Zoooomaya and speed guns

Radar guns, and their efficacy have always been a hotly debated topic, largely because no one is ever sure how accurate they are. This year the tongue wagging intensified with the emergence of perhaps the hardest thrower ever to step on to a pitching mound: the flame-arm tattooed Joel Zumaya.

In 2006 Zumaya finished with a 1.94 ERA, struck out over 11 per nine innings, and was easily the most dominant,—as well as the most exciting—pitcher in the Tigers pen. Zumaya consistently overpowered hitters with raw pace: Few will ever forget Game 2 of the ALDS, where he left Alex Rodriguez floundering after a volley of 100-plus mph pitches to strike out the side.

Two questions nearly always pervade a discussion about Zumaya. One is whether he is the hardest thrower in the game, and two is how reliable, or unreliable in many cases, radar guns are. We can’t answer the first question without at least understanding the second. It sounds like a short primer on speed guns is in order.

Tell Me About Speed Guns

There are many types of radar guns, and all work on a similar principle. Simply put, a radar gun launches a beam of electromagnetic waves at a moving object. On hitting the object the waves are reflected back toward a detector on the gun, which then calculates the speed of the object by analyzing the nature of the reflected beam.

In the major leagues, the most common gun is made by Jugs Company, and is a Doppler radar. A Doppler radar measures speed by detecting minuscule changes in the wavelength of the reflected beam. What does this mean? Imagine a radar gun has fired an electromagnetic wave (e.g., light) toward a moving object. When the wave reaches the object, it is not only reflected but also given an extra “push” by the motion of the object. A slow moving object will “push” less than a fast one. The detector calculates speed by measuring the amount of “push.” In reality, this “push” causes the wavelength of the wave to change—a phenomenon known as the Doppler Effect.

Those of you who recall high school physics may remember that we experience the Doppler Effect on a daily basis, most notably when being passed by a police car or an ambulance with sirens blaring. Police cars have directional sirens, usually stapled to the roof or fender and facing forwards. As the siren approaches, the waves of sound are squeezed together, thereby reducing the wavelength, resulting in a stationery observer hearing a higher pitched sound. When the car passes by, the sound waves from the siren are dragged apart, causing an observer to hear a lower pitch noise.

Another quite cool, but totally unrealistic, application of the Doppler Effect is that if a car were to travel toward a red traffic light at 1/3 of the speed of light then, to the traveler, the light would appear green (green light has a shorter wavelength than red light)—probably not an excuse to proffer next time you get pulled over by the cops for jumping a stop light! Anyway, we digress; the point is that exactly the same principle is used to measure the speed of a baseball. A gun shoots a beam of radio waves that reflects off the ball. By measuring the wavelength change of the reflected beam we can calculate speed.

Understanding how radar guns work is all well and good, but the controversy surrounding them is their measurement reliability. Let’s have a look at some different sources of error, of which there are at least three.

1. Point of measurement
2. Angle of incidence
3. Gun calibration

By understanding each effect, we can start to pinpoint the size of radar measurement error and what the uncertainty is in pitch speed. Let’s take each in turn:

1. Point of Measurement

A number of things happen to a pitch that cause the ball to slow as it leaves a hurler’s hand and meanders to the plate. Robert Adair, a baseball physicist, worked out that a pitched baseball typically loses 7 to 8 mph from the point of release by a pitcher to when it crosses the plate, largely because of drag forces. Suddenly, a 100 mph heater measured as it leaves the hand registers a more sedentary 92 mph as it nestles in the catcher’s mitt—still quick, but not jaw-droppingly fast. The obvious inference is that if a gun is set up to measure velocity as the ball crosses the plate it is going show a reading that is a darn sight slower than when the ball leaves the hurler’s hand.

So, depending on what point of motion the gun is measuring, we get different speeds. This is what many scouts or commentators mean when they say that a park has a fast gun—it is measuring the point of release and not the point where the ball crosses the plate.

2. Angle of Incidence

The best place to measure the speed of a pitch is directly behind the batter. Unfortunately this is seldom possible as the hitter is in the way! This means that the gun is usually positioned at an angle, either to the side of or above the hitter, which has a corresponding impact on speed.

An easy illustration is to consider a gun positioned above the batter. The gun measures speed in the plane perpendicular to the face of the gun. Because the ball flight is on a different trajectory to the measurement plane, we generate a small error. Have a look at the diagram below, which attempts to explain what I mean:

The main force acting on the ball in this example is gravity. This causes the ball to move down, away from the measurement plane. As a result, the gun reads the ball as going more slowly than it really is.

The same is true for a sideways positioned gun. Lateral movement either toward or away from the measurement plane will have a commensurate impact on recorded speed. The effect, in both cases, is small—somewhere around 0.5 mph if the angle is 20 degrees, less if the angle is smaller. When comparing fastball speeds of different pitchers, the effect largely cancels out, if measured with the same gun. However, a breaking ball, for example, will register a little slower (or faster, depending on the gun position) than it should because there is more movement on the pitch.

