Baseball Physics & Coors Field – May 1, 2007

Amongst the more interesting topics to discuss, and least understood by the layman (including this author), is the physics of a pitched and batted ball. The forces and measurements at play are numerous: Drag Coefficient, Reynolds Number (Re), Coefficient of Restitution (COR), Spin Rate (in RPM), Muzzle Velocity (in MPH), Magnus Coefficient, Backspin (in RPM), Wind Velocity (in MPH), Altitude (in feet), Temperature and Launch Trajectory (in degrees) are amongst the ordinary banter that physicists use in describing what a baseball does in flight.

For our discussion, the importance comes in determining what can change a baseball’s flight from ordinary (a fly out to the warning track) to extraordinary (a towering home run.)
Baseballs are certainly constructed by a set of rules; yet that is where it begins, not where it ends. The Official Baseball Rules (circa 2001) calls for the baseball to be made specifically:

Rule 1.09: “The ball should be a sphere formed by yarn wound around a small sphere of cork, rubber, or similar material covered with two stripes of white horsehide or cowhide, tightly stitched together. It shall weigh not less than 5 nor more than 5 ¼ ounces avoirdupois and measure no less than 9 nor 9 ¼ inches in circumference.”[1]

From Dr. Adair’s The Physics of Baseball, manufacturing of MLB Baseball has moved around over the years. From Chicopee, Massachusetts (while A.G. Spalding was still the sole manufacturer)[2], it moved to Haiti, then Taiwan and now in Costa Rica.

The making of the ball consists of: A cork-rubber center of a baseball is wrapped by 121 yards of 4-ply, blue-gray wool yarn, 45 yards of 3-ply white wool yarn, 53 yards of 3-ply gray wool yarn and 150 yards of fine cotton then cemented together with the two strips of cowhide .05-.055 inches thick, which was horsehide before 1974, then hand-stitched with 216 red-cotton stitches. [3] But the storage, shipment and pre-game rituals are not so standard or clear cut. (HOF Manager John McGraw was known to freeze balls for several hours before the game, then “dry” them out so the umps would not notice.)

Just upon inspection of those limited criteria, a great deal could be variable about the construction and impending usage from baseball to baseball, year to year. Much has been neglected in determining the overall actuality of these changes (through the years) in how they apply to statistics generated by fielders, hitters, and pitchers. Even the testing grounds utilized to determine this might not accurately portray the conditions that will ultimately exist for the ball at the stadium.
A study done over several seasons in the mid-to-late 1990’s by the University of Colorado at Denver suggests that a humidor was used by the Colorado Rockies starting in 2002 (and has continued to be used by this team at the time of this writing.) This devise maintains the baseballs in a “controlled environment” to adhere to the weight and circumference requirements of Major League Baseball [4] The humidor settings were initially at 40% humidity and 90° Fahrenheit. This “altering” of the baseball is considered acceptable, yet the statistical outcomes were not yet in line with the desired change: a reduction of home runs and runs scored at Coors Field during the next few seasons.
Yet, now looking at the 2006 season, so far, run scoring is down and pitchers are beginning to cope with the park effects at Coors Field. (Seen in the first month ever the Rockies pitching staff amassed an ERA below 4.00 in May 2006.) This could be due to adjusting the settings of the humidor to create the optimal effects. (Namely, high humidity and lower temperatures – opposite of the initial settings.)

As Baseball America writer Tracy Ringolsby recently wrote in the December 2006 issue of Baseball America, Humidors Might Be Next Trend, the Rockies have adjusted their settings to 50% humidity and 70° Fahrenheit and noticed improved adherence to the Rawlings specifications of 5 oz. in weight and 9 in. in circumference. (Before, the ball weighed 4.6 oz. and shrunk to 8.5 in.) In the same article, Jimmie Lee Solomon, MLB executive VP of Baseball Operations states, “Baseballs are stored in all kinds of environments. They are subject to varying temperatures and levels of humidity.” As a result, the Colorado Rockies’ quality controls on baseballs have put the balls back to their designed specifications.

Dr. Adair tests confirms this modest assertion, “ …found that the weight of balls stored at 100% humidity for four weeks increase by 11 percent (ball weight) and the coefficient of restitution at an impact velocity of 25 MPH decreased by 10 percent – when dropped on concrete from a height of 20 feet, the humidified balls will bounce only about 80 percent as high…if that proportional decrease in elasticity would hold at greater-impact velocities, the swing of the bat that would drive a “dry” ball 380 feet would proper the ball stored at high humidity only 350 feet.”


