Thesis Committee Members
Dr. Youngmin Yoon- Eastern New Mexico University Assistant Professor, Kinesiology
Dr. William Andersen- Eastern New Mexico University Professor of Physics
Dr. Weizhong Tian- Eastern New Mexico University Assistant Professor of Statistics
Dr. Alan Nathan- University of Illinois at Urbana-Champaign Professor Emeritus of Physics
The proper way to swing a baseball bat has always been a highly debated skill. Numerous theories exist in regards to what is considered the ideal baseball swing bat path. Also, numerous theories exist as to which type of batted ball gives a hitter the best chance to get on base. This study looks to create a clearly defined answer to the question of what type of swing and batted ball gives a hitter the best chance for in game success. This information will give the baseball world better information to drive instruction and player development in the area of hitting. In order to find the ideal bat path and batted ball three questions need to be addressed:
1. What is the ideal batted ball outcome?
2. What type of bat-ball collision most consistently creates the ideal batted ball outcome?
3. Which bat path most consistently creates the ideal batted ball collision?
With the recent technology surge in baseball and the availability of it on the consumer market, a much more in-depth approach can be taken to answer these questions.
CHAPTER 1: INTRODUCTION
The evolution of environmental constraints of a baseball game have shaped hitting theory throughout baseball’s history. The equipment, rules, playing surface, and players themselves all contributed to what type of swing path would be successful over the course of a baseball season. Hitters self-organized the optimal swing coordination patterns needed to succeed while interacting with the contextual demands of in game environments. (Newell, 1986) This review will start by looking at how the different eras of historical environments in Major League Baseball (MLB) shaped hitting theory.
In the 1850s and 1860s, club teams were very popular as Major League Baseball wouldn’t be formed until 1903. (Augustyn, 2020) Club teams desperately needed players and would often invite inexperienced players to fill out their rosters. To adapt the game to these novice players, rules were adjusted, such as an out could be made as long as the baseball was caught within one bounce. (Diamond, 2020) This rule created an environment where balls hit in the air were easier to convert into outs. Groundballs were harder to field partially due to gloves not being commonly used in baseball until the start of the 19th century. (Stamp, 2013a) Pitchers made their own baseball before the game. Pitchers would often loosely wrap the yarn around the core of the baseball so it wouldn’t be as lively. Left over rubber pieces from shoemaking were typically used as the core of the ball. The production materials of the baseball often varied as there were reports that some regions would use the eye of a sturgeon fish for the core of the baseball. The same baseball would be used for an entire game, causing the ball to lose its “liveliness” due to repeated strikes to the ball from the bat. No standardized baseball was used until 1876, choosing to use Spalding’s rubber core baseballs. (Stamp, 2013a & Rymer, 2013) Playing fields were poorly maintained, causing unpredictable hops on groundballs. The 35 most error prone seasons in MLB history all happened before 1918. (Diamond, 2020) In 1884 there were 14,556 errors in a single season, the most ever recorded. By comparison the most errors in a season in the past twenty years happened in 2001 with a grand total of 3357. Fielding percentage between 1871-1920 was .924%, compared to the .983% fielding percentage of the past twenty MLB seasons. (Palmer & Gillette, 2020a) With bad equipment, poorly maintained fields, one hop fly ball outs and defensively error prone environments the groundball would quickly become the ideal batted ball of early baseball games.
In 1920 Spalding began using tightly wound Australian wool inside the baseballs. This new production method caused the baseball to be livelier and the term “Rabbit Ball” was frequently used to describe the new baseball. The Rabbit Ball was tightly wound, smoother, and the laces were “countersunk so as to be flush with the leather of the seam.” Starting in the 1920s baseballs were being switched out more frequently during games. Previously, one baseball would be used as long as possible during a game. The baseball would become scuffed up and softer from the abuse of contact, this caused the baseball to have lower coefficients of restitution and be less aerodynamic. The new “Rabbit Ball” performance was due in part to the new method of production. Also, in part to umpires constantly switching out new baseballs during the game. (Dodd, 2019) As the U.S. plunged into WWII and rubber was deemed a needed war material baseball had to get creative and began using “balata” in the middle of the baseball. In the decade prior to 1943, MLB averaged 4.73 runs per game and .546 homeruns (HRs) per game. Offensive production during the 1943 season was down to 3.91 runs per game and .37 HRs a game across the league and it is possible it was due in part to the balata core of the baseball. (Rymer, 2013) However, it is just as likely that the decline in offensive production could have been due to many of MLB’s best hitters serving in WWII. In 1944 rubber cores were put back into the baseball and offensive production increased to 4.17 runs and .42 HRs per game. The increase continued into the 1950s with HRs at the highest rate they’d ever been, .85 HRs per game over the course of the decade. (Palmer & Gillette, 2020b)
Baseball has always been regarded as the “thinking man’s game”. According to Henry Chadwick in The Art of Batting and Baserunning published in 1886, all efforts of the hitter should be put towards sharp groundballs and a willingness of the batter to sacrifice his own record to “play for the side”. (Diamond, 2020) Spalding’s Official Base Ball Guide was published in 1896. The book adamantly condemns slugging or trying to hit a HR, calling sluggers “stupid”. Henry Chadwick writes there is no skill involved in hitting a HR and that a “scientific & skilled hitter” can tap the ball over the infielders and bunt the baseball. According to Chadwick, the ideal hit is a “placed hit”. HRs do not allow the defense to put forth any effort as the ball is no longer on the field and were deemed less desirable. The strategy of hitting sharp groundballs and sacrificing an at bat to advance a runner was championed by Chadwick and would solidify hitting theory for decades to come. (Chadwick, 1896) The next book on hitting instruction would not be published until 1968 by Ted Williams. The Science of Hitting would be a paradigm shift in regards to hitting strategy that opposed Chadwick’s viewpoints on the topic. Williams spoke of an uppercut bat path and putting the ball in the air. (Figure 1-1) For more than a century hitting theory had prioritized hitting a groundball and sacrificing a hitter’s at bat to advance the offensive position of the team. William’s strategies of pulling the baseball in the air to maximize offensive production of the hitter was not a very popular strategy in the baseball world as it directly questioned the old paradigm.