This raises the question as to where exactly we should be measuring the pitch from. The most accurate point is at release, which is the fastest point and where the angle of incidence is lowest—this is where most guns in the majors take measurements. Because different pitchers have different release points and positions, the point of measurement isn’t always constant. With current technology, the measurement happens within the first 5 to 10 feet or so.

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3. Gun Calibration

This covers three errors: measuring accuracy of guns (usually 0.5 mph), wrongly calibrated guns, and juiced guns, where the reading is artificially inflated by the reader. Guns should be, and often are, recalibrated on a regular basis. If this doesn’t happen, then more error will creep in. Poorly calibrated and juiced guns certainly exist, but research by Baseball Info Solutions (BIS) shows that its independent guns calibrate well with TV and scoreboard guns. For our purposes, we can largely ignore the last two factors. The only error we need to take in to account is the measurement error.

All three factors have the potential to add (or subtract) 1.5 to 2 mph to each speed reading:

Measurement error             0.5  mph
Release error (5-10 ft)       0.75 mph
Angle of incidence            0.5  mph
Mirror, Mirror On the Wall, Who is the Fastest of Them All?

Right, now that we are all experts in radar gun technology, let’s turn our attention back to the question of whether Joel Zumaya really is the fastest pitcher in the game. First, take a look at 2006 data for the average speed of a fastball (data courtesy of John Dewan and BIS):

Player               Avg Fastball
Joel Zumaya          98.56
Billy Wagner         96.47
Bobby Jenks          96.29
Kyle Farnsworth      96.2
Ambriorix Burgos     96.04
Brad Lidge           95.78
Francisco Cordero    95.75
Daniel Cabrera       95.74
Derrick Turnbow      95.68
Mark Lowe            95.61

Wow! Zumaya’s gas is over 2 mph faster than Billy Wagner’s. Is that a statistically robust result? Absolutely. Running a simulation of pitch speeds for a typical reliever shows that the standard deviation of a fastball is around 2 mph. That gives a sample standard deviation of about 0.2mph, which yields a difference of about 10 standard deviations between the two hurlers.

But while this tells us that Zumaya consistently had the fastest arm in the game in 2006, it doesn’t tell us with how much regularity he broke the 100 mph barrier. Before tackling that, the first question is how easy is it for your Joe Average hurler to break the aforementioned 100 mph mark? The short answer is that it isn’t:

Season  #of 100 mph pitches
2002    106
2003    204
2004    82
2005    134
2006    335

To give an idea of relative magnitude some 3.5 million pitches are tossed in the majors each year of which 75% or so have accurate speed measurements. Two things jump out. First, the very low number of 100+mph pitches (less than 0.01% of all balls pitched), and second, the spike in 100+mph pitches in 2006. Yup, you’ve guessed it; the 2006 spike was caused by the emergence of one man: Joel Zumaya. If we look at pitch speed leaders each year we see that Zumaya was responsible for nearly 70% of the 100+mph fastballs in 2006, and, incredibly, his individual total exceeded the league total in each of the previous four years:

Season   League Leader     #of 100 mph pitches
2002     Billy Wagner      42
2003     Billy Wagner      159
2004     Kyle Farnsworth   30
2005     Daniel Cabrera    37
2006     Joel Zumaya       233

Although Zumaya’s numbers are off the chart it is interesting to note the large discrepancy in Wagner’s numbers between 2002 and 2003, which could be suggestive of a data issue. Digging deeper, in 2003 his home/road split was 120/39, suggesting that the gun at Minute Maid may have been juiced that year. But who knows? Identifying the real cause of the jump is difficult; it could equally have been to do with a particularly hot Texas summer, or the roof being closed more frequently in 2003, or any other extraneous factor that you care to think of.

Another problem with looking at home/road splits is that with the unbalanced schedule, 75% of games are played in just six parks, so there is still a lot of potential bias. The only way to reliably work out relative pitch speed among different hurlers is to compute a park factor for each gun and adjust accordingly. Given that Wagner doesn’t lead the 2004 list (the year he moved to the Phillies) suggests that park is important—definitely something to add to the to-do list.

To understand just how dominant Zumaya was in 2006, consider a game against the Chicago White Sox on July 20, where he touched 103 mph on the gun. Here is the pitch breakdown by speed:

Speed      # of pitches
103        1
102        4
101        5
100        7
95-100     4
<95        7

Over half of his pitches clocked over 100 mph, with one reaching 103 mph. Astonishing. But that isn’t even the fastest he has ever thrown! There was a Japanese ESPN video on YouTube that showed Zumaya clocking 104mph against St Louis! Sadly, because of copyright violation the link has been deleted so you’ll just have to trust me on this one.

