For baseball fans who are no longer young, it is easy to conjure up the once-common image of a man behind home plate with a radar gun pointed at the pitcher. But as technology has advanced, the once cutting-edge radar gun has been replaced by new and better equipment. Today, advanced systems, such as TrackMan and Hawk-Eye, provide more, and better, data about what happens on the field than the radar gun did, and one no longer sees the familiar gun at major league games. Does this mean that radar guns are outdated and no longer useful? The somewhat surprising answer is no. Just like cell phones, radar guns are becoming more, not less, common in the world of baseball. This article will discuss three aspects of the current radar gun phenomenon: what is driving the demand for radar guns, factors affecting the accuracy of a radar gun reading, and a comparison of velocity results from widely used guns.
WHAT IS CREATING DEMAND FOR RADAR GUNS?
In today’s data-driven baseball environment, one of the most important data is the speed of a pitch. Baseball commentators regularly discuss the speed of a pitcher’s fastball and the difference in miles per hour between his fastball and changeup, and the pitch speed appears on most big-league scoreboards. The speed, flight, and location of every pitch thrown in a major-league stadium is tracked. Some of the tracking data are made available to fans via websites such as Baseball Savant and Brooks Baseball. But this very useful information is routinely recorded only at big-league ballparks. Increasing demand for radar guns is coming from other participants in the world of baseball who have the same need for velocity data that major league players do.
Two large groups of players who need velocity data are pitchers at the college and high school level who aspire to pitch in the big leagues. It’s no secret that one of the primary things big-league scouts look for is velocity. This quotation from a scout emphasizes that idea: “You hate to say it, but velocity is kind of the first thing that jumps out at you. There are plenty of kids out here that can pitch but are throwing 80 and that just isn’t going to work.”1 Thousands of pitchers at these levels need radar guns to know where they stand from a velocity perspective.
In addition to providing aspiring big-league pitchers with peak pitch-velocity numbers, radar guns can also be useful in training. Radar gun data can show if these pitchers are improving their velocity over time. Mike Reinold of Elite Baseball Performance says that radar gun data can help a player with power development and can be used as a way to monitor the intensity of training.2 Players who use a medicine ball in order to increase power can use radar gun measurements of the medicine ball to improve power output over time. In terms of intensity of training, radar guns can be used to develop a preseason program that slowly increases the capacity of the arm to handle the stress of the regular season and can be used during the season to carefully monitor workload.
The intensity of training load on the arm is also important after arm surgery. Post-surgery recovery programs have historically tried to limit the load on the recovering arm by asking the player to throw at 50 percent or 75 percent effort. But it is difficult for the player to know what these levels of effort are with any precision. This can result in higher-than-intended arm load. A recent study shows that radar guns can help with this issue. Players can easily target a pitch velocity when they know the pitch speed from a radar gun. This reduces the chance of overloading the surgically repaired arm unintentionally.3
Although radar guns have traditionally been used to measure pitch speed, other parameters from the action on the field are also valuable. For example, the exit speed of the ball coming off the bat is an important parameter for hitters. A common rule of thumb is that each additional mile per hour of ball exit velocity results in four to six feet of additional flight distance, depending on the launch and spray angles (dead center field is zero spray angle).4 Given the emphasis on home runs in today’s game, this gives hitters (at every level) an incentive to measure (and to try to increase) their batted-ball exit velocity.
The need for data is not limited to baseball. Pitchers and hitters in fast-pitch softball want data for the same reasons as baseball players. Ball exit velocity is also important for players improving their skills in slow-pitch softball. The participants in these sports form another large group who want to be able to measure pitch speed and ball exit velocity.
These examples show that there is strong demand for ball-related data both inside and outside of major league baseball. This has resulted in the tremendous growth in radar gun sales that can be seen in Figure 1.
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Figure 1 shows the relative year-over-year growth in radar guns sales during the past five years for a leading radar gun provider. The company provided the data in Figure 1 on the condition that specific numbers of units sold would not be released. But the data still allow us to see that the compound annual growth rate over this period is 40 percent. It’s not an exaggeration to say that radar gun sales are booming for this firm. Although industry-wide data are not available, it is likely that demand has increased across the industry and not just for this one manufacturer.
THE ACCURACY OF A RADAR GUN READING IS CRUCIAL
Radar guns appear to be easy to use. You just point the gun at the target to get a reading, right? But if a radar gun reads 94.2 mph, is that the end of the story? Was that pitch velocity exactly 94.2 mph? How much confidence can you have that the reading is accurate? Could the true velocity be lower or higher? Given the importance attached to high-velocity readings, the purpose of this section of the article is to examine some of the issues associated with the use of radar guns in order to better understand how these issues can impact the accuracy of the reading.