The next environmental constraint that would change the path of hitting theory would be changing the height of the pitcher’s mound in 1969. After pitchers dominated the 1968 MLB season, the height of the mound changed from fifteen inches to ten inches. From 1951-1968, HR rates per game was .84. The following eighteen seasons from 1969-1986 saw a decreased HR rate of .76 per game. (Palmer & Gillette, 2020b) Lower pitch vertical release angles and flatter pitch descent angles could have caused the decrease in HR rates. The hitters self-organized their bat-paths to the lower pitch descent angles, therefore causing lower attack angles, lower launch angles, and fewer HRs. It was also during this time period that the influence of Charlie Lau and his straight down to the baseball, low line drive hitting approach gained momentum as the most popular hitting theory of its time. In 1966, Astroturf made its debut in MLB. With it came another change to the game that further strengthened the strategy of hitting more groundballs. The baseball traveled faster on the new surface. In 1980, teams playing on turf fields hit 42% more triples than teams who played on a grass field. Teams who played on turf also saw a slight reduction in HRs. There seemingly was no benefit to hitting on a turf field with batting averages resulting in .2649 on grass fields, .2641 on turf fields. (Seaver, 1981) Research on The Effect of Artificial Turf vs. Grass compiled by David W. Smith shows a similar trend. Between 1984-1994 grass fields in MLB averaged a .259 Batting Average (BA), while turf fields averaged a .258 BA. Triples and doubles were both more prevalent on turf fields during the same time period. Turf fields were first introduced to MLB in 1966; with it MLB started to see a decline in HRs per game. As more turf fields were installed throughout MLB, HRs per game were the lowest in the past seventy years during the 1970s and 1980s. Eleven new ballparks were built between 1990-2000 and with it the phasing out of turf fields. HRs per game then rose as well from .79 in 1990 to 1.17 in 2000. The perceived benefit of using the speed of the turf to create more base hits was no longer an option for hitters and another adaptation took place. The straight down to the baseball swing that became popular with Charlie Lau and turf fields would begin to run into “Chicks Dig The Longball” and the Steroid Era. In 1987 HRs per game would go above 1.0 for the first time in MLB history. Fielding percentage would also reach .980% for the first time in league history. (Palmer & Gillette, 2020a) The year 1987 was the introduction to a new era of hitting in baseball. Ever climbing strikeout and HR rates and the best defensive fielding in MLB history (Figure 1-2) replaced the “Scientific and Skilled” approach of the early 19th century. The environment and task of the current state of the game of baseball is vastly different than the time periods in prior decades.
Batted balls will be classified using Statcast’s defined ranges as either a flyball (25-50 degrees), groundball (Less than 10 degrees), or a line-drive (10-25 degrees). (Statcast: Launch Angle. 2020) The ideal exit velocity and launch angle will also be examined. Finding a batted ball that gives hitters the largest chance for success will provide the desired outcome when measuring the various baseball bat attack angles. Data provided by the company 6-4-3 Charts, which tracks and analyzes data for all levels of the National Collegiate Athletic Association (NCAA) Baseball, paints a clear picture of what the ideal batted ball should be. Most colleges do not have a Trackman unit or any other type of radar tracking device. The initial clarification of the batted ball launch angles for 6-4-3 Charts Data was left to the interpretation of the sports information direction of the particular game. For MLB Data, the Statcast database via Baseball Savant was used to filter the analytics.
Based on tables 1-1 through 1-4, an observation of success can be seen between line-drives and batting average in NCAA Division I Baseball and MLB. Line-drives were more than .500 batting average points higher than flyballs and groundballs in the NCAA in both seasons. MLB recorded that line-drives were over .400 batting average points higher as compared to groundballs and flyballs. Line drives (10-25 degrees) in MLB baseball from 2015-2019 resulted in the highest wOBA, exit velocity, and BABIP among all batted ball types. Line-drives also accounted for the smallest percentage of outs made during the 2018 and 2019 seasons of NCAA Division I Baseball. (Table 1-1, 1-2)
|Batted Ball Type||Percentage of Outs Made||Batting Average|
|Batted Ball Type||Percentage of Outs Made||Batting Average|
|Batted Ball Type||Batting Average||BABIP||wOBA||Exit Velocity Average (mph)||HRs|
|Batted Ball Type||Pull||Center||Opposite||Overall|
In MLB a groundball is an out 75.5% of the time. (Verducci, 2018) Mike Schmidt claimed that 95% of all flyballs are certain outs and are always less productive than groundballs. Taking a deeper look into 2018 MLB batting average on balls in play by field (BABIP), line-drives still remain the clear leader in batted ball results. It should be noted that flyball BABIP is misleading because HRs are not counted towards BABIP and most HRs are considered flyballs. However, it is interesting to note that groundball BABIP more than doubled in comparison from pull side groundballs to opposite field groundballs. (Table 1-4) In terms of run production, line-drives produce 1.26 runs per out, flyballs produce .13 runs per out, and groundballs produce .05 runs per out at the MLB level. (Slowinski, 2010) After looking at the data it is clear that hitting a line-drive is the ideal batted ball outcome and that groundballs are less offensively productive than flyballs at the MLB level.
The optimal launch angle for HRs is 24-26 degrees. (Sawicki, Hubbard, & Stronge, 2003) According to well renowned baseball writer Tom Verducci, in 2017 the sweet spot for HRs in terms of launch angle and exit velocity was 26 degrees at 90-plus mph. More HRs were hit at this launch angle than any other in that year. Performing a Baseball Savant Statcast search showed that in 2015, 2016, 2018, 2019 a launch angle of 27 degrees produced the most HRs. Statcast classifies a hard-hit ball as any ball with an exit velocity over 95mph and anything under a weakly hit ball. Hard-hit balls in 2018 resulted in a .524 BA and a .653 wOBA. In comparison weakly hit balls resulted in a .219 BA and a .206 wOBA. Performing a search in the same database for the launch angles with the highest batting average and wOBA it was discovered from 2015-2019 launch angles from 10-15 degrees averaged a 93mph exit velocity, a .757 BA, .733 wOBA, and 27 HRs. The Science of Baseball by Terry Bahill states that a launch angle of 27-32 degrees is the most desirable for HRs, while a 10-15 degree launch angle is better for a high batting average. In an article written by Dave Sheinin in 2017, the sweet spot for the highest hit probability is a launch angle between 25-35 degrees and an exit velocity of 95-plus mph. Batted balls hit at a launch angle between 25-35 degrees from 2015-2019 resulted in a .397 batting average, .631 wOBA, an average exit velocity of 90.5mph, and 18,452 HRs. To classify the ideal batted ball in this experiment, the goal will be an exit velocity at or above 95mph. This study will examine which swing will produce the ideal high batting average launch angle of 10-15 degrees and the optimal HR launch angle of 25-35 degrees.
CHAPTER 2: LITERATURE REVIEW
The Level Swing
The most commonly taught baseball bat attack angle is that of the “level” swing. For the purpose of this study a “level swing” will be defined as any swing with an attack angle of zero to four degrees upward on a horizontal plane at the time of impact with the baseball. It is believed that having a completely horizontal swing at impact with the baseball will result in the best plate coverage and maximize the chance for success. Major League Baseball Hall of Famer Mike Schmidt stated in his book The Mike Schmidt Study that pitches thrown from a pitcher towards the catcher level off on their way to home plate due to the amount of backspin imparted on the ball by the pitcher, so a hitter must swing with a zero vertical bat angle and a level attack angle to match the pitch plane. If a hitter’s vertical bat angle becomes steeper than 45 degrees, Schmidt claims the effects of gravity pulls the head of the bat into a “loopy” swing and negatively effects hip rotation. (Schmidt & Ellis 1994, Rose & Golenbock 1980) MLB career hits leader Pete Rose and former influential MLB Hitting instructor Charlie Lau are in agreement that a hitter should try to swing a bat completely level at contact. While Pete Rose believes in producing a level swing path throughout most of the swing, Lau and Schmidt state that swinging down on the baseball to get on top of the baseball helps produce a more level swing for hitters. Lau’s belief was that by encouraging hitters to swing down and to get on top of the baseball it would cancel out their natural tendency to uppercut. (Schmidt & Ellis 1994, Rose & Golenbock 1985, p. 114-115)
The Undercut Swing
An undercut swing is any swing of the baseball bat that produces a negative attack angle at impact with the baseball. Former MLB All-Star and Most Valuable Player Alex Rodriguez has recently taken to YouTube to better explain this hitting style. Claiming that a hitter should swing down on a baseball to impart backspin to the baseball and get the ball up in the air. Rodriguez compares the baseball swing to a golf swing stating, “You swing down to get the ball up”. Rodriguez also makes the claim that swinging down or having a “line-to-line” swing is more conducive for contact. (Rodriguez, 2019)
Former Detroit Tiger’s Hitting Coach Lloyd McClendon explained to Fangraphs.com what the philosophy is behind swinging down at the baseball. McClendon instructs hitters to strike the top half of the baseball while driving the hands down through the baseball. The belief is by driving the bat downward the hitter can impart backspin to the baseball. The imparted backspin will then help the baseball travel a much further distance. (Verducci, 2018) MLB hitter Anthony Rendon credits his success to being able to impart backspin on the baseball by swinging down on the baseball, striking it just above the mid-line and driving down through the baseball. (Wagner, 2013) No reference to vertical bat angle was found or mentioned in regards to an undercut swing.
