# You shall know our velocity

This article borrows its title from a book by Dave Eggers, but it could more aptly be named after an earlier work by Eggers entitled, “A Heartbreaking Work of Staggering Genius.” The work of genius, however, was not my own, by derived a brilliant hypothesis put forth by John R. Mayne in 2010. Mayne emailed to alert me of this piece earlier this year, after my release of SIERA (Skill-Interactive ERA) at FanGraphs, and I recently tested it. Despite initial pessimism, I was shocked by what I found.

Everyone now knows how important velocity is for a pitcher. For years, pitching coaches scolded amateurs about over-reliance on velocity. Prepubescent pitchers are lectured about Greg Maddux, told that movement and location are more important than a couple digits on a radar gun.

I’m no PITCHf/x expert, but everything I’ve read by those capable of studying that data says that velocity is actually very important, perhaps more important than movement and location after all. It’s hard to throw a 100 mph fastball that is easy to hit, and you have to be Jamie Moyer to get away with an 80 mph, lukewarm heater. Even a few ticks in the ones column of a radar gun can make world of difference.

However, until very recently, I believed that a proper study of a pitcher’s peripherals could tell you which of two guys with a 92 mph fastball has the superior arm, and I also believed that two pitchers with the same SIERAs with different fastball speeds were no different in future skill level.

When discussing SIERA’s ability to adjust for pitcher control of BABIP, Dave Cameron once noted that velocity may explain some of the missing pieces of the puzzle that correlated with both strikeout and BABIP skills. However, I found that if you control for peripherals, age, year, and role, then knowing a pitcher’s velocity is not useful.

In fact, running a regression on all of these, you will actually get an insignificant and positive coefficient of .00035 on velocity; in other words, a 3.0-mph increase in velocity with the same characteristics will correspond with a BABIP that is a full point higher!

When Mayne emailed me with this suggestion, I expressed my skepticism, but I was thinking about the idea the wrong way. Mayne was talking about projections in that article—predicting the future. What I now found was that knowing a pitcher’s velocity tells you about his potential to improve the statistics that express skill level better.

If you just run a regression of a pitcher’s ERA next season on his ERA from the current season, you get the following equation:

ERA_next = 2.76 + .368*ERA

Include velocity, and you get:

ERA_next = 9.49 + .327*ERA – .073*velocity

This formula says that, of two pitchers with the same ERA last season, the one who threw faster is more likely to improve. That’s not surprising. We know that a pitcher was probably more capable if he threw faster, so he probably had better peripherals and worse luck if he had the same ERA and more velocity. Right?

Actually, let’s take a closer look at the pitcher’s true skill level and replace his ERA with his SIERA to see what happens. If you run a regression of a pitcher’s ERA next season on SIERA from the current season, you will get the following equation:

ERA_next = 1.21+ .733*SIERA

However, if you run a regression of ERA next season on SIERA and velocity, you get the following result:

ERA_next = 4.52 + .677*SIERA – .034*velocity

Both coefficients are statistically significant at the 99.9 percent level. In words, this means that a 2.9-mph increase in velocity will correspond with a 0.10 lower ERA, even if you know the pitcher’s SIERA from the previous season.

What’s going on here? Well, the pitchers who throw faster are doing something better than others with the same peripherals. What is that? I looked at various components of pitcher performance to find the answer and found why Mayne’s hypothesis was accurate.

Suppose you know a pitcher’s strikeout rate. In this case, you can predict his future strikeout rate next year very well:

K%_next = 3.87 + .764*K%

However, once you know that pitcher’s velocity, you have a lot more information.

K%_next = -16.1 + .701*K% + .233*velocity

Verbally, this mean that if you have two pitchers with the same strikeout rate the previous year, the pitcher who throws 4.3 mph faster will strike out one percent more batters the following year than the pitcher who throws slower.

What about walks?

BB%_next = 2.864 + .644*BB%

BB%_next = 0.237 + .638*BB% + .296*velocity

In the case of walks, more velocity actually portends an increase in free passes.

However, if you start to include more terms, its significance disappears. Higher velocity is just correlated with other variables that are related to increases in walk rates, such as relief role, age, and strikeout rate itself!

Including strikeout rate in the regression on next year’s walks renders the velocity coefficient insignificant (p = .224), while it remains very significant (p = .000) in the regression on next year’s strikeouts:

BB%_next = 1.04 + .0151*K% + .6361*BB% + .0179*velocity

K%_next = -15.9 + .6984*K% + .0752*BB% + .2254*velocity

Controlling for both rates, more speed foreshadows an improvement in strikeout rate. Including a slew of other variables (results omitted for brevity) did not alter this conclusion.

If you look at BABIP, you start to see more of an effect of a good fastball. If you try to predict BABIP next season using only this season’s BABIP, and then try to do so with BABIP and velocity, you can create a clearer picture:

BABIP_next = .238 + .191*BABIP

BABIP_next = .283 + .191*BABIP – .00050*velocity

Velocity helps predict next season’s BABIP pretty well, though this effect is somewhat minimized when considering the effect on other variables.

The rate of home runs per fly ball is another metric that is mostly determined by luck but incorporates some skill as well. Velocity actually corresponds well with a decreased rate of home runs per fly ball, even in the same season.

Running a regression of home runs per fly ball while incorporating peripherals with interactions, season, year, age, and role, we will still get a coefficient of -.00066 on velocity. This means that a pitcher who gives up 3.0-mph in velocity will yield one fewer home run every 500 fly balls. It’s not a big deal, but it’s statistically significant.

It also matters because the coefficient only goes down to -.00063 when changing the dependent variable to next year’s home run-per-fly ball rate. The skill is something that shines through over time, revealing an ability to get hitters out that gets behind the luck mashed in with other statistics.

However, if we simply check how much velocity adds to HR/FB itself in predicting next year’s HR/FB rate, we can see that:

(HR/FB%)_next = 8.39 + .186*(HR/FB)

(HR/FB%)_next = 20.17 + .173*(HR/FB) – .129*velocity

Knowing velocity is important for this as well.

Velocity is an even bigger deal than we thought, and Mayne hit the nail on the head. Not only do pitchers who throw faster succeed more often, but they improve more as well. It foretells a higher strikeout rate, lower BABIP, fewer home runs per fly ball, and a subsequently lower ERA than other pitchers with similar yearly statistics.

Incorporating velocity into projection systems would appear to be not only a useful tool, but perhaps a pivotal one in better understanding the importance getting the ball to the batter sooner has on getting him out.

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Many of my fantasy leaguemates are now reading this. Can we screen them out?

(Seriously, Matt, thanks for the followup. Having the degree of the effect quantified is huge, and I don’t think this has been done before. A big step forward – and while my ideas were surely worth something, they weren’t worth as much as the execution.)

—JRM

Colleague: This will just inflate your ego.

JRM: How is that possible?

Matt interesting article. You guys are way above in the math—too many years since college.

I do not understand the statement “This means that a pitcher who gives up 3.0-mph in velocity will yield one fewer home run every 500 fly balls” Does this mean a pitcher with lower velocity gives up less HRs per flyball than high velocity pitcher? It seems to be opposite of the rest of the article—Velocity is good.