1) What a drag it is getting home
After a pitcher releases a pitch there are three primary forces that act on the ball. Gravity pulls the ball toward the ground, spin on the ball creates what is referred to as Magnus force, and air resistance creates drag which slows the ball. All three of these forces are important in order to fully understand what happens to a pitched ball as it travels toward the plate, but from a radar-gun usage perspective, the most important parameter is drag. The force of drag on a pitched baseball is proportional to the square of the velocity that the ball is traveling. This means that drag on the ball increases significantly as pitch speed increases.
The magnitude of the drag effect on a pitched baseball is surprising. A pitch released at 100 mph will be 12 mph slower when it crosses home plate.5 A 90 mph pitch will lose 10 mph before it crosses the plate. This is roughly a ten percent decrease in speed between the mound and the plate. A ten miles per hour decrease in the 0.4 seconds it takes the ball to reach the plate is an average of 25 mph/sec deceleration of the ball. Motor Trend magazine reports that the 2015 Porsche 918 Spyder goes from zero to 60 in 2.4 seconds.6 It’s hard to believe that the average deceleration of the baseball is equivalent to the average acceleration of a top-end sports car, but it is. The car accelerates at an average rate of 25 mph/sec. It is also interesting to note that 25 mph/sec is about 37 ft/sec2. The acceleration due to gravity is roughly 32 ft/sec2. So the deceleration of a pitched ball—and the acceleration of the sports car—are roughly equivalent to the acceleration of a ball that is dropped with zero initial velocity. Because the ball decelerates so quickly, where a radar gun picks up the pitch along its flight has a big impact on the velocity reading.
This discussion of the deceleration of a pitched baseball leads naturally to an exploration of the history of pitch-speed measurement and then to the question of who was the fastest pitcher ever. Although this is an interesting topic in itself, the subject is tangential to the main points of this article, so the digression will be brief. (A detailed discussion of the topic can be found at the website eFastball.com.)
The question of who threw the fastest pitch is worthy of an entire book and Tim Wendel has written a good one on the subject. Wendel’s book, High Heat: The Secret History of the Fastball and the Improbable Search for the Fastest Pitcher of All Time, describes his quest to figure out who threw the hardest. The issue is also explored in the interesting documentary film Fastball. In both the book and the documentary, three of the leading candidates are Walter Johnson, Bob Feller, and Nolan Ryan. But because pitch speed was measured differently for each pitcher, how each measurement was made has bearing on the answer.
Lindsay Berra provides a good summary of the results in her review of the documentary.7 Johnson’s fastball was measured at a munitions laboratory and was clocked at 83.2 mph. Feller’s fastball was measured at 98.6 mph using Army equipment (Feller also famously tested his fastball velocity by comparing it to a speeding motorcycle and the documentary shows film of the test) and Ryan’s fastball was measured at 100.9 mph using a Rockwell laser device. This makes Ryan the fastest, right? Not necessarily. The readings were not all taken at the same distance from the release point. Johnson’s speed reading was taken behind where home plate would have been, Feller’s was measured at home plate, and Ryan’s reading was taken about ten feet in front of home. After adjusting for the loss of speed due to drag, Wendel, the film, and eFastball.com all conclude that Ryan threw the hardest. After adjustment for ball deceleration, Ryan’s fastball is considered the fastest of all time at 108.1 mph.
More recently, the rapid deceleration of the baseball is the primary reason there can be a difference in radar gun readings. A gun that measures the speed of the ball soon after it leaves the pitcher’s hand will register a higher speed than a gun that measures the speed of the ball as it nears home plate. Where the radar gun measures the speed is a function of the physics of the signal emitted by the gun, the reflected signal received at the gun, and the sophistication of the measurement algorithms inside the radar. In the early days of radar gun usage, you would often hear references to “fast guns” versus “slow guns.” The JUGS gun became know as a fast gun because it measured the speed of the ball midway along the flight path. Another early gun, the Decatur RAGUN, measured the speed near home plate. There was often a four-mile-per-hour difference between readings from the two guns.8 The Stalker guns that came out in the 1990s measured pitch speed closer to the release point than either of these others. The JUGS gun then became the “slow” gun compared to Stalker gun readings.9
2) The accuracy of radar guns is impacted by the margin of error
The accuracy of any given radar gun reading is a function of the margin of error associated with that gun. For example, one popular model, the Stalker Sport 2, has a performance specification that the gun’s accuracy is ± 3% of the reading.10 This means that the true speed of a pitch that reads 100 mph on the gun could range from 97 to 103 mph. This isn’t necessarily bad, but it is something else to be aware of when using a radar gun and utilizing the output. The margin of error means that one cannot put too much stock in any single velocity reading. A series of readings at roughly the same velocity is more likely to be correct than a single reading.