The Upper Cut Swing
An uppercut swing will be defined in this study as any swing that has an attack angle of five degrees or higher at the time of contact. Sawicki, Hubbard, & Stronge suggest that a 9 degree uppercut is the ideal swing plane for HRs. Ted Williams believed an uppercut in the range of 4.5-15 degrees was needed in order to cover the angles various pitches cross the plate. (Williams & Underwood, 2013) The average attack angle in MLB from 2015-2017 was 12.4 degrees. (Marshall, 2017) Dr. Alan Nathan, Terry Bahill, and Tom Verducci all agree that a fastball should be swung at with a 6 degree attack angle and a curveball swung at with a 10 degree attack angle. Dr. Nathan stated a 6-degree attack angle will put you on plane with the pitch, but an 18-degree attack angle is optimal for distance. Nathan also mentioned that an 18-degree attack angle could make a hitter more susceptible to swing and misses. (Nathan, 2015, p. 7) Baseball think tank Driveline Baseball has stated players should have a different attack angle based on their exit velocity. If the hitter averages under 105mph then the attack angle should be 5-15 degrees, while over 105mph the hitter should focus on 10-20 degrees. Baseball tech company Blast Motion Baseball designs bat sensors to read metrics of a hitter’s swing. While collecting data, Blast Motion has discovered that the MLB average for attack angle was 8 degrees and can range from 2-16 degrees. Blast Motion also confirms that fastballs typically travel along a 6-degree angle and curveballs travel along a 10-degree angle. Having a flatter vertical bat angle makes it more difficult to square up inside pitches. Blast Motion has found the MLB average for vertical bat angle to range from -25 degrees to -35 degrees. According to Fangraphs Columnist D.K. Willardson, a flatter vertical bat angle can also cause a higher rate of infield flies. Increased vertical bat angle decreases the likelihood of clipping the bottom of the baseball, decreases back spin, and creates a lower launch angle range. (Willardson, 2018) These are all results that would help increase offensive output numbers.
Pitch Descent Angle
A pitch thrown from a pitcher will travel downward within a range of -4 to -21 degrees. (Ochart, 2018) As stated previously numerous entities agree that the average fastball crosses the plate at -6 degrees and the average curveball crosses the plate at -10 degrees. (Nathan, 2015, Bahill, 2019, Blast Motion) Mike Schmidt argued that while the pitch starts out on a downward plane initially the backspin imparted on the baseball by the pitcher will cause the pitch to flatten out around 15 feet in front of home plate, giving the baseball a zero descent angle.
Physics, Backspin, and Baseball Aerodynamics
Imparting backspin to the baseball during the swing has been taught to hitters for decades. The idea is the more backspin a hitter can impart into the baseball, the further the baseball will travel. The more backspin rpms that a batted ball has the longer it will stay in the air and the more distance it will travel (Cross, 2009) Alex Rodriguez and MLB hitting coaches Lloyd McClendon, and Victor Martinez all believe that imparting backspin to the baseball via a negative attack angle will increase the distance the baseball travels. (Rodriguez, 2019 & Verducci, 2018)
Momentum is transferred in a linear plane. As backspin rpms increase, optimum launch angle decreases. (Sawicki, Hubbard, & Stronge, 2003) Ball spin has been shown to increase the lift on the baseball. However, the type of collision needed to impart high amounts of backspin to the baseball significantly decreases the linear momentum transferred to the baseball. (Kensrud & Smith 2013) Baseballs hit with less spin have higher exit velocities and baseballs hit with higher spin rates carry further. There is a tradeoff between exit velocity and backspin, you sacrifice one for the other. A balance of both is the desired outcome. (Sawicki, Hubbard, & Stronge, 2003, Cross 2009, & Kensrud & Smith 2013) The “offset” (Figure 2-1) or the vertical distance between the center of mass of the baseball and the center of mass of the bat directly influences the tradeoff between exit velocity and batted ball spin rates. (Nathan, 2015) The offset in regards to this study will be launch angle subtracted from attack angle (launch angle – attack angle =offset). The centerline angle is the angle the “normal force” of batted ball collision follows in relation to the horizontal plane.
The centerline angle is determined by the offset. Where the attack angle strikes the baseball in relation to the centerline will greatly influence the spin direction of the baseball. (Nathan, 2015) The ability to measure and calibrate the center of masses of the bat and ball is beyond the capabilities of this study and the centerline angle will not be measured.
Recently, the company Rapsodo has introduced a ball flight tracking unit to the baseball industry. Rapsodo has found the ideal spin rate for a batted ball to range between 1500-2500rpms. Anything above 3000rpms is likely due to too much linear momentum going into the spin of the baseball and not the exit velocity. (Kensrud & Smith, 2013) Lift on the baseball does increase with the rate of spin. However, after 2500rpms the effect starts to plateau. After 3000rpms the air drag on the baseball begins to decrease distance and increases the baseball’s hangtime. (Nathan et al., 2006 & Sawchik, 2019) After analyzing the research the ideal batted ball for this study should sit in the range of 1500-2500rpms.
CHAPTER 3: METHODOLOGY
The comparison of the correlational relationship between negative, level, and positive attack angles and batted ball outcomes used a quantitative approach to collect data. One hundred and twenty-five samples were collected per swing type. The rational for using one hundred and twenty-five batted balls is as follows:
- 502 plate appearances are required to be eligible for a batting title.
2. MLB wide batting average in 2018 was .248. (Palmer & Gillette, 2020)
3. 125/502 =.249.
The experimental design used current and former college baseball players ranging in ages from 18-40. The players hit a baseball shot out of Hack Attack Three-Wheeled Pitching Machines set to 75mph at 46ft and set at a downward angle of -6 degrees using any BBCOR approved metal bat. The Rapsodo Hitting Unit (Rapsodo, 2018) was used to track pitch speed and a variance of speed ranged from 68-72mph. Each player took twenty swings off the machine using a positive attack angle, then level attack angle, and then twenty swings with a negative attack angle. The pitching machine will be set at 46ft so that it will be more accurate at the closer distance. It is also set to 75mph to mimic the reaction time of a 90mph fastball from a regular 60ft mound. Convenience sampling will be used with the access to available current and former college baseball players. Repeatable measures will be used to compare swing paths. Quantitative data collection and analysis will be used in the case study of whether fly balls, line drives, or groundballs result in the high chance of in game success in regards to batting average and HRs. A qualitative data collection will be used to determine if a ball struck the barrel of the bat during the collision. Any ball that was hit off the handle of the end cap will not be used at it could skew the datasets.
