In Search of the Perfect Fastball: Velocity, Movement, and Location

Mark Buehrle's pinpoint control has served him well in his 15 years in the Majors (via Keith Allison).

Mark Buehrle’s pinpoint control has served him well in his 15 years in the majors (via Keith Allison).

In a recent interview at Amazin Avenue, Matthew Yaspan asked former Mets analyst Benjamin Baumer what he’d like to see done with PITCHf/x data. Here’s Baumer’s response:

I’ve always thought the relationship between location and velocity would be interesting to study. That is, what velocity is required to make a fastball right down the middle as effective as a 90 mph fastball on the outside corner?”

Baumer asks a fascinating question. In fact, I’d argue his question couldn’t be more relevant to someone evaluating pitching talent today. With fastball velocities consistently increasing each year across the game, shouldn’t we ask ourselves if we’re overvaluing velocity as a requirement for success at the major league level?

I’m not sure if Baumer has seen this 2008 piece by John Walsh, but it begins to provide him with an answer. True, many factors come into play when we think about the “what” that makes a pitch effective. Baumer and Walsh allude to a few, like sequencing and contextual information, but I think that relationship between velocity and location is worth another look.

We like velocity because it is quantifiable. Radar gun readings are to scouts as SAT scores are to college admissions departments—they serve as quick and dirty estimates of potential success. Even better, quick and dirty benchmarks make it easy for scouts to weed out potential prospects.

If a 19-year-old version of today’s Mark Buehrle traveled to a showcase tomorrow, he could count on receiving little (if any) attention. Yet Buehrle continues to pitch for the Toronto Blue Jays every five days, often tossing his way into some nice final pitching lines with a mix of 81 mph fastballs and junk. We love him for it.

What’s Buehrle’s secret? It surely isn’t his “stuff” (which I’ll define here as the combination of velocity and pitch movement). If you’ve watched him, you probably have a pretty a good idea. Buehrle’s secret sauce is his ability to locate his fastball.

In his under-appreciated piece, Walsh concluded that low and away fastballs thrown to right-handed hitters are really effective pitches. That point may be obvious, but his second claim was more nuanced: for pitches thrown to this “perfect location,” an 81 mph fastball is just as good as a 98 mph heater.

Today, I’ll revisit that claim. I’ll also extend the analysis a bit to incorporate fastball spin deflection. In my last article, I noted that fastballs come in all shapes and sizes. Is a low-and-away sinker as valuable as a straight fastball thrown to that same location? Should “rising” fastballs (fastballs with a lot of vertical spin) be thrown higher in the zone, or are they just as effective no matter where they’re placed? Let’s dig in and find out.

What Does the Strike Zone Even Look Like?

Walsh completed his work in the Stone Age of PITCHf/x—way back in 2008. We know a little bit more about the strike zone nowadays. Jon Roegele has done some really great work in this area, and he’s shown us that the real-life strike zone is not the constant rectangle we see drawn on television broadcasts, but instead a constantly changing shape that molds itself to the situation. As Jon and many others have pointed out, the called strike zone actually resembles more of an oval than a rectangle.

So, quantifying the boundaries of the strike zone is a tricky endeavor. I decided to construct a 3×3 grid of the strike zone that reflected reality, but I also wanted to ensure some uniformity across each of my nine strike zone sections. With all this in mind, I decided to create a zone that is a little bit narrower on the edges than Roegele’s (or Mike Fast’s, for those familiar with his work).

Here are the horizontal edges we’ll be working with. These numbers might not matter to you if you aren’t familiar with the PITCHf/x system, but I feel obliged to include them if I’m going to talk about the strike zone: -1 ft < px < .96 ft (Measurements are made from the center of the plate.)

Nailing down the top and the bottom of the zone is a little bit difficult, because these measurements depend on the height of the batter. Bill Petti came out with a superb article on the top and bottom edges of the zone here on Monday. My research was conducted independent of his, but the results you’ll see below line up quite well.

Fast has evaluated a wide variety of different vertical boundaries of the strike zone, but I will borrow one of his most simple estimates. Again, I’ll squeeze the top and bottom of the zone a little bit to avoid catching that oval shape I mentioned earlier.

A Hardball Times Update
Goodbye for now.

