Several years removed from a Berkeley physics class, I had the realization that the measurement of spin rates in baseball was actually giving us the angular velocity of the ball itself. Though there are other forces at play, we now can describe the energy of the ball itself with a relatively complete set of information.
We know a few things about a baseball right? Right. (googles furiously... yeah, we know a few things)
- A baseball is 9.00 - 9.25 inches in circumference, 2.86–2.94 inches in diameter.
- A baseball has a mass of 5.00 to 5.25 ounces.
And that's all we'll need for now! We also remember some things from high school physics right? (googles with slightly more patience over the course of a few evenings).
K_{E} = ½ mv^{2}
Kinetic Energy = 1/2 x mass x velocity-squared.
We're gonna need this one.
K_{ROT} = ½ Iω^{2}
^{}
Rotational Kinetic Energy = 1/2 x Moment of Inertia x angular velocity-squared.
Ohhhh yes, here's the goldmine for spin rate's application. Spin rate is measured in RPM, Rotations per minute, which is precisely angular velocity (albeit in different units). And Inertia...
I_{SPHERE} = ⅖ mr^{2}
^{}
Moment of Inertia (of a solid sphere) =2/5 x mass x radius-squared.
We're going to consider a ball a solid sphere for this exercise.
RPM = 2π/60 rad/s
Rotations Per Minute = 2π/60 radians per second
To put RPM into proper angular velocity consider that a "rotation" means 360 degrees, or 2π radians. So we're measuring in 6.28319 rad/minute, or 0.10472 (2π/60) rad/second. So a 2500 RPM fastball has an angular velocity of 261.80 rad/s.
So lets get cracking.
We're going to take the ball of the middle ground, 5.125 oz and 2.90 in. diameter (1.45 in. radius). Since baseball is globalizing and we're being a little more scientific here, better get a little metric.
- Mass(ball): 0.145291 kg
- Radius(ball): 0.03683 meters
- Inertia(ball): 2/5 x 0.145291 kg x 0.03683^2 = 0.0000788320950516236 kg(m^2)
- K.E.rot= 1/2 x I(ball) x (Spin Rate * 2π/60)^2
So let's get to leaderboards. Simply put, who puts the most energy into the ball on a per-pitch basis?
Player Name |
Total Pitches |
Avg. Spin (rpm) |
Avg Velo (mph) |
Avg. Spin (rad/s) |
Avg Velo (m/s) |
KE Rot (J) |
KE Fwd (J) |
KE TOT (J) |
Trevor Rosenthal |
164 |
2433 |
97.1 |
254.78 |
43.41 |
2.56 |
136.88 |
139.44 |
Aroldis Chapman |
171 |
2435 |
96.2 |
254.99 |
43.01 |
2.56 |
134.35 |
136.92 |
Tommy Kahnle |
158 |
2173 |
96.2 |
227.56 |
43.01 |
2.04 |
134.35 |
136.40 |
Matt Bush |
160 |
2548 |
95.6 |
266.83 |
42.74 |
2.81 |
132.68 |
135.49 |
Zach Britton |
134 |
2100 |
95.7 |
219.91 |
42.78 |
1.91 |
132.96 |
134.87 |
Ariel Hernandez |
30 |
2484 |
95 |
260.12 |
42.47 |
2.67 |
131.02 |
133.69 |
Jeurys Familia |
124 |
2211 |
95.2 |
231.54 |
42.56 |
2.11 |
131.58 |
133.69 |
Enny Romero |
218 |
2319 |
94.9 |
242.85 |
42.42 |
2.32 |
130.75 |
133.07 |
Jose Ramirez |
172 |
2365 |
94.4 |
247.66 |
42.20 |
2.42 |
129.37 |
131.79 |
Justin Wilson |
202 |
2490 |
94.1 |
260.75 |
42.07 |
2.68 |
128.55 |
131.23 |
Craig Kimbrel |
202 |
2488 |
94.1 |
260.54 |
42.07 |
2.68 |
128.55 |
131.23 |
Dovydas Neverauskas |
25 |
2402 |
94 |
251.54 |
42.02 |
2.49 |
128.28 |
130.77 |
Tony Cingrani |
76 |
2225 |
94.1 |
233.00 |
42.07 |
2.14 |
128.55 |
130.69 |
Kelvin Herrera |
157 |
2172 |
94.1 |
227.45 |
42.07 |
2.04 |
128.55 |
130.59 |
Jose Alvarado |
17 |
2239 |
94 |
234.47 |
42.02 |
2.17 |
128.28 |
130.45 |
Garrett Richards |
76 |
2693 |
93.6 |
282.01 |
41.84 |
3.13 |
127.19 |
130.33 |
Koda Glover |
129 |
2266 |
93.9 |
237.29 |
41.98 |
2.22 |
128.01 |
130.23 |
Jake McGee |
187 |
2248 |
93.8 |
235.41 |
41.93 |
2.18 |
127.73 |
129.92 |
Noah Syndergaard |
432 |
2056 |
93.9 |
215.30 |
41.98 |
1.83 |
128.01 |
129.83 |
So far, nobody puts more energy into each pitch than Trevor Rosenthal (This data was pulled on 5/4/17). He puts an average of 139.44 Joules of energy into each pitch. If you wanted to drop a pitch out of your window, how high would you have to be to match an average Trevor Rosenthal pitch?
Potential Energy= mass * gravitational acceleration (9.8 m/s/s) * height (meters)
P_{E}= mgh
Potential Energy= mass * gravitational acceleration (9.8 m/s/s) * height (meters)
At a height of 98 meters, or 321.5 feet, you could drop a ball and it would reach an energy close to that of a Rosenthal pitch. So if you're a St. Louis Cardinals fan, go to the top of Queeny Tower and drop a baseball and by the time it reaches the bottom, you'll have thrown like Trevor Rosenthal.
What does this tell us? Nothing at all! This is simply the first step of many more to come. This exercise is heavily influenced by pitch selection as well. The pitcher himself is not a 100% efficient transferor of energy, often times losing energy into the ground or with a lighter grip on the ball or other muscles that are not in perfect sequence. This is an initial study of what is given to the ball, nothing more or less.
P.S. In 2016, Aroldis Chapman lead the league with 147.33 Joules/Pitch.