An Edgertronic high speed camera was used to capture batted ball collision and spin imparted to the baseball after contact from the various baseball bat attack angles. The Edgertronic Camera allowed for a high-speed observational video analysis of batted ball contact. The camera was placed behind contact and to the side of contact. A Blast Motion Baseball Bat Sensor was used to capture all bat metrics and monitor the attack angles and vertical bat angle of hitters’ swings during the experiment. A Rapsodo Hitting Unit calculated exit velocity, spin rates, spin axis, distance traveled, and launch angles of every batted ball. (Rapsodo, 2018a) Exit velocity, launch angle, distance, spin rate, attack angle, spin direction, and vertical bat angle was entered in a Microsoft Excel spreadsheet in real time as the experiment was being conducted. Time stamps between the two platforms do not match and manually entering datasets was the only viable solution. The Rapsodo Hitting Unit 3D spinning ball and spin direction was used to determine the most dominant spin direction. The batted ball was labeled as a backspin, sidespin, or topspin batted ball outcome. (Figure 3-1)
The Eastern New Mexico University Baseball Team (ENMU Dataset) was used to collect the first dataset. A team of twenty-five hitters were used whose ages ranged from 18-25. A second dataset (Amarillo Dataset) was collected to determine the effects of swing speed on batted ball the collision. All participants were asked to sign an informed consent form (see Appendix). Swing speed was not monitored during the ENMU dataset. After examining the differences in exit velocity from the ENMU Dataset it was theorized that swing speeds must be different among the various swing types. The Amarillo dataset posed complications due to the COVID-19 Pandemic. Convenience sampling was again used to find any former or current college baseball players. Ages ranged from 18-40, with the majority of participants being incoming college freshmen. The participant sample size for the Amarillo dataset was 10 total participants.
Rapsodo updated their software in 2020 and observationally it was noticed that the application capped spin rates at 5000rpms before the Amarillo Dataset began collection. A constraint was added to try to alleviate the variability in batted ball results. In the Amarillo Dataset only batted balls with an exit velocity of 75mph or higher that were determined to come off the barrel of the bat would be used.
Data collection and regression analysis was completed via Microsoft Excel and R Studio. The mean and standard deviation of all metrics were calculated within Microsoft Excel. The collected swing type launch angle and exit velocity means will then be put into Statcast’s 2019 Exit Velocity and Launch Angle Field Breakdown website (https://baseballsavant.mlb.com/statcast_field). The website will be able to show the types of batted balls and the in-game results that occurred during the 2019 season at the corresponding launch angle and exit velocity.
Regression analysis in R Studio was run using the Pearson Correlation linear model to quantify the relationships between batted ball metrics collected via the Rapsodo and swing metrics collected via the Blast Motion Bat Sensor. Then the correlation coefficient was used to find the t-statistic, the degrees of freedom, and the significance level of the correlation of batted ball variables by calculating the p-value. This showed the strength of the correlation across all batted ball relationships.
CHAPTER 4: RESULTS
2019 ENMU Dataset
The total sample size for this dataset was 375 swings, 125 for each swing type. Batspeed was not measured in this dataset. Undercut swings had the lowest exit velocity at a mean of 80.5mph and the highest standard deviation in exit velocity at 9.83. (Table 4-1) Undercut launch angle mean was the lowest of all swing types at -2.86 degrees, but had the smallest standard deviation of 12.45. Entering the undercut means into the Statcast Exit Velocity & Launch Angle Breakdown (Figure 4-1) resulted in a .122 BA. Undercut swings did result in the highest backspin mean at 2938.38rpms, however only 13% of batted balls had backspin imparted on them from the batted-ball collision. Undercut swings resulted in 46% of the baseballs hit having topspin and 41% with sidespin. The mean Undercut attack angle from this dataset was -5.16 degrees with a mean distance of 57.48ft. The Undercut standard deviation for distance was 67.78 and compared with the mean distance of 57.48ft it would be very difficult to consistently hit the baseball out of the infield. Only 7% of undercut batted balls made it into the 10-15 high BA launch angle window. In regards to the optimal HR launch angle window only one batted ball or .8% was hit into that specific window. Only 2% of undercut batted balls were 95mph or harder and most notably 86% of undercut batted balls resulted in groundballs. Only 13% of undercut batted balls resulted in a line drive and 1% resulted in a flyball. Undercut swings resulted in the most groundballs and slowest exit velocity among the various swing types. With Undercut swings having the lowest standard deviation in launch angle, but the highest standard deviation in exit velocity and overall spin rate an offensive performance will consistently result in a smaller ground ball laden launch angle window with lower, less consistent exit velocities.
Level swings ranked second in performance with an exit velocity mean of 85.28mph and launch angle mean of 2.15 degrees. Level swings showed the lowest standard deviations in exit velocity, attack angle, and overall spin rate. (Table 4-1) This is most notably due to level swing attack angle range varying from 0-4 degrees, mitigating the probability of deviations from the mean. The Statcast Exit Velocity & Launch Angle Breakdown (Figure 4-2) resulted in a .340 BA. Level swings resulted in the lowest spin rate means in every spin direction. Level swings also resulted in the smallest standard deviation in top spin and side spin. Batted ball collisions had a close to even split in spin direction with 36.8% resulting in topspin and 35.2% resulting in sidespin. The attack angle mean for level swings was 2.15 degrees with a standard deviation of 1.52. Distance had a mean of 103.78ft of distance with a 100.91 standard deviation. Level swings achieved the optimal BA launch angle 11% of the time and the optimal HR launch angle 5% of the time. The 95mph threshold was reached 7% of the time and the majority of batted balls resulted in groundballs at 70%. Level swings had the most consistent exit velocity and the highest Optimal BA Launch Angle %. However, with the low launch angle mean of 2.63 and the majority of batted balls produced being groundballs the level swing is not the most optimal bat path for offensive production.
Uppercut swings maintained the highest overall exit velocity mean at 87.35mph with a standard deviation of 8.37 and a launch angle mean of 15.1 degrees. (Table 4-1) Uppercut swings were the only swing type to have a mean within an optimal launch angle range. The launch angle standard deviation was highest among Uppercut swings at 17.82 degrees. The Statcast Exit Velocity & Launch Angle Breakdown (Figure 4-3) resulted in a .954 BA. Uppercut batted ball collisions resulted in the highest spin rate means in topspin and sidespin. Uppercut collisions resulted in backspin 42% of the time compared to 30% with topspin and 28% with sidespin. Backspin standard deviations were lowest in Uppercut swings at 1403.4 with a mean of 2671.06. The attack angle mean was 11.14 degrees and had the highest standard deviation at 4.09. Distance resulted in a mean of 192.03ft with the highest standard deviation in distance at 127.08. The optimal launch angle threshold for BA was achieved 10% of the time and the optimal launch angle for HRs was achieved 22% of the time. The 95mph threshold was achieved at the highest rate of any swing path at 14%. Finally, line drives were produced at the highest rate of the various swing paths at 28% as well as flyballs at 33%. Groundballs were still the majority of batted ball types at 39%. Uppercut swings outperformed all other swing types in every offensive production metric except for Optimal BA Launch Angle %. While exit velocity was highest among Uppercut swings, high standard deviations in attack angle and launch angle resulted in a larger launch angle window and a less predictable batted ball outcome. Batted ball type percentages were more distributed among Uppercut swings. While batted balls in Uppercuts swings were on average hit harder and further, the consistency of expected batted ball type was less predictable when compared to Undercut and Level swings.