The vertical zone boundaries: (.95 ft + batter height * .136 ft) < pz < (2.57 ft + batter height * .136 ft)

The Perfect Spot

I should cut to the chase—the values Walsh assigned to various velocities and locations look to be pretty consistent with data from the last four seasons. Walsh made use of a season’s worth of data to make his claim, but it continues to be consistent for every strike thrown by right-handed pitchers since 2010.

In the graphic below, you’ll see average run values (also developed by Walsh) plotted for each velocity group and zone location. For those unfamiliar with pitch run values, positive values are attached to positive pitcher outcomes (strikes, outs, etc.) and negative values are attached to events that pitchers find undesirable (balls, home runs, etc.).


Strike zone drawn from the catcher’s perspective.

This graphic was generated from 315,755 fastballs thrown in the strike zone from 2010-2013. You’ll notice that speed does matter—for fastballs thrown on the inside third. Pitches thrown 94-plus mph are far more effective than any other inside fastball. In fact, the worst type of pitch on this graph for a pitcher is an 86-90 mph fastball thrown low and in to a right-handed hitter.

According to this graphic, even the slowest of fastballs thrown to the outside third of the plate is just as effective as (and in some cases, more effective than) the average 94-plus mph fastball thrown to the inner third. It’s a pretty amazing result, and it explains why Buehrle can make a make a living on the outer third of the plate with this:

courtesy of

Even if he misses high every so often, he’ll be better off than a pitcher who can’t command a hard fastball. The data continue to support Walsh’s claim. He evaluated around 4,000 fastballs thrown to this spot, and I looked at roughly 23,000 thrown there.

Doesn’t Movement Matter, Too?

I mentioned earlier that we’re looking at an incomplete picture of fastball effectiveness. PITCHf/x provides us with information that can be used to gauge just how much tail or sinking action a pitch achieves, and I’ve shown previously that these spin deflection measurements probably are linked to run prevention.

Spin deflection values also help us differentiate between different types of fastballs (sinkers, straight fastballs, rising fastballs, etc.). So, are you wondering what the relationship between velocity and location looks like for each type of fastball?

I’ll start with sinkers. In the chart below, I’ve pulled a group of pitches that all meet a minimum spin deflection standard that fits the basic profile of a sinking fastball. These pitches have a lot of horizontal tail, and they tend to generate a lot of ground balls. Think of these pitches as ranging from hard-breaking two-seam fastballs to textbook sinkers.


The sample size for each of these sections obviously shrinks when we pull out a group of fastballs to look at, and I should mention that the sample size is notably lower for the up-and-away (around 1,700 pitches) and the low-and-in (about 4,800) areas of the zone in this chart.

In the middle and inner thirds of the plate, we see that velocity generally does make sinking fastballs better pitches. That trend appears to break when we consider the hardest-thrown sinking fastballs to the inner and outer thirds. It is pretty clear that sinking fastballs thrown 93-plus mph to the edges aren’t any more effective than those thrown 90-93 mph. Furthermore, sinking fastballs thrown to that “perfect spot” seem to become less effective the harder they’re thrown.

This is a really interesting issue to think about, and I’ll get to it in a second, but let’s see what the trend looks like for rising fastballs first:

rising_fb_chart_jNote: the sample size for the outside edge exceeds 15,000 fastballs, while we have a limited amount of low-and-in risers to evaluate (slightly less than 1,500).

Rising fastballs tend to defy gravity better than the average fastball. For this reason, these pitches tend to get hitters to swing underneath them. Before I created this chart, I assumed these types of fastballs would be most effective when they’re thrown almost at shoulder level or higher. This guess turned out to be true only for rising fastballs that beat the 90-plus mph mark.

The chart demonstrates that elevated, rising fastballs are highly dependent upon speed. An 85-90 mph riser isn’t a great pitch, but a 93-plus mph riser is one of the best performing combinations we’ve looked at thus far. As always, the outside edge appears to be the exception to the rule. We see consistently high values attached to rising fastballs thrown to the outside edge.

Hard Fastballs and the Outside Edge

The trend isn’t as sharp on the outside edge as we saw for velocity on the inside third, but it does seem to appear for the large group of fastballs (our first chart) and sinking fastballs. Why does it look like slow fastballs are actually more valuable than harder thrown fastballs to the low-and-away section? Is that just noise, or is there something going on that explains why a group of slow fastballs has proven to be the most effective set of pitches of any velocity/location combination?

To address this question, I’ll consider another cool Walsh finding: slow fastballs are more likely to receive a called strike call from an umpire than hard fastballs. This argument makes sense, especially considering that velocity appears to be pretty important for sinking fastballs and rising fastballs thrown down the middle of the plate.

