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Jonathan Hale has been using PITCHf/x to answer baseball questions all over the 'net since 2008. He once missed a Duane Ward curveball by three feet. You can read his writing about the Blue Jays or tell him what he should be analyzing next at The Mockingbird.

The obsession with velocity starts early: from the time a player is drafted, there is an almost ridiculous concentration on how hard he throws. Raw speed, more than anything else, is what turns heads and makes prospects fly up the rankings, even though it is widely accepted that velocity alone is not enough to get major league hitters out, and that there are plenty of pitchers who are very successful in the majors with underwhelming fastballs.

Once a player makes it to the majors and people have some first-hand experience with his pitches, we start to hear about the virtues of their moving, darting, or “electric” fastball. And often, starters break into the league at a certain velocity and then after a few years settle into throwing a few miles per hour slower, at which point the suggestion is made that they “backed off” their heater a little in order to get more movement (or “put a wrinkle on it”), which actually makes the pitch harder to hit. I’ve always wondered whether it was true that pitchers willingly give up their maximum velocity either for the sake of control, increased movement, or self-preservation.

Is there a sweet spot for velocity? Is there a point at which throwing harder gives diminishing returns? PITCHf/x should be able to provide some answers (although command is the missing ingredient). For the sake of the following, I am defining “movement” (or “break”) as the maximum distance between a given pitch and a straight line between where it was released and the catcher’s glove. Think of it as the “bend” on a pitch (or “break length” for those familiar with PITCHf/x terminology), which is not dependent on the specific left/right/up/down movement on a pitch.

Relationship between movement and velocity
First, let’s take a very simple look at the relationship between velocity and movement, just to confirm what seems likely: on average, pitches thrown harder will be straighter (or “flatten out”). Here is a heat map showing all the four-seam fastballs in the league since 2009, with velocity on the horizontal axis and movement on the vertical axis:

The most commonly thrown four-seamer in the majors is around 91 mph with a four-inch break, and in addition to a general downward trend (more speed = less movement), the maximum break that pitchers achieve decreases rapidly at speeds above 95 mph. There is simply nobody who throws in the high 90s who has the kind of eight-inch bend on their fastball that is achievable around 90 mph.

Now let’s look at the ability to miss bats with either movement or velocity. From here on, I am considering both four-seamers and two-seamers as “fastballs,” as there is so much overlap between the two—one man’s natural movement on his heater is another’s second pitch, and there is enough variation from one pitch to the next that often two-seamers that just don’t have a lot of action on them are classified as slower four-seamers.

When gauging the nastiness of a particular pitch, I like to take misses per swing, with all foul balls ignored since there is no way to differentiate between 400-foot drives inches foul and barely-contacted pop-ups. So for the following two graphs (done using conditional density in R for every pitch since 2009), we’re looking at how often someone decided to swing at a pitch and came up completely empty. First, here’s how movement affects swings-and-misses:

We see high values at the left side of this graph because pitches with that little movement are also going to be the fastest—but remember that pitches with movement between 8-10 inches don’t touch any of the higher velocities, and still we see their swings and misses climbing back up. Between 4-8 inches, though, there’s no real difference in miss percentage, which implies that adding a couple of inches from average movement is just not enough to start missing bats.

Now the same thing, looking at velocity:

Again, the bump at the bottom is likely because those are the really slow two-seamers with big bend. It makes sense that these two graphs are mirror images since we know there is an inverse relationship between speed and movement. Still, I think it’s interesting that the graph is flat from about 82 to 90 mph, at which point there is a steady rise in misses up to the very fastest pitches. I would have expected a steeper curve, with the high-90s especially being through the roof.

However, there is clearly a problem in pretending that we can isolate just movement or velocity when they are intertwined. So now here is a 3-d graph, with velocity “into” the graph, movement from side to side, and the height of the columns representing misses per swing:

In a way this is stating the obvious: velocity is the consistent key for missing bats, except for those at the slowest end of the range (i.e. fastballs with the most two-seam action), where the slowest and bendiest also get the job done (like a mini-changeup). But what I find interesting that high 90s fastballs with lots of movement are actually less effective at generating swings and misses than straighter ones.,

So often you hear about a guy overthrowing so that his fastball “flattens out” and is easy to hit, but at the highest velocities, literally “flat” fastballs are actually the best kind (although they probably get called “explosive” or “rising” instead). The problem with most guys overthrowing is probably something even worse than lack of movement: a lack of control, leading to pitches coming down the middle of the strike zone, where it just doesn’t matter how fast they are.