Table 4-1: ENMU 2019 Dataset
|Bat Speed Mean||Not Measured||Not Measured||Not Measured||Not Measured|
|Bat speed SD||Not Measured||Not Measured||Not Measured||Not Measured|
|Exit Velocity Mean||80.45||85.28||87.35||84.36|
|Exit Velocity SD||9.83||6.45||8.37||8.8|
|Launch Angle Mean||-2.86||2.63||15.1||4.96|
|Launch Angle SD||12.45||14.35||17.82||16.78|
|Attack Angle Mean||-5.16||2.15||11.14||2.71|
|Attack Angle SD||3.72||1.52||4.09||7.45|
|Vertical Bat Angle Mean||-32.95||-32.14||-31.78||-32.3|
|Vertical Bat Angle SD||7.13||7.03||6.91||7.02|
|Spin Rate Mean (rpms)||2565.06||2218.9||2694.2||2492.71|
|Spin Rate SD (rpms)||1551.03||1296.31||1515.99||1468.71|
|Backspin Rate Mean||2938.38||2610||2671.06||2691.64|
|Backspin Rate SD||1449.15||1466.31||1403.4||1421.91|
|Topspin Rate Mean||2524.52||2378.46||2689.89||2447.13|
|Topspin Rate SD||1586.36||1425.98||1539.55||1497.5|
|Sidespin Rate Mean||2494.04||2367.8||2733.77||2383.02|
|Sidespin Rate SD||1554.22||1440.99||1690.42||1496.56|
|Optimal BA Launch Angle %||7%||11%||10%||9.6%|
|Optimal HR Launch Angle %||.8%||5%||22%||9.3%|
|Line Drive %||13%||24%||28%||21.6%|
2020 Amarillo Dataset
The total sample size for this dataset was 375 swings, 125 for each swing type. Undercut swings again resulted in the lowest average exit velocity mean of 82.1mph and had the lowest standard deviation at 4.69. (Table 4-2) Undercut swings resulted in the lowest bat speed mean at 58.54mph with a standard deviation of 3.39, which accounted for the lower exit velocities reported. Undercut swings produced a launch angle mean of -6.14 degrees the lowest standard deviation at 13.25. The Statcast Exit Velocity & Launch Angle Breakdown (Figure 4-4) resulted in a .183 BA. Undercut swings again resulted in the highest backspin mean, but in this dataset had the lowest standard deviation at 1096.7. However, only 16% of batted balls had backspin imparted on them from the batted-ball collision. Undercut swings resulted in 45% of the baseballs hit produced topspin and 39% resulted in sidespin. Topspin rate means were the highest in undercut swings and sidespin rate means were the lowest as was the sidespin standard deviation. (Table 4-2) The attack angle mean from this dataset was -4.65 degrees and a mean of 53.02ft of distance. The distance standard deviation was 66.003ft which again makes it difficult for Undercut batted balls to clear the infield. Only 6% of undercut batted balls made it into the 10-15 high BA launch angle window. The optimal HR launch angle window had no batted balls. 2% of undercut batted balls were 95mph or harder while 89% of undercut batted balls resulted in groundballs. Only 10% of undercut batted balls resulted in a line drive, while 1.6% resulted in a flyball. Undercut swings in this dataset produced similar results. Undercut swings again had the lowest standard deviation in launch angle, and a negative mean launch angle. Offensive performance will consistently result in a smaller ground ball laden launch angle window with lower exit velocities.
Level swings again ranked second in performance with an exit velocity mean of 83.87mph with a 4.96 standard deviation and launch angle mean of 1.73 degrees with a 14.02 standard deviation. (Table 4-2) Level swings resulted in the second highest swing speeds at 61.51mph with the highest standard deviation of 5.99. The Statcast Exit Velocity & Launch Angle Breakdown (Figure 4-5) resulted in a .299 BA. Level swings produced the highest overall spin rate mean, but was second in all other spin type means. (Table 4-2) Batted ball collisions resulted in 29% with topspin, 37% resulting in sidespin, and 34% with backspin. The attack angle mean for Level swings was 2.16 degrees with a 1.42 standard deviation and a 101.16ft distance mean with a 97.16 standard deviation. Level swings achieved the optimal BA launch angle 9% of the time and the optimal HR launch angle 5% of the time. The 95mph threshold was reached .8% of the time and the majority of batted balls resulted in groundballs at 71%. Line drives were hit 25% of the time and flyballs 4% of the time. Level swings again produced low launch angles that are not conducive to high offensive in game production.
As in the ENMU Dataset uppercuts maintained the highest overall exit velocity with a mean of 87.32mph with a 5.52 standard deviation and a launch angle mean of 16.06 degrees with a 16.06 standard deviation. (Table 4-2) The bat speed mean was the highest in Uppercut swings at 64.94mph with a standard deviation of 3.77. The Statcast Exit Velocity & Launch Angle Breakdown (Figure 4-6) resulted in a .922 BA with one notable outlier seemingly at a distance that was miscalculated. Uppercut batted ball collisions resulted in the lowest overall spin rate mean as well as backspin and sidespin rates. (Table 4-2) Uppercut collisions resulted in backspin 57% of the time compared to 19% with topspin and 24% with sidespin. The attack angle mean was 14.73 degrees with a 6.32 standard deviation and distance resulted in a mean of 214.02ft with a 118.28 standard deviation. The optimal launch angle threshold for BA was achieved 16% of the time and the optimal launch angle for HRs was achieved 17% of the time. The 95mph threshold was achieved at the highest rate of any swing path at 7%. Finally, line drives were produced at the highest rate of the various swing paths at 42% as well as flyballs at 31%. Groundballs were produced during uppercut batted ball types at 39%. Batted ball type percentages were more distributed again among Uppercut swings. While batted balls in Uppercuts swings were on average hit harder and further just like the ENMU Dataset, the consistency of expected batted ball type was less predictable when compared to Undercut and Level swings.