Stephen Strasburg may be the best living example of this effect. As soon as he debuted with the Nationals, we saw umpires struggle to catch up to the combination of his fastball’s movement and velocity. He saw a lot of impressive running fastballs called as balls near the edges of the plate, and some argued that he’s been punished unfairly as a result.

The sinking fastball chart explains Strasburg’s fastball pretty well. The chart suggests that his fastball would work best if it were thrown down the middle of the plate, and that he shouldn’t try to be fine with it.

Let’s evaluate the data we have on called strikes, velocity, spin deflection, and location. Believe it or not, you can fit all this information in one chart. Here, we’re looking at the ratio of called strikes to balls for each velocity group. To keep things as simple as possible, I only looked at the outside third of the plate.


It is pretty clear that slower fastballs are called for strikes more often than fastballs thrown 93-plus mph. This trend is just as true for straight/rising fastballs as it is for sinking fastballs. Umpires miss sinking/tailing fastballs more often than straight/rising fastballs, but it appears that velocity doesn’t amplify this effect. That’s good news for someone like Strasburg.

Wait a second–it didn’t look like rising fastballs became less effective on the outside edge with additional velocity, yet we see that they’re penalized in the form of fewer called strikes. If we think the “faulty umpire” effect can explain the decline in effectiveness for sinking fastballs on the outside edge, we should see it affecting results for rising fastballs, too.

For now, I won’t go looking for other explanations for why slower sinking fastballs are better pitches when thrown to the outer third of the plate than harder ones. It could be that we’re looking at a noisy relationship, or that the difference in runs prevented isn’t large enough to care about, but who knows? Maybe harder sinkers are easier to hit to the opposite field, or that hitters swing at slower sinkers more often than they do at harder ones. I’d love to hear a player’s perspective on different approaches to this type of pitch.

Wrapping It Up

There are so many factors that go unaccounted for here, but this study brings one more feature to the table. We came away with a few noteworthy bits:

1) Slow, moving fastballs are probably undervalued pitches.

Who knows how many 19-year-old Buehrles there are out there, but I want as many as I can get in my farm system.  Slower throwers also may come with the added benefit of being less injury-prone than those who throw 95-plus mph. That’s just one more reason to go looking for soft tossers with a knack for finding the outside corner.

2) If your rising fastball is a hard one (93-plus mph), throw it up in the zone. If it isn’t, stay away from the inner half of the plate.

This point seems obvious, but it’s nice to have the numbers to back it up. Some pitchers are able to get by with a relatively slow, rising fastball. Koji Uehara is a great example. Those who do survive usually either: a) have deceptive deliveries, or b) throw this pitch to the edges (while mixing in a few up in the zone).

3) A straight, slow fastball is more likely to receive a strike call from an umpire than a laterally moving, hard fastball

This one probably seems pretty obvious, too, but consider the magnitude of the effect. On the outside third of the plate, 85-90 mph rising fastballs are called for strikes almost twice as often as 93-plus mph moving fastballs.

4) For fastballs thrown to the “perfect spot,” speed may not pay

Should we tell major league pitchers to stop throwing so hard? Well, no. Pitchers who throw harder have a larger margin for error with the location of their fastballs, and this caveat really only applies to a section of the strike zone that is no bigger than a catcher’s glove. What’s more, a soft-tosser doesn’t have too many viable options when it comes to aiming his fastball.

The only application I can think of for this last point (if it does wind up being true) is that a hard-throwing pitcher may find it beneficial to ease up a bit on his fastball in a situation when he knows he can go low and away to a right-handed hitter.

Baseball can be a pretty rewarding game. Even if you throw the slowest, worst-looking fastball in the game, with near-perfect execution you can hang with the best of ‘em.

References & Resources

Noah writes for The Hardball Times. He has previously written for Beyond the Box Score and Fire Brand of the American League. Follow him on Twitter @woodwardps, or email him here.
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Paul Singman
9 years ago

Interesting article and cool charts! Good stuff Noah.

Peter Jensen
9 years ago

In his under-appreciated piece, Walsh concluded that low and away fastballs thrown to right-handed hitters are really effective pitches.

If Walsh’s early Pitch Fx articles are under appreciated today it is only because today’s readers have failed to educate themselves about past research. I can assure you that no one who was interested in baseball analysis from 2007 to 2010 “under appreciated” John Walsh’s innovative contributions at the time.

