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00005768-201112000-0001200005768_2011_43_2321_nagami_fastballs_12miscellaneous-article< 77_0_22_6 >Medicine & Science in Sports & Exercise©2011The American College of Sports MedicineVolume 43(12)December 2011p 2321–2327Spin on Fastballs Thrown by Elite Baseball Pitchers[APPLIED SCIENCES]NAGAMI, TOMOYUKI1,2; MOROHOSHI, JUN1; HIGUCHI, TAKATOSHI1; NAKATA, HIROKI3; NAITO, SHIGETO1,4; KANOSUE, KAZUYUKI31Graduate School of Sport Sciences, Waseda University, Saitama, JAPAN; 2Japan Society for the Promotion of Science, Tokyo, JAPAN; 3Faculty of Sport Sciences, Waseda University, Saitama, JAPAN; and 4Yomiuri Giants, Tokyo, JAPANAddress for correspondence: Tomoyuki Nagami, M.S., Graduate School of Sport Sciences, Waseda University, 2-579-15 Mikajima, Tokorozawa, Saitama 359-1192, Japan; E-mail: for publication March 2011.Accepted for publication April 2011.ABSTRACTPurpose: In this study, we analyzed the direction of the spin axis angles and the spin rate of baseballs pitched by elite collegiate and professional pitchers.Method: The video image of a ball being pitched was taken from the period just before release until 200 ms after release with a high-speed video camera at a rate of 1000 frames per second. A custom-made device was used to analyze the spin axis angle and the spin rate.Results and Conclusion: There were no significant differences in the direction of the spin axis angles or the spin rate between collegiate and professional pitchers. A significant correlation was obtained between spin rate and ball speed; that is, the higher the ball speed, the greater the spin rate. In addition, the spin rate deviated more across subjects than did ball speed. For all subjects, the azimuth and elevation of spin axis were 19° ± 14° and −32° ± 9°, respectively. Some of the pitchers were able to put a characteristic spin on their fastball; the nature of this spin could be related to their pitching success.Baseball pitchers manipulate ball velocity and trajectory to get hitters out. The vertical drop of not only breaking balls but also fastballs needs to be varied by the pitcher in order for these pitches to be effective. The delivery of the most successful fastball throwers is said to produce a ball that has “hop.” This term is well understood by batters but is only poorly understood by the fans who variously think that “hop” refers to a good pitch, a particularly fast pitch, or a pitch that “rises.” The latter term is the one used by batters. In fact, a pitch with “hop” does not actually rise but is only perceived to do so by the batter. Although it is not physically possible for a pitched baseball to rise, it can fall significantly less than the batter’s mind “predicts” based on the pitch’s initial characteristics. This leads the batter to “see” the ball as rising (8). Pitches with “hop” are quite difficult for batters to hit. Producing such an altered trajectory requires the production of an extraordinary spin rate and/or spin axis. Thus, for appropriate and efficient training, it is important that pitchers and their coaches understand the physical characteristics that determine the vertical and horizontal movements of thrown balls.Despite the importance of ball spin in baseball pitching, it has been rarely studied, because until recently it was too fast a phenomenon to analyze with the equipment that is ordinarily available. Therefore, most studies on baseball spin have used numerical simulation or wind tunnel experiments. In one such experiment, Briggs (3) measured the effect of spin and speed on the lateral deflection of a baseball by using a wind tunnel. He demonstrated not only the Magnus force, which is created by a pressure differential caused by ball spin, but also the drag crisis, in which a dramatic change in drag occurs under a particular combination of ball velocity and spin (4). Both the Magnus force and drag crisis influence pitch trajectory. Watts and Ferrer (11) and Alaways and Hubbard (1) suggested that the lift force of a baseball is proportional to spin parameter, rω/v, where r is the radius of the ball (m), ω is the spin rate (rad·s−1), and v is the translational velocity (m·s−1). Moreover, Nathan (10) filmed pitches thrown by a machine and verified that the lift coefficient, a dimensionless coefficient that relates lift generated by an aerodynamic body, does not depend strongly on v for fixed values of the spin parameter. However, it is difficult to make the jump from simulated results to how a pitcher should actually throw a ball to obtain a specific type of spin. Technological advances have made it possible to overcome earlier difficulties, and recent studies have measured the spin of pitched balls. Thus, Jinji and Sakurai (5) and Jinji et al. (6) made a detailed analysis of the spin rate and spin axis of fastballs and curveballs thrown by actual pitchers. They found that the lift force of a ball was closely correlated with the product of spin rate and the sine of the angle between the spin axis and the pitching direction, just as predicted