DCDS Project ID: DCDSx-MATH-099
SEFMD Project ID: 2263
Category: Mathematics
Senior Division
https://www.istockphoto.com/phot
os/spinning-baseball
Mathematical and Statistical
Analysis of Spin in Baseball
Introduction and Purpose
https://rocklandpeakperformance.com/baseba
ll-spin-axis-spin-rate-spin-efficiency-explained/
https://www.researchgate.net/figure/Forces-on
-a-spinning-baseball-in-flight-The-drag-force-FD-acts-in-the-v-direction-the_fig1_259103270
Note: All photos,
graphs, images are created by researcher
unless cited below
What is Spin?
● As pitch is thrown, the ball spins back pushing air behind in creating a equal magnus force up
● Forces on a Baseball: The drag force acts in the opposite direction of v. The magnus force
acts as the cross product of omega, the spin force, and the velocity force. Gravity acts down
Types of Spin
● Transverse Spin- Perpendicular to Axis- movement in direction front of ball
● Gyro Spin- parallel to velocity- no movement
Purpose
● Modify/Improve understanding of baseball, and the way a baseball spins and travels
● Analyze how spin plays a role in a various different types of pitches
● Improve existing tracking technologies that may be miscalculating spin rates (improve how
data is collected)
● Discover new types of movements on the baseball previously unaccounted for
● Help players strategize how to spin the ball to maximize output/success
Research Summary
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I collected online data from various MLB websites as well as from university laboratory
experiments to conduct many different kinds of mathematical and statistical analyses in order
to refine my understanding on how spin works, how data about spin is collected, and how to
improve existing theories about types of spin
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Exploration of Spin Rates
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Top Left: Fitted probability function for all swings where Miss (1) or Not-Miss (0), and logit
function log(x) = log(x) – log(1 – x) between the variables
○ Color represents fitted probability to miss
○ Can compensate for speed with spin
Top Right: Statcast data, plotted average spin rate vs average velocity
○ Too many data points to make proper conclusion, even when broken down by pitch
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Data Collection and Analysis
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Compiled dataset of statcast 2015-16 pitches (n=1,286,980)
Calculated the probability of a swinging strike based on spin rate and
velocity for each pitch
● Plot has mean spin rate and one standard deviation above and below
the mean
Analysis
● For all 3 types of fastball, the greater the spin rate, higher probability
of swinging strike
● Cutter- faced greatest disparity between high and low spin rate- not
effective swing and miss pitch without spin
● Sliders- had more swings and misses as spin increased
● Changeups- Spin rate not as effective- dependent on fastballvelocity/arm angle play bigger role than spin rate on swing probability
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Pearson residual R = (O – E) / sqrt(E).
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I utilized a generalized additive model (GAM) to predict the
probability of a miss for each pitch using the velocity and spin rate
data
● For all fastballs, used expected number of misses from the fitted
model (E) and actual number of misses (0)
● To compare these values, I computed the the Pearson residual
● Left: Displayed model of residuals for 12 pitchers
Analysis:
● Velocity and spin are incomplete descriptions of a pitcher's success
● Large residuals- disparity due to several outside factors due to to
pitching motion and pitch location
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I also constructed parallel boxplots of the spin rates from 2018
pitchers who threw more than 1500 fastballs
Analysis:
● There is variation in the spin rates within pitchers, but there is also
sizeable variation between pitchers
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Comparing Tracking Technologies to Analyze Spin
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Tracked 33 pitches from collegiate level pitcher, and
analyzed their metrics and data accuracy
Total Spin: Pitch Logic correlation (R=0.936). Rapsodo
(R=0.979)
Correlation doesn’t examen full differences in instruments
Used Bland Altman Plot- to measure differences in means
from both. Allows us to see bias or paired differences clearly
Mean difference in spin rate (pitchLogic spin minus Rapsodo
spin) is 8 rpms ± 30 rpms
Spin Efficiency- Measures % of total spin contributing to
movement Strong correlation between Rapsodo and Pitch
Logic (R=0.985)