|Bat Speed Mean||58.54||61.51||64.94||61.67|
|Bat speed SD||3.39||5.99||3.77||4.29|
|Exit Velocity Mean||82.1||83.87||87.32||84.42|
|Exit Velocity SD||4.69||4.96||5.52||5.5|
|Launch Angle Mean||-6.14||1.73||16.06||3.88|
|Launch Angle SD||13.25||14.02||15.56||16.98|
|Attack Angle Mean||-4.65||2.16||14.73||4.08|
|Attack Angle SD||3.28||1.42||6.32||9.06|
|Vertical Bat Angle Mean||-23.82||-28.49||-25.6||-25.97|
|Vertical Bat Angle SD||7.86||5.99||7.17||7.29|
|Spin Rate Mean (rpms)||2067.7||2176.16||1952.83||2065.57|
|Spin Rate SD (rpms)||1075.07||1046.62||1166.11||1098.31|
|Backspin Rate Mean||2571.9||2470.3||2100.56||2289.56|
|Backspin Rate SD||1096.7||1102.64||1196.03||1162.012|
|Topspin Rate Mean||2155.54||2117.72||2003.58||2057.65|
|Topspin Rate SD||1212.51||859.58||1320.89||1207.5|
|Sidespin Rate Mean||1761.53||2084.91||2115.14||1832.79|
|Sidespin Rate SD||787.39||857.28||874.39||853.67|
|Optimal BA Launch Angle %||6%||9%||16%||10.4%|
|Optimal HR Launch Angle %||0%||5%||16%||10.4%|
|Line Drive %||10%||25%||42%||17.1%|
CHAPTER 5: DISCUSSION
The data collected from both datasets showed that an uppercut bat path is by far the most effective bat path. Out of all thirty-five participants tested only one hitter had a natural undercut swing. All other hitters had a slight uppercut as part of their normal swing. Higher exit velocities, higher bat speeds, and more offensively productive batted balls all occurred more regularly with an uppercut bat path. The ideal batted ball of 95mph or more was achieved at higher rates with the uppercut bat path. The ideal launch angles for BA and HRs also were achieved at higher rates with the uppercut bat path. A comparison of the performance of previous mentioned uppercut attack angle theories illustrated that using an attack angle range within 5-15 is the most ideal for in game offensive performance. (Table 5-1) The exit velocity and launch angle mean was calculated from each attack angle range from within the study and then entered into Statcast’s Exit Velocity & Launch Angle Field Breakdown website using 2019 MLB datasets. An attack angle range from collected batted ball data of 10-20 degrees produced the highest average exit velocity at 89.73mph.
Table 5-1: Attack Angle Predicted On Field Performance
The ideal batted ball collision is one in which the center of mass of the bat is moving upward and slightly below the center of mass of the baseball, causing a backspin rate of 1500-2500rpms and exit velocities of over 95mph with a launch angle range between 10-15 degrees for BA and 25-35 degrees for HRs. Because the baseball will always be pitched with a downward trajectory, an Uppercut Bat Path creates the most efficient path to create the ideal batted ball collision. The hitting theory of swinging down on the baseball to create higher backspin rates does hold to be true. However, the low probability (13% & 16% in both datasets) of striking the baseball to create this batted ball is not conducive to prominent offensive on-field success. Undercut batted ball collisions that produced backspin the average exit velocity was reduced to 78.45mph in exchange for 2755.14rpms of average spin rate. An undercut bat path has more than an 85% chance of resulting in a groundball that is the least productive of all batted ball types. The baseball is pitched with a downward trajectory and swinging with an undercut bat path creates a very small window of time to align the center of mass of the bat below the center of mass of the baseball. Furthermore, with momentum being transferred on a linear plane from the bat to the baseball, asking a hitter to swing down and create backspin is directly cueing a miss-hit baseball. The hardest hit baseballs trended the highest at the launch angles of -1 to 25 degrees in MLB with the highest exit velocities peaking at 3 degrees. (Figure 5-1)
Experiment exit velocities were highest when the launch angles were between -10 and 30 with the highest exit velocities peaking at 12 degrees. (Figure 5-2) This could cause teams to misdiagnose on field performance. Launch angles closer to more common pitch descent angles have higher exit velocities. Exit velocity will be the highest when the attack angle of the bat matches the centerline angle of the incoming pitch. (Kensrud, Nathan, & Smith, 2017) These launch angles would result in more groundballs during in game performances. 2015-2017 MLB bat attack angles averaged 12.4 degrees while launch angle averaged 11 degrees. (Marshall, 2017)
The 2015-2017 MLB Statcast Data supports
Marshall’s claim, and of the 2,139,368 pitches thrown in that time period, groundballs were the most commonly produced batted ball type at 8.3%. The other batted ball types produced were line drives at 4.7%, flyballs at 3.8%, and pop ups at 1.3%. It should be taken into consideration that batted ball collisions resulting in groundballs can result in the highest exit velocities due to the offset created most frequently by this type of collision. When launch angle was subtracted from the attack angle to determine the offset, a small negative correlation of -.283 between exit velocity and offset was found using both experiment datasets. (Figure 5-3, Table 5-2)
|Relationship||Pearson r correlation||t||df||p-value|
|Attack Angle & Bat Speed||.641||16.139||373||<0.001|
|Bat Speed & Vertical Bat Angle||-.35||-7.21||373||<0.001|
|Bat Speed & Batted Ball Spin Rates||.01||.19||373||.85|
|Exit Velocity & Launch Angle||-.051||-1.4||748||.16|
|Exit Velocity & Vertical Bat Angle||-.069||-1.9||748||.058|
|Batted Ball Spin Rates & Vertical Bat Angle||-.095||-2.62||748||.009|
|Launch Angle & Vertical Bat Angle||-.03||-.82||748||.414|
|Attack Angle & Vertical Bat Angle||.102||2.81||748||.005|
|Batted Ball Distance & Vertical Bat Angle||-.008||-.21||748||.84|
|Exit Velocity & Batted Ball Spin Rate||-.31||-8.95||748||<0.001|
|Batted Ball Spin Rate & Distance||.12||3.27||748||.00113|
|Launch Angle & Distance||.89||55.99||748||<0.001|
|Launch Angle & Attack Angle||.507||16.108||748||<0.001|
|Attack Angle & Distance||.56||18.41||748||<0.001|
|Attack Angle & Exit Velocity||.392||11.65||748||<0.001|
|Attack Angle & Batted Ball Spin Rate||-.027||-.735||748||0.46|
|Bat Speed & Exit Velocity||.558||12.98||373||<0.001|
|Bat Speed & Launch Angle||.413||8.75||373||<0.001|
|Bat Speed & Distance||.46||9.99||373||<0.001|
A level swing path resulted in lower exit velocities and bat speeds compared to the uppercut. The launch angle of the level bat path resulted in groundball rate of 70% or higher in both datasets. As previously stated, groundballs are the least productive batted ball type. The level bat path theory is also a less than optimal hitting strategy. Bat speed means and peaks were highest among uppercut bat paths.
This could be due to the lumbar spine being more active during the down swing as opposed to the thoracic spine. The lumbar spine only has 25 degrees of rotation versus the thoracic spine which has 67 degrees of rotation. (Loebl, 1973) Essentially, due to the lack of range of rotation the hitter has to apply the brakes earlier due to the limitations of sectional spine rotation. It is also possible that the slow bat speed is due to the loss of energy from the redirection of kinetic energy up from the ground to a downward bat path.
Using R Studio, the ENMU Dataset was combined with the Amarillo Dataset and a regression analysis was completed to analyze the correlations between the various swing metrics. A Pearson Correlation linear model was used to quantify the relationships between batted ball metrics collected via the Rapsodo Hitting Unit and swing metrics collected via the Blast Motion Bat Sensor. Then a Pearson Correlation test was run in the R Studio program to calculate the significance level of the P-value in each batted ball metric relationship. (Table 5-2) This showed the strength of the correlation across all batted ball relationships.