by earlier theories. However, they only analyzed the pitches of ordinary collegiate pitchers and children.Therefore, to extend the findings of the previous studies, we set three objectives for this study. The first purpose was to create a new device for analyzing ball spin more easily compared with previous studies because previously existing methods required motion analysis software. The second purpose was to analyze the individual differences of fastball spin of elite pitchers because it remains unclear as to what the special characteristics of elite pitchers’ ball spins are. We were able to conduct an experiment on 11 professional pitchers and 11 pitchers who belonged to a top college baseball team. The final purpose was to provide coaches, pitchers, and trainers with scientifically based guidelines to help improve pitching skills.METHODSSubjects.The mean height, weight, and age (±SD) of the 11 collegiate and 11 professional pitchers that participated in the experiment were 1.81 ± 0.07 m, 75.5 ± 6.0 kg, and 21 ± 1 yr and 1.81 ± 0.05 m, 82.5 ± 4.0 kg, and 26 ± 6 yr, respectively. All of the players were healthy males who were active on their teams at the time of testing. Ten collegiate and seven professional pitchers were right-handed, and the others were left-handed. All collegiate pitchers belonged to the varsity team of a top-level university baseball league in Japan. All professional pitchers belonged to the Nippon Professional Baseball Organization (NPB), which corresponds to the highest baseball league in Japan. One of them (subject S) had played Major League Baseball in the United States. Informed consent forms approved by the Human Ethics Committee, Waseda University, were obtained from all subjects before obtaining any data.Experimental design and procedure.After completing the informed consent and history forms, the subjects warmed up until they felt ready to throw with a 100% effort. Each subject threw five “four-seam” fastballs from an official pitching mound to a catcher positioned behind home plate, which was at a standard distance (18.44 m) from the pitching plate. The four-seam fastball is the most common pitch thrown in baseball games. In this pitch, the ball rotates such that four seams move past a point just in front of the moving baseball. The collegiate pitchers used balls (Mizuno Corp., Osaka, Japan) authorized by the All-Japan University Baseball Federation, and the professional pitchers used balls (Mizuno Corp.) authorized by the NPB. To facilitate analysis of the spinning ball easily, two sets of the letters E, M, and I, which are easily distinguishable, were marked on the balls (Figs. 1A, B). A high-speed video camera (frame frequency = 1000 frames per second, exposure time = 1/10,000 s, resolution of xy = 640 × 480 pixels; Fastec Imaging Corp., San Diego, CA) was set 3.5 m behind the subjects at the height of ball release. The ball images were taken in the period from just before until 200 ms after release. Ball speed was measured with a radar gun (JUGS, Tualatin, OR) positioned behind the catcher.FIGURE 1. Analysis of ball spin. A, Custom-made apparatus for the ball spin analysis. B, Replication of ball orientation (bottom) based on ball spin recorded by the high-speed camera (top). C, Definition of the direction of ball spin axis with elevation ϕ and azimuth &thetas;.Ball spin rate and spin axis.Ball spin rate just after ball release was calculated from the number of video frames necessary for one rotation of the ball: 1000/number of frames (rotations per second, RPS).Orientation of the spin axis was obtained using a custom-made apparatus made of aluminum frames (Tri-Axis Feature; Furusawa Lab, Saitama, Japan; Fig. 1A). The ball used in a particular trial was subsequently mounted in the center of the apparatus. The ball could then be rotated on axis A, which could then be tilted around axis B and axis C so that ball spin with any orientation in three-dimensional space was able to be reproduced (Fig. 1A). The rotation angle around each axis was measured on a protractor attached in the proper orientation to evaluate the angle of that axis. The ball image taken in the experiment was displayed on a video monitor in which the direction of the ball’s translational movement corresponded to the direction of depth. A video camera was set above the apparatus, and the image of the camera was displayed on another monitor. The experimenter compared the marks on the balls in the two video images side by side and adjusted the relative setting of the ball and direction of the two axes (B and C) of the apparatus so that the two images coincided (Fig. 1B). The direction of the spin axis was obtained when the whole set of experimentally obtained ball images in one rotation could be matched with the ball images on the apparatus only by rotating the ball around axis A.The direction of the spin axis was defined by the right-hand rule (2). The x-axis was directed from the pitcher’s plate to third base, the y-axis was directed to home plate, and the z-axis indicated a vertical (upward) direction. The