One of the guns with a small margin of error is the Pocket Radar Smart Coach. This gun has a margin of error of ± 1 mph.11 A reading from the Smart Coach of 100 mph means that the actual velocity could be anywhere between 99 mph and 101 mph. But some radar guns display the velocity reading to the tenth of a mile per hour (94.2 mph, for example). Because of the margin of error associated with any reading, a display to the tenth of a mile per hour is misleading the user. Users are being given a false sense of accuracy when the gun displays the velocity to the tenth of a mile per hour when the margin of error is much larger.
3) Angle error or cosine error
In order to get the most accurate measurement of ball speed, a radar gun must be placed directly in line with the direction the ball is moving. It doesn’t matter if the gun is in front of the ball or behind the ball, as long as the radar beam is aimed along the line of travel. All radar guns direct radio waves into a narrow, focused beam. If the radar beam is aimed at an angle relative to the flight path of the ball, a measurement error is introduced. This error, known as cosine error, is proportional to the cosine of the angle between the radar beam and the line of travel. The measured speed of the ball will be equal to the actual ball speed times the cosine of the angle. This means that the measured speed will be lower than the actual speed if the gun is not properly positioned. That’s why radar gun operators were always placed in the area behind home plate in the early days of radar gun usage in major league baseball.
Cosine error is relatively insignificant at small angles. For example, at a five-degree angle to the line of flight, cosine error reduces the measured speed by only 0.4 percent. That means a true 100 mph pitch will read 99.6 mph on the gun. But cosine error becomes more significant at larger angles. The error increases to 1.5 percent at 10 degrees and 3.4 percent at 15 degrees. Ten degrees seems like a pretty small angle. But the gun operator needs to be only about 12 feet off the line of travel at a distance of 70 feet from the mound to be at an angle of 10 degrees. In this case, a true 100 mph pitch will read 98.5 on the gun because of cosine error.
Cosine error is not difficult to avoid, and some guns can adjust for cosine error if the radar gun operator inputs the angle to the line of travel. But it is something for both radar gun operators and users of the data to be aware of.
Radar guns can give spurious and erroneous readings. The police refer to these as “Ghost Readings.” These readings can be caused by interference from other devices that operate in the same frequency range as the gun. Possible sources of electrical interference include cell phone towers, fluorescent lights, television monitors, and power transformers. It’s also possible that nearby moving objects like fans, motors, or blowing debris can cause an improper reading. The use of multiple guns in the same area can also cause interference! As with cosine error, interference is something an operator needs to be aware of when using a radar gun.
COMPARISON OF VELOCITY READINGS FROM COMMONLY USED RADAR GUNS
The accuracy and consistency of a radar gun’s readings are important. Both of these parameters can be tested by comparing readings of the same pitch from different radar guns. If both radar guns produce the same reading, that suggests that the two guns are accurate. Conversely, a wide variation in the readings suggests that one or both guns are not accurate. This portion of the paper describes the results of pitchvelocity readings from three pairs of guns.12
There are a number of companies that sell radar guns. These include (but are not limited to) Stalker, JUGS, Pocket Radar, and Bushnell. The Stalker Pro II is widely considered to be the gold standard in radar guns.13 But it’s expensive, costing well over $1400. The Stalker Sport 2, which enjoys a similar reputation, is less expensive at roughly $600. Velocity readings from these two Stalker guns are compared first.
The experimental setup was simple. The pitcher stood about 40 feet away from a net and threw about 35 pitches toward the net. The guns measured the pitch speed from behind the net. A common technique for comparing readings of the same datum from different devices is a Bland-Altman plot. In this type of plot, the average of the two readings is shown on the X-axis and the difference between the two readings is plotted on the Y-axis. Bland-Altman plots are good at showing systematic error: in this case, systematic error means one gun is consistently slower, or faster, than the other and excessive variability between measurements. A Bland-Altman plot for the two Stalker radar guns is shown in Figure 2.