From Bland Altman Plot- mean difference in spin efficiency3.15 percent ± 2.7 percent (bias is small)
Overall, Pitch Logic tracks well under established radar units
like in terms of velocity, spin rate, spin efficiency, and spin
direction
○ Further studies need to be done whether these
measures can compare to other units, and whether it
accounts for all type of spin
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Hawkeye Technology Spin Data to Track Non-Magnus Movements
https://www.baseballprospectu
s.com/news/article/62912/not-j
ust-about-magnus-anymore/
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Table reveals improvements in technology, Hawkeye measures trajectory as well as 3-D Spin axis
Direction of Magnus determined, and direction of actual movement measured
I created a graphic that displays total lift and side (magnus and non magnus, red/blue) movements in xz plane of
a sinker and fastball which add up to resultant green vector
Large reduction in spin efficiency needed to get same shift in movement as 2S fastball
Pitchers have similar spin axes (from armslot) but very different movements
Differences between magnus and actual movement give evidence for a new Non Magnus movement previously
accounted for (aka Seam Shifted Wake)
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Alternative Method to Track Non-Magnus Movements
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I conducted a new analysis directly comparing the
direct spin axis to inferred axis (presence of non
magnus forces)
Created 3 graphs display axis shift
All 3 sway to one side or another based on the
pitch (changeup, fastball, slider) or left or right
handedness
Next figure plots the same pitches but normalized
to show correlation of a pitch’s total movement
with shift in the axis
Large shifts in axis are often correlated to less
movement, especially for fastballs
In flat region of sinker plot from -20 to 20 degrees,
non magnus force reduces the magnus force lost
from gyrospin
○ Does not occur for 4 seam fastball
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Data Analysis Comparing Types of Spin with Different Pitches
Transverse vs Total Spin
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Key: Blue Tri- FAST,
White- SINKER, Light
Blue CHANGE, Black
Squares- SPLITTER,
Black Ast- CUT,
Green-SLIDERS, RedCURVEBALLS
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All spin is not alike, and has different components of gyrospin
and transverse spin
Below I plotted, the transverse spin vs total spin using 2012
MLB data
Greater gyrospin would fall below the line
Scatterplot considerably random from random measurement
error
Results: Fastballs/changeups have less gyro spin while
sliders/curveballs have it significantly (surprising)
I created a histogram of spin differences from
fastballs/changeups (blue) and breaking pitches (red).
○ Fitted a dotted curve using a normal distribution with
mean=0, and standard deviation of 500rpm
Mean of 0 also indicated that points in first figure don't follow
the line if useful spin is identical to total spin.
○ Confirms that technique used to relate useful spin is
correct (points do follow line if useful spin=total spin)
Curve not linear, so doubling transverse spin won’t necessarily
double movement
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Conclusions and Applications
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Importance of Spin, Spin rate, and Spin Axes in Baseball
From the spin rate and swinging strike probability analysis, depending on the pitch type, spin rate
can either be very important at inducing swinging strikes, or not play a central role at all.
Tracking technologies for measuring velocity, spin rate, spin efficiency, and spin direction, such
as Pitch Logic perform well under established radar units but are often unreliable due to various
discrepancies
Spin rate needs additional context of velocity and spin axis
Seam Shifted Wake describes non-magnus movements, (vertical motion by changing orientation
of seams relative to spin axis)
Laboratory experiments suggest this axis shift which is enhanced with gyro spin
Fastballs and Changeups appear to be consistent with their spin being useful, but curveballs and
sliders have varying degrees of gyrospin
I developed a technique to separate the spin into transverse (or useful) and gyrospin parts.
Avenue for Further Research
○ Refine the 3D spin axis to compare whether the reduced movement is really a result of
spin efficiency.
○ Analyze the seam orientation and see how SSW depends on it
-Only scratched the surface, and there is still a lot that is unknown!!!
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References
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