In the ENMU Dataset there was little difference in vertical bat angle. Undercut (-32.95 degrees), Level (-32.14 degrees), and Uppercut (-31.8 degrees) vertical bat angles stayed within .34 degrees of each other. In the Amarillo Dataset a difference of 4.67 degrees occurred between Undercut (-23.824 degrees), Level (-28.49 degrees), and Uppercut (-25.6 degrees) vertical bat angles. This may be due more to personal swing styles than the result of bat path and more research would be needed to determine a relationship between vertical bat angle and bat path. Vertical bat angle had a weak negative correlation coefficient of -.35 to bat speed. (Table 5-2) Vertical bat angle is dependent on pitch location. Pitches inside tend to have higher bat speeds and lower vertical bat angles. The small negative correlation between bat speed and vertical bat angle and bat speed is more likely due to pitch location and point of impact. There was little to no correlation (r=.01) between batted ball spin rates and bat speed. (Table 5-2) Vertical bat angle had little to no correlations to all other metrics in the study. (Table 5-2) Comparing both datasets collected the same trend holds true. There was a small negative correlation of batted ball spin rates and decreased exit velocity increased. (Table 5-2) Overall batted ball spin rate had a small correlation to distance. (Table 5-2) To maximize batted ball performance a hitter should swing within -25 to -40 vertical bat angle and maintain spin rates 1500-2500rpms.
Attack angle and bat speed had the highest correlations to all other metrics in the study except for the .89 correlation between launch angle and distance. (Table 5-2) Attack angle had a moderate correlation of .641 (Table 5-2) to bat speed with the highest bat speeds occurring between 12-23 degrees. Filtering out the top 10% of bat speeds by attack angle, the swings ranged from 27 degrees to -1 degrees. 75% of all swings in the top 10% of bat speed recorded during the study fell between the 12-23 degree range. There were moderate correlations between attack angle and launch angle at .507 (Table 5-2) as well as attack angle and distance with a correlation of .558. (Table 5-2) Attack angle had a weak correlation to exit velocity. (Table 5-2) There was little to no correlation between attack angles and vertical bat angle or batted ball spin rates. (Table 5-2) Bat speed had moderate correlations to exit velocity, launch angle, and distance. (Table 5-2)
The strongest correlational relationships came from attack angle and bat speed. Attack angle had the highest correlations and most significant P-values in its relationships with other batted ball metrics followed by bat speed. Attack angle is the most influential catalyst in batted ball contact and in game offensive production followed closely by bat speed. This is due to attack angle having the largest influence over the offset of the center of masses between the bat and the baseball at contact. It is recommended that to optimize offensive production a hitter swing within the range of 5-15 degrees. If bat speed optimization is the goal the recommended range for attack angle is 12-23 degrees.
Limitations and Delimitations
Film from the Edgertronic Camera showed that the predictive algorithm of the Rapsodo will occasionally miscalculate spin direction and spin axis, though the miscalculation rate is unknown. It was also observed that the timing of the point of contact in regard to location over home plate of the incoming pitch during the swing had a large influence on the type of collision and batted ball created. Observationally, baseballs struck further out in front of home plate tended to have higher attack angles than those with points of impact deeper into the hitting zone. The timing of the point of impact drastically influences the size of the offset between the center of masses. (Nathan, 2015) Newer baseball technologies systems such as Hawkeye could be utilized to better understand the relationship between batted ball contact and side spin. Pairing the Rapsodo and Blast Motion Sensor with a HitTrax unit would also prove beneficial if all the data was timestamped and synchronized properly. From the observations of the Edgertronic Camera video vertical bat angle combined with the offset of batted ball collision, attack angle, and point of contact all were contributing factors to batted ball outcomes. Point of contact appeared to influence all of the other swing factors more directly when compared to the other factors. It is recommended that future studies take a more four-dimensional approach when examining batted ball outcomes. It is also recommended that spin direction be further examined deeper as spin direction is not mutually exclusive to one spin direction. Frictional force from the horizontal angle of batted-ball contact creates sidespin on the baseball. (Kagan, 2014) Horizontal bat angle also influences the direction of the batted ball after impact. (Figures 5-4 & 5-5) Vertical bat angle directly influences the spin axis of the baseball which will affect the flight path of the baseball in the air. Examining the spray angle in relation to vertical bat angle, timing, and point of contact should be the next step in continuing studies. The two biggest limitations of this study are that batted ball collision were examined in a two-dimensional outcome and time nor horizontal spray angles were not taken into consideration.
6-4-3 Charts LLC, personal communication, August 29, 2019.
Augustyn, A. (2020, April 10). Major League Baseball. Retrieved October 23, 2020, from https://www.britannica.com/topic/Major-League-Baseball
Bahill, T., & Rybarczyk, G. (2019). The science of baseball: batting, bats, bat-ball collisions, and the flight of the ball (2nd). Cham, Switzerland: Springer Nature.
Baseballsavant.com. Statcast search. (2019) available at: https://baseballsavant.mlb.com/statcast_search. Accessed October 1, 2019.
Blast Connect: What is Attack Angle? (2020). Retrieved November 27, 2020, fromhttps://blastconnect.com/training_center/item/207
Blast Connect: What is Vertical Bat Angle? (2020). Retrieved November 27, 2020, fromhttps://blastconnect.com/training_center/item/179Blast Motion Baseball.
What should Bat Path Angle be?. Retrieved October 6, 2019, from https://blastmotion.com/training-center/baseball/metrics/bat-path-angle/what-should- bat-path-angle-be/#gref.
Chadwick, H. (Ed.). (1896). Spalding’s Base Ball Guide and Official League Book for 1896. New York, NY: American Sports Publishing Company. Retrieved October 23, 2020, fromhttps://books.google.com/books?id=hSbwAAAAMAAJ&pg=PA186&lpg=PA18 6&dq=spaldings+art+of+hitting+and+baserunning&source=bl&ots=VPDd36Oc- v&sig=ACfU3U3jBsu0aPYFL4xJglmtWydIKl2pgA&hl=en&sa=X&ved=2ahUKEwi Wt_DzoMLsAhVOHqwKHdMxA0g4ChDoATABegQIARAC
Cross, R. (2009). Mechanics of swinging a bat. American Journal of Physics, 77(1), 36-43.
Cross, R, & Nathan, A. M. (2006). Scattering of a baseball by a bat. American Journal of Physics, 74(10), 896-904.
Diamond, J. (2020). Swing kings: The inside story of baseball’s home run revolution (pp. 68-70). New York, NY: William Morrow, an imprint of HarperCollins.
Dodd, R. (2019, November 19). The rabbit ball: The story of baseball’s original juiced ball controversy. Retrieved April 08, 2021, from https://theathletic.com/1380075/2019/11/19/the-rabbit-ball-the-story-of-baseballs-first-juiced-ball-controversy/
Kagan, D. (2014, May 22). The physics of a foul down the line. Retrieved March 01, 2021, from https://tht.fangraphs.com/tht-live/the-physics-of-a-foul-down-the-line/
Kensrud, J. R., Nathan, A. M., & Smith, L. V. (2017). Oblique collisions of baseballs and softballs with a bat. American Journal of Physics, 85(7), 503-509. doi:10.1119/1.4982793
Kensrud, J. R., & Smith, L. V. (2013). Spin from Oblique Impact of Batted Sports Balls. Procedia Engineering, 60, 130-135. doi:10.1016/j.proeng.2013.07.005
Lau, C., & Glossbrenner, A. (1980). The art of hitting .300. 114-115 Toronto: Fitzhenry & Whiteside Limited.
Loebl, W. Y., Regional rotation of the spine, Rheumatology, 12(4), November 1973, 223, https://doi.org/10.1093/rheumatology/12.4.223
Marshall, D. (2017, September 14). Reverse Engineering Swing Mechanics from Statcast Data. Retrieved September 4, 2019, from https://community.fangraphs.com/reverse-engineering-swing-mechanics-from-statcast-data/.