orientation of the ball spin axis was expressed using two parameters, elevation ϕ (the angle between the spin axis and x–y plane) and azimuth &thetas; (the angle between the x-axis and the projection of the spin axis on the x–y plane), as was described by Jinji and Sakurai (5) (Fig. 1C). The direction of the spin axis and the spin rate for each subject were reported as the mean of five pitches. For comparisons between pitchers, elevation (ϕ) and azimuth (&thetas;) for the left-handed pitchers were obtained by converting the original data into symmetrical values about the y–z plane. During preliminary experiments, we evaluated the precision of the method. The angles were measured to a precision of 2.5°.Statistics.We analyzed the mean and SD for ball spin rate, ball speed, angle of elevation ϕ, and azimuth &thetas; for each subject. Pearson product–moment correlation coefficients were calculated to determine the relationship between ball spin rate and ball speed as well as the relationship between the angles of &thetas; and ϕ. Student t-tests were used to assess significant differences between collegiate pitchers and professional pitchers for each variable. A probability of P < 0.05 was chosen to indicate significance.RESULTSSpin rate and ball speed.Table 1 shows ball speed, spin rate, and orientation of spin axis (&thetas;, ϕ) of each subject for both collegiate and professional pitchers. The initial speeds of collegiate and professional pitchers were 37.7 ± 1.2 m·s−1 (135.6 ± 4.4 km·h−1; 84 mph) and 37.6 ± 1.2 m·s−1 (135.5 ± 4.4 km·h−1; 84 mph), respectively. The spin rates of collegiate and professional pitchers were 35.6 ± 4.2 and 33.0 ± 2.1 RPS, respectively. There was no significant difference between these values for the two groups. A significant correlation was obtained between the spin rate and ball speed; the higher the ball speed, the greater the spin rate (r = 0.477, P < 0.05; Fig. 2A). Figure 2B depicts a similar relationship between ball speed and spin rate, but in this case, each value is normalized to the mean value. Note that between subjects, spin rate has more scatter than ball speed, where the values are packed into a range of 1.0 (±0.1).TABLE 1 Subjects’ profiles and characteristics of pitched balls.FIGURE 2. A, Relationship between initial ball speed and ball spin rate. B, Variability of initial ball speed and ball spin rate.Orientation of spin axis.The azimuth (&thetas;) values of spin axis in collegiate and professional pitchers were 19° ± 14° and 19° ± 15°, and the elevation (ϕ) values were −33° ± 9° and −32° ± 8°, respectively (Table 1). There was no significant difference between the values of the two groups. The azimuth (&thetas;) was widely distributed and ranged between −3° and 52°. On the other hand, the elevation (ϕ) exhibited a narrower range of about 30° ± 10° except for subject F (Fig. 3). This pitcher used a side-arm delivery, while all the others threw overhanded. The azimuth (&thetas;) and the elevation (ϕ) as defined here can be initially difficult to grasp. To further elucidate these definitions, the spin axes from the pitcher’s view (A) and from the top view (B) are shown in Figure 4. The axis tilt in the pitcher’s view determines the direction of the Magnus force acting on the ball. The azimuth (&thetas;) is the angle between the spin axis and the x-axis in the top view (Fig. 4B).FIGURE 3. Relationship between elevation ϕ and azimuth &thetas;.FIGURE 4. The direction of spin axes: view from pitcher (A) and view from top (B).DISCUSSIONThe aim of this study was to understand the characteristics of the spin put on fastballs thrown by elite baseball pitchers, using a new apparatus to establish the spin axis. The results indicated that there were no significant differences in the various characterizations of spin properties (translational speed, spin rate, and orientation of spin axis) between balls thrown by collegiate and professional pitchers. This suggests that the quality of the collegiate pitchers in the present study is comparable to that of the professional pitchers, at least relative to the spin properties they impart to the ball. Indeed, 4 of the 11 collegiate subjects (B, C, F, and G) played in the NPB after they participated in this study. Clearly, however, the pitchers’ quality does not depend solely on the spin properties of their fastball. Nevertheless, elucidating the spin properties of the most used pitch is an important step in the development of a method that permits scientific evaluation of the performance of elite pitchers.Spin rate and ball speed.There was a correlation between initial ball speed and spin rate (Fig. 2A) over the speed range of 36–40 m·s−1 (81–89 mph). Jinji et al. (6) obtained a similar correlation at a lower range of ball speeds (20–36 m·s−1; 45–81 mph). Interestingly, the regression of ball speed on spin rate produced almost identical values in the two studies (Fig. 5). This would suggest that common factors, such as finger/arm movements and orientation, determine both the ball speed and spin rate that pitchers produce