I used to see a lot of Brandon League during his time with the Blue Jays, and it always seemed strange that he would throw in the high 90s with incredible sinking action but didn’t strike out a lot of hitters, although he did put up phenomenal ground-ball rates. Which leads us to…

How velocity plus movement keeps the ball on the ground
Obviously, sinking or two-seam action induces grounders. Here is a look at what factors contribute to that effect, with movement on the horizontal plane and ground ball (per all balls in play) percentage vertically:

So while slightly-above average movement doesn’t help pitchers miss bats, it certainly helps them induce grounders. The part of the graph just above four inches of movement (league average) shows the steepest slope of increased ground balls, as opposed to a much smaller difference between pitches that bend six inches and 10. Even if you’re not a pure sinkerballer, a little downward action on your fastball goes a long way.

Now for how velocity affects ground ball rate:

Interestingly, although it’s a much lesser effect, high velocity also induces ground balls, despite the fact that harder fastballs are thrown up in the zone more often and tend to have less movement. It makes sense, though, that faster fastballs would be harder to “square up,” one of the reasons—aside from their ability to record strikeouts—why fireballers are more effective.

How movement plus velocity keeps the ball in the park
Clearly, more grounders is going to mean fewer extra-base hits, but what about home runs specifically? I can’t count the number of times I’ve heard that extremely hard-throwing pitchers are actually easier to hit homers off of because you can just stick your bat out and “let them do all the work.” As the saying goes, the harder a ball comes in, the harder it goes out.

First, the effect of movement on home runs per ball in play:

No surprise there; I would fall off my chair if sinkers weren’t harder to hit out of the park. Although again, notice how there’s no real change for below-average break, but right above the average of four inches there is a steady decline in homers. Now for velocity:

While fireballers might still be more prone to giving up homers if they can’t control their velocity, it’s not a result of the speed of their pitches. In fact, the opposite is true: even though they tend to be straighter and up in the zone, the more velocity a pitch is thrown with, the harder it is to hit it for a home run. Any possible result of having to “provide all the power” oneself is overshadowed by the fact that pitches with higher velocities are simply harder to square up.


  • Fastball movement doesn’t help pitchers miss bats. In fact, the opposite is true for the fastest pitchers.
  • Fastball velocity translates to missed bats at a steadily increasing rate after 90 mph—there are no diminishing returns.
  • Fastball movement significantly contributes to more grounders and fewer home runs.
  • Fastball velocity also helps keep the ball on the ground and in the park.
  • It’s not until around four inches of additional movement over a normal fastball that pitchers start missing bats, but they start inducing more grounders and allowing fewer homers right away.

If a pitcher doesn’t have the ability to put movement on his fastball up there with the best in the league, he’s not going to be able to use more movement to miss bats and increase his strikeout rate (and the opposite could be true). However, it doesn’t take much extra movement to start seeing dramatic changes in groundball and homer rate, and since break becomes increasingly elusive above 95 mph, you can see why pitchers (especially starters) who are not elite flamethrowers might want to take a little off their fastball for the sake of more movement (although this analysis doesn't prove that pitchers can increase movement by decreasing velocity; it simply shows that pitchers with slower fastballs tend to make their pitches move more). At extremely high velocities, though, who cares about movement? Bring the heat!

Thank you for reading

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This is brilliant stuff. I'd always wanted to see something that addressed and quantified some of the "old scout's tales". Thanks for answering a few questions and posing a few more I hadn't thought of.
Awesome stuff here. Question though, as physics is not my strong suit and I never played the game (and maybe this is outside of the scope of this article). The distance from the mound to the plate is the same (assuming release points are at the same position). Gravity is a constant. So if two pitchers throw 4-seamers at the same velocity over the same distance; with the same downward effect of gravity, then one would expect the same downward movement. Yet, we know that pitchers vary in the relative movement of their pitches. What other factors contribute to this? I guess that arm angle is one, but what other factors come into play.
Grip, finger pressure, and sunscreen come immediately to mind.
Spin --> upward or downward force
^^ What they said. Even with the exact same arm slot, release point, and initial velocity, some pitchers will generate a lot more backspin on a 4-seam fastball than others due to a different combination of their arm action and how they grip/release the ball. That causes the ball to resist gravity on the way in, which looks like upwards movement compared to a typical pitch (although it's not physically possible to actually get the ball to rise). And then, yeah -- arm angle is a whole other kettle of fish.
Spin imparts movement due to the Magnus effect:
Great stuff.