9 years ago

Very good stuff. Clearly this is just the tip of the iceberg. There are many other variables that must be teased out, like the count, batter, the actual amount of spin deflection, game theory, etc.

One very important point regarding the speed of a fastball and location, in or out, is this:

In order to hit an outside pitch on the sweet spot, a hitter generally must be late with the swing (or “lag” the barrel with an “inside out” swing). To hit an inside pitch on the sweet spot, one must swing quite early (or get the hips out of the way early, pull the hands in, and get the barrel out front). So, in general, a fast pitch on the outside gets hit hard and a slow pitch on the inside gets hit hard. That is basic physics.

Jesse Jeter
9 years ago

These are interesting findings, Noah. Mitchel aptly noted that many additional variables should be considered before reaching any grand conclusions. However, much of what you’ve found is both useful and unintuitive.

You made multiple references to varying, albeit large, sample sizes. If you included standard error bars for the each of the sample means, I think you’d leave the reader little doubt of your hypothesized effects. I’m simply finding it hard to reconcile the amount of variability in some of the plots with my assumption that that runs prevented would be monotonic in mph.

9 years ago

I want to make another important point. Let’s say that a pitcher has a good fastball. He might think, if he is aware of this data, “Hey, my best pitch is a high, especially high and tight fastball.”

Now, why is it that we see so many good fastballs thrown down and down and away, and it is not often that a pitcher with a good fastball liked to throw up in the zone?

Well, we are only looking at the result of a pitch, after we know that it is thrown in a certain location. We are NOT looking at the result of a pitch that was INTENDED to be thrown to a certain location. That is a huge distinction and it will mislead us into thinking that pitchers with good fastballs should be throwing more high and especially high and inside fastballs. This is not unlike when we only look at one result of a sacrifice bunt attempt (when the batter is out and the runner(s) advances). That is not a useful framework for an analysis because we want to know if a sacrifice ATTEMPT is warranted in a certain situation, and not only one result of a sacrifice attempt, which only happens 50-60% of the time. All kinds of other things can and do happen with a sacrifice attempt and the frequency of those things are critical in the analysis. As I’ve said many (too many) times, you cannot do an analysis of a sacrifice bunt attempt without knowing the frequencies of all the possible outcomes. Assuming an out and a runner advance is useless. That is like assuming that a ball in play is always an out because it happens 70% of the time!

So, we (and especially a pitcher) NEED to know what happens when he INTENDS to throw a fastball up in the zone and especially high and tight. I will give you a clue why pitchers don’t often do that and are not taught to do that, at least on a regular basis, even though it appears that the high and tight fastball is the best pitch in baseball. Unfortunately, that is only when the intended high and tight fastball ends up in its intended location, which obviously doesn’t happen all the time, or even close to all the time.

So what happens when a pitcher misses the low and away fastball. Let’s assume that he is equally likely to miss in all four quadrants around his target. If he misses toward the plate, the pitch ends up middle away and low, still a good pitch. If he misses high, it ends up middle away, still a decent pitch. If it misses low, it ends up very low and away, which is either a ball or a great pitch if the batter swings. Finally, if he misses away from the plate, again, it is either a ball, or a very good pitch if the batter swings.

But what happens when a pitcher tries to pitch high and tight and misses in the same 4 quadrants, inside, outside, low, or high? Those results are not nearly as good. If he misses high, it is very high, and either a ball or a good pitch if the batter offers. If he misses low, it is inside and middle, which is a pretty good pitch to hit. If he misses toward the plate, it is high and middle in, which is a very good pitch to hit. If he misses away from the plate, it is either a ball or it hits the batters, and is rarely swung at.

So, you can see why pitchers, even with great fastballs don’t often intentionally try and throw inside, high or high and inside. While it is a great pitch if you hit your target, if you don’t, it is often a good or great pitch to hit or a hit batter.

Not so with the outside and low pitch. Even when you miss your target, it is a ball or not a very good pitch to hit.

This is why all pitchers are taught to throw down and away. Obviously there are times to throw in and high, and it is true that you need a good fastball to do that more than occasionally, but it is probably never correct to throw high and inside a lot.

One more thing. Control is extremely important when throwing high and inside. If you don’t have good control, because of the possibility of the hit batter and leaving the pitch middle in, you should rarely throw inside. If you miss your location a lot, you want to miss low and/or away as often as possible.