Morgan, J. T. (2018, October 23). How the Rays embraced the groundball in 2018. Retrieved October 6, 2019, from https://www.draysbay.com/2018/10/23/18008342/tampa-bay-rays-hitting-babip-line-drive-ground-ball.
Nathan, A. (2015, November 11). Optimizing the Swing. Retrieved October 6, 2019, from https://tht.fangraphs.com/optimizing-the-swing/.
Nathan, A. M., Cantakos, J., Kesman, R., Mathew, B., & Lukash, W. (2012). Spin of a batted baseball. Procedia Engineering, 34, 182-187. doi:10.1016/j.proeng.2012.04.032
Nathan, A. M., Hopkins, J., Chong, L., & Kaczmarski, H. (2006). The Effect of Spin on the Flight of a Baseball. The Engineering of Sport 6, 23-28. doi:10.1007/978-0-387-46050- 5_5
Newell, K. M. (1986). Constraints on the Development of Coordination. Motor Development in Children: Aspects of Coordination and Control, 341-360. doi:10.1007/978-94-009-4460-2_19
Ochart, J. (2018, May 30). Using Swing Plane to Coach Hitters: a Deeper Look. Retrieved October 6, 2019, from https://www.drivelinebaseball.com/2018/05/using-swing- plane-coach-hitters-deeper-look/.
Palmer, P., & Gillette, G. (2020a). Major League Baseball Fielding Year-by-Year Averages. Retrieved October 23, 2020, from https://www.baseballreference.com/leagues/MLB/field.shtml
Palmer, P., & Gillette, G. (2020b). Major League Baseball Batting Year-by-Year Averages. Retrieved October 23, 2020, from https://www.baseballreference.com/leagues/MLB/bat.shtml
Qualifier. (n.d.). Retrieved October 27, 2020, from https://www.baseballreference.com/bullpen/Qualifier
Raabe, M. (2011). Comparing the Performance of Baseball Bats.
Rapsodo Baseball. (2018a). Hitting Unit 2.0. [Apparatus and software]. https://rapsodo.com/baseball/hitting/
Rapsodo Baseball. (2018b) Rapsodo Hitting Data Guide. Retrieved October 6, 2019, from https://rapsodo.com/wp-content/uploads/2019/07/Baseball-HittingDataGuide.pdf
Rex, A. F. (1985) The effect of spin on the flight of batted baseballs. American Journal of Physics, 53(11), 1985, 1073–1075., doi:10.1119/1.14034.
Rodriguez, A. [Alex Rodriguez]. (2019, May 3) How to hit home runs: tips for the best approach at the plate. Retrieved September 23 2019 from https://www.youtube.com/watch?v=yPXS-EyOmLA
Rose, P., & Golenbock, P. (1985) Pete Rose on hitting: how to hit better than anybody. New York, NY: Putnam Publishing Group
Rymer, Z. (2013). The evolution of the baseball from the Dead-Ball era through
today. Retrieved April 08, 2021, from https://bleacherreport.com/articles/1676509-the-evolution-of-the-baseball-from-the-dead-ball-era-through-today
Sawchik, T. (2019, September 12). Home Runs Are Soaring. Could Declining Backspin Be A Factor? Retrieved October 6, 2019, from https://fivethirtyeight.com/features/home-runs-are-soaring-could-declining-backspin-be-a-factor/.
Sawicki, G. S., Hubbard, M., & Stronge, W. J. (2003). How to hit home runs: Optimum baseball bat swing parameters for maximum range trajectories. American Journal of Physics, 71(11), 1152-1162.
Schmidt, M., & Ellis, R. (1994). The Mike Schmidt Study: Hitting Theory, Skills, & Technique. Atlanta, GA: McGriff & Bell.
Seaver, T. (1981, September 13). Tom Seaver On How Baseball Turf Has Speeded Up Baseball. Retrieved October 25, 2020, from https://www.nytimes.com/1981/09/13/sports/tom-seaver-on-how-baseball-turf-has-speeded-up-baseball.html
Sheinin, D. (2017, June 1). Why MLB hitters are suddenly obsessed with launch angles. Retrieved October 6, 2019, from https://www.washingtonpost.com/graphics/sports/mlb-launch-angles-story/?utm_term=.a536074513cd.
Slowinski, S. (2010, February 17). GB%, LD%, FB%. Retrieved October 1, 2019, from https://library.fangraphs.com/pitching/batted-ball/.
Smith, D. W. (1995, June 17). Baseball extras: Effect of artificial turf vs. grass. Retrieved October 09, 2020, from http://www.bostonbaseball.com/whitesox/baseball_extras/turf.html
Stamp, J. (2013a). A Brief History of the Baseball. Retrieved September 30, 2020, fromhttps://www.smithsonianmag.com/arts-culture/a-brief-history-of-the-baseball-3685086/
Stamp, J. (2013b). The Invention of the Baseball Mitt. Retrieved October 23, 2020, from https://www.smithsonianmag.com/arts-culture/the-invention-of-the-baseball-mitt-12799848/
Statcast: Glossary. (2020). Retrieved October 27, 2020, from http://m.mlb.com/glossary/statcast
Statcast: Launch Angle. (2020). Retrieved October 27, 2020, from https://www.mlb.com/glossary/statcast/launch-angle
Verducci, T. (2018, March 21). The Launch Angle era has transformed the baseball swing. Retrieved October 6, 2019, from https://www.si.com/mlb/2018/03/21/evolution-swing-home-run-opening-day.
Wagner, J. (2013, March 4). How Anthony Rendon puts backspin on the ball to make it carry. Retrieved October 6, 2019, from https://www.washingtonpost.com/news/nationals-journal/wp/2013/03/04/how-anthony-rendon-puts-backspin-on-the-ball-to-make-it-carry/.
Watts, R. G., & Baroni, S. (1989). Baseball–bat collisions and the resulting trajectories of spinning balls. American Journal of Physics, 57(1), 40-45.
What is a Batting Average on Balls in Play (BABIP)?: MLB Glossary. (2020). Retrieved November 27, 2020, from http://m.mlb.com/glossary/advanced-stats/babip
What is a Batting Average (AVG)?: MLB Glossary. (2020). Retrieved November 27, 2020, from http://m.mlb.com/glossary/standard-stats/batting-average
What is a Exit Velocity (EV)?: MLB Glossary. (2020). Retrieved November 27, 2020, from http://m.mlb.com/glossary/statcast/exit-velocity
What is a Launch Angle (LA)?: MLB Glossary. (2020). Retrieved November 27, 2020, from http://m.mlb.com/glossary/statcast/launch-angle
What is a Weighted On-base Average (wOBA)?: MLB Glossary. (2020). Retrieved November 27, 2020, from http://m.mlb.com/glossary/advanced-stats/weighted-on- base-average
Willardson., D.K. (2018). Quantitative hitting: surprising discoveries of the game’s best hitters. Columbia, SC. Hitting Tech Inc.
Williams, T., & Underwood, J. (2013). The science of hitting. New York: Simon & Schuster.
Willman, D. (2020). Statcast Exit Velocity & Launch Angle Breakdown. Retrieved October 30, 2020, from https://baseballsavant.mlb.com/statcast_field