It doesn't change your conclusions, but I wonder if the big break, 80mph "fastballs" at the back end are actually mis-read changeups? How many pitchers throw an 82-mph fastball?
I think that's highly likely. The algorithm pitch f/x uses to identify pitches has gotten better and better, but the lines between pitches are so blurred it's not perfect. On the one hand, that means those pitches are extremely similar to the slowest of fastballs in both direction and magnitude of movement (which would make me think they would lead to very similar results), but it does cloud the conclusions somewhat.

Since you asked, here are some of the lowest (4-seam) fastball averages that probably fluctuate down to 82 mph. Looks like mostly knuckleballers, sidearmers, and guys who are no longer in the league.

Tim Wakefield: 72.77 mph
Jamie Moyer: 79.55
Charlie Haeger: 82.68
R.A. Dickey: 83.35
Pat Neshek: 83.54
Brad Ziegler: 84.22
Lenny Dinardo: 84.33
Joe Paterson: 84.53
Barry Zito: 84.64
Great information, smartly and engagingly presented.
I, too, thought of Brandon League for much of your article. I remember when he lowered his arm angle, sacrificing a few mph, but gaining tremendous wiggle. I still wouldn't give him a three year, 8-figure deal though.

Is it possible that those "straight" upper 90's pitches are what is commonly referred to as "rising fastballs"? IOW, they sink so much less than expected, they seem to the batter to be rising?

Great work.
Yes, precisely. I try to avoid the term 'riser' because it makes people think the ball actually moves upwards, but that's just me being pedantic. A "flat" or "straight" pitch appears to be rising since it is hardly affected by gravity on the way in, unlike a typical fastball. I was surprised that there were so many that only "bend" downwards around an inch over the 60 feet, 6 inches to the plate. I feel like that would look incredibly unnatural from the batter's box. Well, what you could see of it as it blew by you at 100 mph. :)
A request for clarification: when you say "straight line between where it was released and the catcher’s glove", you mean literally a straight line in space? Because a real fastball feels the effect of gravity and would end up a bit below that straight laserbeam line.

In fact, I believe the downward 'movement' due to gravity is ~4 inches, so your results might more accurately be described as "more movement = better" with the understanding that movement might be "up" as well as down. Echoing Wagman's rising fastball comment.

In fact, now I'm visualizing it, and isn't a straight line between release point and glove below the ball's actual trajectory at all points? If I'm understanding that right, then I might suggest that it's better to measure movement relative to a spinless projectile rather than a true straight line.

Also, it might be instructive to break down the data by up/down vs. left/right movement -- is some subset more whiff/GB/homer-friendly?

And finally, is it possible to convert the whiff+HR+GB effects into runs and deduce an "optimum" fastball?

This is very interesting, good work!
Yes, a perfectly straight line. It's a bit of an awkward definition. I'm not sure what the effect of gravity alone on the way to the plate is, but it is overshadowed by the magnus force caused by the spin on the ball. I know the average fastball tails away from the pitcher's body ~5 inches and "rises" ~10 compared to a mythical completely straight pitch unaffected by drag or spin or gravity on its way to the plate.

I agree that these "flat" pitches are the exact same thing as what is called and perceived as "rising" pitches. But when someone refers to "movement" on a fastball, it usually refers to the kind of down and away action you see on 2-seamers and change-ups, not the ability to resist gravity (which is "late life" or "explosive", etc). We need some better definitions since in this case how a pitch appears to the batter (which is arguably the only thing that's important) is the opposite of what's literally, physically, happening. I think I'm going to start using the term: "anti-gravity fastball" in the place of "riser".

Yes, and comparing a pitch to a spinless projectile is actually how horizontal/vertical movement is typically measured by Pitch F/X. I decided to use "bend" for the sake of this article since breaking things down into dimensions as well as velocity and movement would have been exponentially more complicated. Next time!

That's an interesting idea -- although exactly what is "optimal" also depends on the baserunner situation, count, etc. 100 mph gas is probably always going to be the 'best', but I like the idea of looking into how the tradeoff between velocity and movement affects runs.

Is "movement" defined using the Pitch F/X measurements of horizontal and vertical movement compared to a pitch with no spin? Or are you also factoring in the effects of gravity?

Great article, by the way.
It's "break_length", which reflects the horizontal and vertical movement (pfx and pfz) values usually reported but is measured in a different way: the maximum difference between the path actually travelled compared to a perfectly straight pitch (with no spin, etc), rather than the difference between where that perfectly straight pitch would have ended up and where the pitch in question actually did.
Fantastic. Just the sort of stuff, amongst a lot of other things, that keeps this site the best on the 'net.