over a wide range of force imparted to the ball (6). An understanding of the exact mechanisms involved will require further study. Still, the coefficient of variance was greater for spin rate than for ball speed (Fig. 2B): that is, even at the same ball speed, there is a definite variation of spin rate between individuals. This result suggests that spin rate is, to some extent, influenced by factors that are separate from ball speed.FIGURE 5. Comparison of the results of Jinji et al. (6) with those of the present study.Orientation of spin axis.The mean value of elevation (ϕ) for all pitchers was −32° ± 9° (Table 1 and Fig. 4A). No pitcher in the present study threw a fastball with perfect backspin, that is, &thetas; = 0° and ϕ = 0°, as was also found in a previous study (6). The larger the absolute value of elevation, the smaller the lift force and the larger the side force that acts on the ball. Thus, all fastballs thrown by right-handed and left-handed pitchers in the present study move to the right and left, respectively, when viewed from the pitcher’s mound. The elevation fell over a range of about −20° to −40° for all pitchers except one: subject F. He used a side-arm delivery, while the others all used the overhand or three-quarter types of delivery. Therefore, the elevation probably depends on pitching style or on throwing arm slot angle in the x–z plane. This should be quantitatively clarified in future studies.The mean value of azimuth (&thetas;) for all subjects was 19° ± 14° (Table 1 and Fig. 4B). The larger the azimuth, the smaller is the lift force that acts on the ball (9). Individual differences in azimuth were greater than those of elevation. The azimuth is mainly determined by the spatial orientation of the palm at the moment of ball release. When a pitcher throws a fastball, forearm pronation occurs. When the forearm is beside the head, the palm of a right-handed pitcher faces toward the first base. Palm position changes as the arm swings forward and eventually faces toward the front. Thus, the azimuth depends on where the ball is released in the front–back plane. The fact that there are large interindividual differences in azimuth indicates that there are large differences in the position of ball release.Function of the fastball.The four-seam fastball that the present study focused on is used by pitchers to overpower hitters, primarily because of the high velocity. The faster the pitch, the more effective it will be. From a certain point in a pitch’s trajectory, batters actually can no longer react (owing to the time necessary to process the information and initiate the swing) and must make a decision at this point whether, and how, to swing at the ball. Thus, they have to form a mental prediction of where the ball will subsequently travel. This gives them a chance to have the swinging bat at the right place at the right time. It requires many, many hours of practice to acquire this predictive ability. However, it is very difficult to tailor the long practice sessions to match the delivery patterns of individual pitchers. As a result, the trajectory the batters learn to expect is probably one for the “average pitcher.” For example, for the top collegiate and professional players such as the subjects in the present study, the average ball speed is about 38 m·s−1 (140 km·h−1; 87 mph), and the spin rate corresponding to this “average” speed is about 35 RPS (Fig. 2A). Thus, batters probably adopt the trajectory of the average speed and spin in establishing their “prediction.” Conversely, the pitcher who can throw a pitch whose trajectory deviates from the average batter’s “prediction” will be at a clear advantage. There are two ways to gain this edge. The first is to throw a ball of extraordinarily high speed. The rationale in this case is to deliver a ball that passes through the batter’s information processing window before the batter has time to process how fast the pitch is moving and where it will be when the ball is in the impact area. The second possibility is to deliver a ball with an unusual spin. Even if the speed is within the average range, a ball with a spin that deviates to a large degree from that of the “average ball” will have a trajectory that is quite different from that of the batter’s “prediction” and will often be mishit. The orientation of the spin axis should also be taken into account. Lift force (not necessarily in the vertical direction) produced by the ball’s spin is maximum when the spin axis is perpendicular to the ball’s translational movement. In addition, if the axis is horizontally oriented, the lift force becomes purely upward, making the ball appear to “hop” (rise), and if the axis is vertical, the lift force is purely sideways. In the situation where the spin axis is in parallel with the translational movement (the so-called “gyroball,” which has a spin axis of &thetas; = 90° and ϕ = 0°), there is no lift force at all and the ball will fall farther than expected. Of course, the ball with such extreme condition in spin would be rare. However, there