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Figure 2 shows that all but four of the velocity readings between the two Stalker guns were within one mile per hour of each other. This shows that these two guns don’t vary too much and can therefore be considered reliable. Three of the readings differed by two miles per hour and one reading differed by three miles per hour. Given the Stalker Sport 2 and the Stalker Pro II both have a margin of error of ± 3% (which is about two miles per hour at a pitch speed of 70 mph), all of the readings are within the margin of error.14 However, more of the readings differed from each other (18 total) than were the same (15 total). These data show that there can be considerable differences in radar gun readings even from reliable guns from the same manufacturer. This test demonstrates why it is unrealistic to believe any radar gun is accurate to within 0.1 mph in a real-world setting.
Pocket Radar (PR) is a relatively recent entry into the radar gun field. The PR devices do not have the traditional radar gun shape and look more like a smart phone than a gun. The firm’s main line has two products for baseball, the Ball Coach at about $300 and the Smart Coach at about $400. The accuracy of both devices is ±1 mph. Figure 3 shows a Bland-Altman plot for the PR Smart Coach compared to the Stalker Sport 2.
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Figure 3 shows that there is good agreement between these two guns. All of the readings but one are within one mile per hour. As with the two Stalker guns, this shows that the PR devices are reliable radar guns. The single reading with a difference of two miles per hour is within the Stalker’s ± 3% margin of error. In this comparison, 16 of the pitches had the same reading while 15 of the pitches had a different reading. As with the results from the two Stalker guns, this shows why you can’t count on any single radar gun reading as being exactly accurate.
The final comparison is between the Stalker Sport 2 and an older Bushnell radar gun. Bushnell guns are less expensive than the other models. This comparison shows what can happen in terms of accuracy with lower-priced guns. Figure 4 shows the Bland-Altman plot for these two radar guns.
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Figure 4 shows that there is a persistent lower-velocity reading bias for the Bushnell gun compared to the Sport 2. The overall average velocity for the Bushnell pitch data is 68.0 mph. The overall average velocity for the Sport 2 for the same set of pitches is 70.2 mph. This bias is clearly evident in the Bland-Altman plot. The Bushnell readings are consistently one to two miles per hour slower than the Sport 2. In addition, the range of the readings on the plot is wider, and there are more data points at the top and bottom of each range, than on the previous Bland-Altman plots. This shows that this less-expensive model is more likely to register an inaccurate reading than the higher-priced guns.
Intuition suggests that the technological advances that have led to the plethora of data now available from a major league baseball game would have made radar guns obsolete. It’s true that radar guns are no longer necessary at big-league ballparks. But the need for data extends beyond the 30 teams in MLB.
Players and coaches at all levels of the game, from the minors to high school and college, have the same desire for data. Advances in technology have lowered the price of radar guns to where participants in baseball at all levels can afford to satisfy their desire for data with their own radar guns. This has led to tremendous demand for radar guns and the boom in radar gun sales shown in Figure 1.
It is also important to be aware of two simple facts about radar guns. First, because of the physics associated with the way guns work, there is always a margin of error associated with every radar gun reading. The true velocity could be higher or lower than the reading. Second, accuracy varies from gun to gun. In general, the more expensive guns are reputed to be more accurate than the least expensive guns. However, just because a radar gun is more expensive does not necessarily mean it is more accurate. Both of these points are demonstrated in the Bland-Altman plots shown in Figures 2, 3, and 4.
DOUGLAS JORDAN, PhD is a professor emeritus at Sonoma State University in Northern California. He’s been a regular contributor to BRJ since 2014. He enjoys hiking and playing chess when he is not watching or writing about baseball. You can contact him at firstname.lastname@example.org.
I gratefully acknowledge the assistance I received from several individuals in the baseball community while researching this paper. I could not have written the article without their input and advice. I also need to thank three anonymous peer reviewers who provided comments on the original draft of the paper. The final result is significantly improved because of their input.
3. Vincent A Lizzio et al.,” Importance of Radar Gun Inclusion During Return-to-Throwing Rehabilitation Following Ulnar Collateral Ligament Reconstruction in Baseball Pitchers: a Simulation Study, Journal of Shoulder and Elbow Surgery, March 2020, https://pubmed.ncbi.nlm.nih.gov/31859036.
4. Physicist (and SABR member) Alan Nathan in his The Physics of Baseball web site, provides a spreadsheet that projects how far a baseball will travel. The web site is, http://baseball.physics.illinois.edu/trajectory-calculatornew3D.html. His spreadsheet shows that reducing ball exit velocity from 100 mph to 99 mph at a launch angle of 27.5 degrees lowers travel distance from 400.5 feet to 395.8 feet (a reduction of 4.7 feet).