1. Technical Advisor, United States Bowling Congress
Quality Sciences and Bowling Answering Decades-Old Questions With Multiple Regression and Designed Experiments
Presented By:
Scott C. Sterbenz, P.E.
Technical Advisor, United States Bowling Congress

2. Mission and Guiding Principles
The United States Bowling Congress, the governing body of the sport of bowling, is dedicated to providing programs and services to uphold the game’s credibility, preserve its future and enhance the bowling experience.
The Equipment Specifications and Certification Team is dedicated to being the leading source of technical information for bowling. This is accomplished through expert technical services and sound statistical analyses.

3. The Original Ball Motion Study
Honor Scores on the Rise
In many sports, advances in equipment technology have significantly enhanced the ability of participants to score well
Today’s athletes are well-trained and educated, but USBC also believes technological advances in equipment have artificially inflated scores—thereby jeopardizing the integrity of the sport
1910 – 1980: (1) 300 game for every 3150 members
2007: (1) 300 game for every 27 members

4. The Original Ball Motion Study
Angle of Entry Versus Strike Percentage
Studies conducted by the USBC have clearly shown that increased entry angle into the pins significantly improves carry of the corner pins
Higher carry percentages allow the bowler to roll more strikes—resulting in higher scores
A greater entry angle increases the probability of striking at many offsets from the headpin. Data generated from USBC’s BowlScore data collection system

5. The Original Ball Motion Study
Technological Advances in Bowling Balls
Bowling Ball Coverstocks and Cores
Increased angles of entry into the pins has been created by:
An increased amount of friction between the ball and the lane created by innovative materials
An increased level of dynamic imbalance in the ball’s core
Advances in ball technology can increase scoring without an increase in bowler skill
Coverstock
Evolution
Core
Rubber Polyester Polyurethane Reactive Particle
Resin Enhanced Resin
Pancake Dynamic Multi-Density

6. Bowling Through the Years
Changes in Ball Motion Through Technology

7. The Original Ball Motion Study
E.A.R.L. – The Robotic Ball Launcher
An Introduction to E.A.R.L.

8. The Original Ball Motion Study
SuperCATS
Ball motion on the lane is captured using a Computer-Aided Tracking System (SuperCATS):
23 sensors located on the bowling lane
Track critical ball characteristics, such as speed, location, rate of revolution, and angle of travel.

9. The Original Ball Motion Study
Response Variables
USBC uses the data from SuperCATS:
Plot ball motion
Determine the nineteen variables that uniquely characterize the motion of a bowling ball down the lane

10. The Original Ball Motion Study
Response Variables
Ball motion is divided into three phases, based on mathematical analysis of the ball's path on the lane:
Skid Phase
The ball has not encountered enough friction to begin hooking.
This ball path is linear with a negative slope.
Hook Phase
The ball has encountered enough friction to transition from a negative slope to a positive slope.
This ball path is parabolic.
Roll Phase
The ball has stopped hooking.
This ball path is linear with a positive slope.
SKID
HOOK
ROLL

11. The Original Ball Motion Study
Illustrating Ball Motion

12. The Original Ball Motion Study
Illustrating Ball Motion

13. The Original Ball Motion Study
Predictor Variables
The original Ball Motion Study was launched in 2005 in order to determine which elements of bowling most affect ball motion
Within USBC and the industry, there was significant disagreement regarding the effect of different ball properties
This disagreement made it extraordinarily difficult for USBC to change current specifications or set new specifications because of the lack of data to support these moves

14. The Original Ball Motion Study
Predictor Variables
Eighteen predictor variables were determined from a y = f (x) cascade, which were expected to influence ball motion:
Coverstock properties
Surface roughness, coefficient of friction, etc.
Core properties
Radius of gyration, RG differential, etc.
Drilling properties (static weights)
Side weight, top / bottom weight, finger / thumb weight
Lane properties
Coefficient of friction, oil application, etc.
Environmental properties
Lane temperature, room humidity, etc.

15. The Original Ball Motion Study
Response Variables
The nineteen response variables were:
Negative Slope
Slope of the theoretical line during the skid phase
First Transition
The distance at which the transition from the skid phase to the hooking phase occurs
A-Score
Parabolic shape of the ball’s curvature during the hook phase (ax2 + bx + c)
Breakpoint
The apex of the hook phase
First Transition to the Breakpoint
The length from Breakpoint to First Transition
SKID
HOOK
ROLL
Breakpoint
&
A-Score
First Transition
Negative Slope

16. The Original Ball Motion Study
Response Variables
The nineteen response variables were (cont’d):
Second Transition
The distance at which the transition from the hook phase to the roll phase occurs
Breakpoint to Second Transition
The length from Breakpoint to Second Transition
Total Hook Length
The distance between the First and Second Transitions, characterizing the length of the hook
Positive Slope
Slope of the theoretical line during the roll phase
Ball Velocity Decrease at 49 Feet / 60 Feet
Angular Deceleration Rate at 49 Feet / 60 Feet
SKID
HOOK
ROLL
Positive Slope
Second Transition
Breakpoint
Total Hook
Length

17. The Original Ball Motion Study
Response Variables
The nineteen response variables were (cont’d):
Intended Path at 49 Feet / 60 Feet
The total number of boards of hook at 49 feet from the foul line and as the ball enters the pin deck (theoretical calculation)
Average Path at 49 Feet / 60 Feet
The total number of boards of hook at 49 feet from the foul line and as the ball enters the pin deck (SuperCATS calculation)
Total Angular Displacement
The total angular change on the lane
Angle Per Foot
The quotient of Total Angular Displacement and Total Hook Length
SKID
HOOK
ROLL
Total Angular
Displacement &
Angle Per Foot