were indeed wide variations in spin rate and orientation of spin axis in the pitches thrown by the subjects of our study, and to a certain extent, these characteristics could be related to the pitchers’ overall performance as explained in the following section.Ball spins of individual subjects.Subject C, one of the collegiate pitchers, was the closer of his team and a member of the collegiate national team in 2009 and 2010 (Table 1 and Fig. 2). He led his league in strikeouts per nine innings for his collegiate league in 2009 and was the No. 1 draft pick not long after participating in this experiment. Batters facing him described his fastball as having good hop. In our study, the spin rate of his fastball was greater than that of other pitchers who threw fastballs with a similar speed; in fact, his spin parameter was higher than that of any other subject. Moreover, his fastball spin axis angles, both &thetas; and ϕ, were also the closest to 0°, that is, to a ball with straight backspin among all the subjects. These data confirm the batters’ judgment that his fastballs had good “hop.” Our physical measurements indicate that his pitches would have a larger upward lift force than fastballs with similar speed thrown by the other pitchers. As a consequence, batters would have a very difficult time anticipating the correct trajectory of the fastballs thrown by subject C and thus would often miss the ball.Another instructive pitcher is subject S (Table 1). At the time of the experiment, he was playing in the NPB and had previously played Major League Baseball in the United States. He had played as professional baseball player for 18 yr. He has excellent pitch control and carries the nickname of “Mr. Control.” He has the ability to throw eight distinctively different types of pitches (Nagami et al., unpublished observations). The &thetas; and ϕ angles of his fastball spin axis are bigger than those of almost any other subject, so his fastball would drop more than that of other pitchers, making the batters’ “predictions” wrong and therefore his pitches difficult to hit.Application for training.In Japan, most pitching coaches consider a good fastball to have a spin axis that is aligned horizontally (ϕ = 0°) and perpendicular to the direction of movement (&thetas; = 0°). The fact that no pitcher so far analyzed throws a fastball with this perfect backspin might mean that it is impossible, or at least very difficult, to throw it. But coaches could give more effective guidance to pitchers by taking each pitcher’s individual characteristics into account. For example, working on the body movements of a pitcher with a large &thetas; angle to reduce the angle to 0 or prescribing supplemental training to a pitcher whose pitched balls have a low spin rate could improve the effectiveness of these pitchers. However, the specific remediation methods required by these examples are currently unknown. At present, there are no studies that relate body motion to ball spin. Definite advances will be made if future studies are able to successfully address this relationship.This study was partly supported by a ``Yamaha Sports challenge research grant,’’ the Waseda University Global COE program ``Sport Sciences for the Promotion of Active Life,’’ and Grant-in-Aid of Ministry of Education, Culture, Sports, Science and Technology, Japan (22650150). The authors appreciate Prof. L. Crawshaw and Prof. T. Yanai’s advice in preparing the article.The authors report no conflict of interest.The results of this study do not constitute endorsement by the American College of Sports Medicine.REFERENCES1. Alaways LW, Hubbard M. Experimental determination of baseball spin and lift. J Sport Sci. 2001; 19: 349–58. [Context Link]2. Bahill AT, Baldwin DG. Describing baseball pitch movement with right-hand rules. 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[CrossRef] [Context Link] SPIN AXIS; SPIN RATE; BALL SPEED; PROFESSIONAL|00005768-201112000-00012#xpointer(id(R2-12))|11065213||ovftdb|SL00003172200737100111065213P60[CrossRef]|00005768-201112000-00012#xpointer(id(R2-12))|11065405||ovftdb|SL00003172200737100111065405P60[Medline Link]|00005768-201112000-00012#xpointer(id(R5-12))|11065213||ovftdb|SL001364902006519711065213P63[CrossRef]|00005768-201112000-00012#xpointer(id(R5-12))|11065405||ovftdb|SL001364902006519711065405P63[Medline Link]|00005768-201112000-00012#xpointer(id(R7-12))|11065213||ovftdb|SL0000646419901954511065213P65[CrossRef]|00005768-201112000-00012#xpointer(id(R7-12))|11065405||ovftdb|SL0000646419901954511065405P65[Medline Link]|00005768-201112000-00012#xpointer(id(R9-12))|11065213||ovftdb|SL0000867920077611911065213P67[CrossRef]|00005768-201112000-00012#xpointer(id(R9-12))|11065405||ovftdb|SL0000867920077611911065405P67[Medline Link]|00005768-201112000-00012#xpointer(id(R10-12))|11065213||ovftdb|SL000086791987554011065213P68[CrossRef]10.1119%2F1.14969Spin on Fastballs Thrown by Elite Baseball PitchersNAGAMI, TOMOYUKI; MOROHOSHI, JUN; HIGUCHI, TAKATOSHI; NAKATA, HIROKI; NAITO, SHIGETO; KANOSUE, KAZUYUKIApplied Sciences1243