17 percent.

To surpass that 17 percent mark one would have to, for example, throw an up-and-in fastball in the pressure zone beyond the strike zone, adding five perceived miles per hour, and then throw a changeup down and away on the level of the hitter’s knees, subtracting four miles per hour-the velocity deltas are different for these pitches because changeups are slower pitches on average. If the fastball registered 90 while the changeup clocked in at 81 mph, we would then be witnessing a 77 mph perceived velocity of the pitch following a 95 mph perceived-velocity pitch, a discrepancy of around 23 percent. These events are not as abundant in frequency, given the absolute velocity requirements, the extreme differences in location, and how pitchers don’t miss that badly on two straight pitches very often.

This segues into the idea that I want to once again hammer home, in that every pitch can be thrown at a multitude of speeds given the amount of time the hitter has to react in order to achieve perfect contact. Bringing back the image below, we see that a pitch in on the hands has to be hit 18 inches out in front of a pitch belt-high, down the middle, in order to achieve this perfect contact. This means the reaction time of the hitter is sped up since the swinging mechanics must begin sooner, which in turn increases the perception of velocity.

The Swing's the Thing

I understand that the ideas revolving around perceived velocity may not be as clear, and that we still have not even introduced deception into the equation-another factor that adds or subtracts perceived miles per hour-but based on the location deltas it seems that pitchers should try and sequence their changeups, following fastballs, to be 13-15 percent slower than the perception of that heater. This type of sequence can be achieved in a multitude of manners. For instance, a 90 mph fastball thrown middle in becomes 92 mph in perception. The optimal changeup following that pitch would register 80 mph on our theoretical “perceived velocity” radar gun. If the pitcher already throws a changeup 80 mph according to the radar gun, then he would want to throw the pitch in one of the locations that adds or subtracts nothing from the registered velocity. In the strike zone, that corresponds to down and in.

If the same pitcher throws his 90 mph fastball down and in, keeping the perceived velocity in line with that which the gun reported, the optimal changeup velocity is 77 miles per hour. Since he averages 80 mph with the off-speed pitch, he would need to throw it down and away in the zone to achieve this gap. As you can see, there is more than one way to achieve the optimal speed separations that would not be evident were pitchers to stick solely to their radar gun velocities and treat every fastball and changeup as equal in perceived velocity to the hitter regardless of location. Following sequencing rules like this provides no warranty or guarantee for success, but the numbers suggest that the pitcher has a much higher probability of being pleased by the outcome.