According to multiple sources[6], the coefficient of restitution (COR), a measure of velocity after collision to the velocity before a collision must be between .514 and .578 of the initial velocity.[7] (In other spherical sports, this number can be significantly higher…) In 1987, a testing lab in Plainfield, New Jersey (Haller Testing) did a scientific analysis of baseballs collected from all teams – only 116 balls were used – to determine if the balls were a causation of the odd outburst of home runs in the league that year.
Meanwhile, scientists at University of Missouri conducted tests on balls from 1985 and 1987. The conclusions were that the 1987 balls were not livelier, but what may not be properly accounted for is that age, temperature and humidity (in storage and testing) can alter balls in ways not immediately testable since gathering them up and transporting the balls for testing takes time. Thus the balls are not the same as when used at the park initially.
Even though studies by R.C. Larsen and Dr. Adair confirm (COR) values nearly equal a decade apart (1988 and 1998), we cannot be completely confident that balls at the stadium are indeed similar unless the testing was done on sight and with nearly identical game conditions in place. Dr. Adair furthers this specific case by suggesting, “ The elasticity of balls stored under extremes of cold or heat can be affected also.”

[8] Case studies done by Dr. Adair and R.C. Larsen reflect that deep freezing to –10° Fahrenheit would take 25 feet away from a 375-foot fly ball and cause grounders to bound through the infield slower than before. Warming up to temperatures found in Death Valley would put enough juice in the ball to make fly balls find plenty of bleacher seats at ordinary ballparks.

Meanwhile, at significant altitude, like [9] A fastball will get to home plate sooner relative to the initial velocity and that also affects the breaking pitches.
The fact the ball has also underwent changes on multiple occasions (1910 – cork center, 1920 – yarn modification & pre-game preparation, 1931 – cushion corked center, 1943 – substandard materials used –“balata ball”[10], 1974 – cowhide substitution, 1977 – Rawlings made sole manufacturer and moving production around which could effect humidity during processing) is not always indicative of variations in statistical measurements (homeruns), but cannot be completely ignored in the grander scheme of measuring players and their outputs. The following table reflects the studies of Dr. Adair and his measurements of a wide variety of conditions in relationship to baseballs struck.
[TABLE MISSING] – From Dr. Adair’s Physics of Baseball -page 97.

Other Possible Theories abound about the reasons players are hitting more home runs:

  • Energetic Players (less substance abuse of alcohol, not staying out later or prevalent Amphetamines cocktails[11])
  • Improved conditioning (workout regiments, better nutrition, Steroid usage)
  • Video taping and gaming (More information game-to-game on other players tendencies, playing hand-eye games improves baseball coordination)
  • New hitter-friendly ballparks (Coors, Ballpark at Arlington, Minute Maid, Citizens Bank)
  • Altered production methods (change of processing of baseballs & ball bats)
  • Climatic changes and favorable wind patterns (El Nino, La Nina. Wrigley Field winds)
  • Watering down of leagues (Increased number of teams in ALL Professional Sports has introduced sub-par players that are overmatched by the elite players)
Certainly, the baseball should be at the heart of any discussion of why players are hitting more homeruns. Given the nature of Baseball Physics, complex, additive and variable from ballpark to ballpark, and even pitcher to pitcher, one should be inclined to attribute more to the nature of the specific equipment (including the shrinking handles on ball bats, which also increases bat velocity beyond 70 MPH and improves hitter’s ability to hit prodigious homeruns) to the change in the game than is currently being reflected.
But then again, as Mark Twain wonderfully states, “There are lies, damn lies and statistics.”
[1] Adair RK, Ph.D. The Physics of Baseball. 3rd Edition. New York: Harper-Collins, Inc; 2002. 5.
[2] Treat S, Turkin H, Thompson SC. editors. The Official Encyclopedia of Baseball. 5th edition. South Brunswick and New York: A.S. Barnes and Company; 1970. 645.
[3] Abid.
[4] Chambers F, Page B, Zaidins C. Atmosphere, Weather and Baseball: How Much Farther Do Baseballs Really Fly at Denver’s Coors Field? Malden, Massachusetts: The Professional Geographer, 55(4); 2003. 502.
[5] Adair RK, Ph.D. The Physics of Baseball. 3rd Edition. New York: Harper-Collins, Inc; 2002. 28.
[6] Abid. 83.
[7] Blanding SL, Monteleone JJ. The Science of Sports: How Things in Sports Work. New York: Barnes & Noble, Inc; 2003. 17.
[8] Adair RK, Ph.D. The Physics of Baseball. 3rd Edition. New York: Harper-Collins, Inc; 2002. 95.
[9] Abid. 67.
[10] Gutman D, McCarver T. The Way Baseball Works. New York: Simon & Schuster, Inc; 1996. 14.
[11] Bryant H. Juicing The Game: Drugs, Power and the Fight for the Soul of Major League Baseball. New York: Plume Book; 2005. 3.

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