So where does the putative 103 or 104 mph rank on the all time list? Right at the very top, that’s where. Have a look at the following list of hurlers purported to have smashed the 100 mph barrier (courtesy of Baseball Almanac)—it only notes a pitcher’s quickest pitch.

Pitcher           Radar Speed   Date        Location
Mark Wohlers      103.0 mph     Mar-95      Spring Training
Joel Zumaya       103.0 mph     Apr-06      McAfee Coliseum
Armando Benitez   102.0 mph     May-02      Shea Stadium
Bobby Jenks       102.0 mph     Aug-05      Safeco Field
Randy Johnson     102.0 mph     Sep-04      Pacific Bell Park
Robb Nen          102.0 mph     Oct-97      Jacobs Field
A.J. Burnett      101.0 mph     May-05      PNC Park
Rob Dibble        101.0 mph     Aug-92      Candlestick Park
Kyle Farnsworth   101.0 mph     May-04      Minute Maid Park
Eric Gagne        101.0 mph     Apr-04      Pacific Bell Park
Jose Mesa         101.0 mph     Jan-93      Cleveland Stadium
Guillermo Mota    101.0 mph     Jul-02      Qualcomm Stadium
Justin Verlander  101.0 mph     Oct-06      Camden Yards
Billy Wagner      101.0 mph     Nov-03      Yankee Stadium
Nolan Ryan        100.9 mph     Aug-74      Anaheim Stadium
Josh Beckett      100.0 mph     Dec-03      Pro Player Park
Daniel Cabrera    100.0 mph     Sep-05      Camden Yards
Roger Clemens     100.0 mph     Oct-01      Yankee Stadium
Bartolo Colon     100.0 mph     Jun-99      Jacobs Field
Francisco Cordero 100.0 mph     Jul-04      Jacobs Field
Rich Harden       100.0 mph     May-05      McAfee Stadium
Jorge Julio       100.0 mph     Sep-04      Skydome
J.R. Richard      100.0 mph     May-76      Candlestick Park
C.C. Sabathia     100.0 mph     Jun-02      Jacobs Field
Ben Sheets        100.0 mph     Oct-04      Miller Park
Derrick Turnbow   100.0 mph     May-05      Miller Park
Kerry Wood        100.0 mph     Oct-05      Wrigley Field

However, when it comes to the world record, the officially recognized number is held by Nolan Ryan for a 100.9mph fastball thrown on Aug. 20, 1974 that was measured using a specially calibrated infra-red gun. Even though many, including Zumaya, have topped this mark their claims are dismissed because of the uncertainty surrounding the accuracy of guns.

The Coming Revolution

So, what is the plan to fix this? Is there one? Yes, there is, and it sits squarely with MLB Advanced Media and its Enhanced Gameday technology, which was first tested in the 2006 post-season.

Enhanced Gameday uses a litany of cameras and whizzy computer software to track pitches from the hurler’s hand all the way to the plate. It calculates the exact location and speed of the ball across the entire pitch trajectory, allowing one to see a visual representation of the flight of the ball. Yes, that means at any point along the trajectory we can tell the speed of the pitch. Enhanced Gameday helpfully provides both the release and plate velocity on screen. If you haven’t seen Enhanced Gameday, have a look at the screenshot below that shows Zumaya’s second pitch to A-Rod in the 8th inning of Game 2 of the ALDS.


The graphic tells us that the pitch left Zumaya’s hand at 102.5 mph and flew over the plate at 93.4 mph for a swinging strike. Out of interest, in Game 1 of the ALCS, Zumaya’s release speed registered an incredible 104.8 mph for a pitch to Frank Thomas.

This is the future. Over the coming years Enhanced Gameday will provide analysts with a new perspective on pitch by pitch plays. The software is very much in trial stage at the moment, and some of the readings can be disputed—for instance many pitches seem to slow down by more than the 7-8 mph predicted by physicists. It is unclear whether this is a software error or a problem with the assumptions in the physics calculations. However, as the bugs are ironed out we will, at some point, have very accurate pitch speed and trajectory data. It won’t be too long before we’ll be able to answer the eternal question: Mirror, mirror on the wall who is the fastest of them all?

References & Resources
Two great resources were very helpful in compiling this article. First, John Dewan's stat of the week was invaluable as it is one of the only sources of pitch speed information on the Internet, and second, Baseball Almanac is generally a legendary resource for all things baseball and was kind enough to provide a list of the so called 100 club.

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Dennis Richardson
Dennis Richardson
Keep in mind people, the scientists of University of California at Berkeley has determined that the results of any calculation cannot have any more precision in the answer than the least precise data that made up that calculation. The scientific community has not argued against this conclusion for several decades, though it has had the opportunity to do so. Thereby, 0. 00 precision on thrown base ball pitch is very doubtful. Position would have to be known to within 0.08448 inches and knowing the time within 0.00008 seconds. NOT possible. Report it as 100. miles per hour but not 100.01… Read more »