18. The Original Ball Motion Study
Analysis Method
Each of the nineteen response variables was analyzed, using multiple regression:
Predictor variables were ranked 1 to 18, based on the p-values obtained from the unreduced regression model
Lowest p-value received a score of 18
Highest p-value (or variables removed because of multicollinearity) received a score of 1
The total score for each predictor was the sum of the rankings over the nineteen regressions
The predictor variable with the highest score indicated the most overall influence on ball motion
Comment here that USBC was primarily interested in identifying which of the predictor variables contribute to ball motion; however, mathematical models were also derived to determine if ball motion could be theoretically predicted.
Q. Why is this ranking method accurate? Don’t the p-values change when terms are removed from the model?
Multiple regression uses ANOVA as the analysis method. Whether a factor is significant or not depends on its F-Value (which is calculated from the quotient of the MS for that variable and the MS of the error) and the F-Table. Therefore, the ranking of the F-Value (which is inversely proportional to the p-value) indicates the order of significance of the factors. As insignificant factors are removed from the model, the MS for that factor is moved to the error term, thereby increasing the denominator for every remaining factor. Thus, the ranking of the F-Values will still be the same for the remaining terms—however, the statistical significance of those factors may change.
Please note that not all insignificant factors are removed from the “best subsets” regression model. Sometimes, insignificant factors are left in because they result in a higher r-squared adjusted value for the model. Since we are interested in trends and not modeling, the F-Value (p-value) ranking method made the most sense for determining these trends. However, we went through the exercise of getting the best models out of curiosity to determine whether we would have adequate predictive ability. As will be noted later in the presentation, we have limited predictive ability—not good enough to say the models could replace our actual measurements at this point.

19. The Original Ball Motion Study
Analysis Method
Abbreviated Example Analysis (Response Variable – Intended Path at 60 Feet)
Predictor Coef SE Coef T P VIF
Constant
Cover
COF
Oil Absorb RG
Total Diff
i-Diff
Ratio
Spin Time
Multicollinearity between Intermediate Differential and Ratio of Differentials.
Expected because Ratio of Differentials is the quotient of Total Differential and Intermediate Differential.
Ratio of Differentials was removed from the model
Predictor Coef SE Coef T P VIF
Constant
Cover
COF
Oil Absorb RG
Total Diff
i-Diff
Spin Time
Multicollinearity resolved. Variables receive points based on p-value ranking.
Total Differential got 8 points
Radius of Gyration got 7 points
Coverstock Mat’l got 2 points
Ratio of Total Differential and Intermediate Differential got 1 point

20. The Original Ball Motion Study
Results
USBC implemented tightened specifications for:
Surface Roughness
Total Differential
Radius of Gyration (RG)
USBC also agreed to investigate widening or removing specifications for static weights:
Side Weight
Top / Bottom Weight
Finger / Thumb Weight
Predictor variable influence on ball motion. Red bars indicate inverse relationships, i.e., as RG increases, overall ball motion decreases

21. Static Weight Study
Background
Static weights in a bowling ball are measured based on the center of grip and the location of the center of gravity.
The difference in weights between the halves of the ball determine the values of the static weights
USBC currently regulates the static weights on a drilled ball:
One ounce of side weight
One ounce of finger / thumb weight
Three ounces of top weight

22. Static Weight Study
Planning
Blind elimination of the static weight specification was not in order because the original ball motion study only showed the effects of static weights on ball motion within the current specifications.
26-1 fractional factorial with a center point DOE was developed
Corner points maximized the amount of static weight that could be designed and drilled in a bowling ball
Rev rate, ball speed, and ball core type were also added as factors

23. Static Weight Study
Phase I Results
The results of the DOE were surprising to both USBC and the ball manufacturers:
The main effects showed curvature in most of the ball motion responses
Several interactions were significant in multiple ball motion responses
Potential damage to bowling center equipment was evident
4th phase of ball motion was discovered
The 4th phase was not consistent
Sometimes the 4th phase augmented the entry angle into the pins
Other times, it diminished the entry angle into the pins
The 4th phase was evident regardless of the ball speed / rev rate combination
In extreme cases, the 4th phase is evident visually
In most cases, the 4th phase was determined through residuals analysis from the linear regression of the roll phase

24. Showing the 4th Phase of Ball Motion Through Residuals Analysis
Static Weight Study
Showing the 4th Phase of Ball Motion Through Residuals Analysis
Ball motion data was always assumed to have three phases of ball motion:
USBC authored an algorithm to calculated the three phases of ball motion
Skid and roll phases are linear, and are calculated first, through linear regression
When the r-squared value drops below 99%, the ball has either transitioned from the skid phase, or has transitioned to the roll phase
Data points between the skid and the roll phases are the quadratic hook phase
In this case, there were quadratic patterns in the residuals of the roll phase
When the last four data points were removed from the roll phase and classified as a 4th quadratic phase, the residuals analysis in the roll phase was acceptable

25. Static Weight Study Showing the 4th Phase of Ball Motion
4th phase where angle into the pins is diminished
4th phase where angle into the pins is augmented
Typical ball motion of skid (linear), hook (quadratic), and roll (linear)

26. Static Weight Study Showing the 4th Phase of Ball Motion Visually
Observed 4th Phase of Ball Motion

27. Static Weight Study
Phase I Results
USBC was convinced at this point that the static weight specifications could not be eliminated, but still wanted to determine if the specifications could be widened.
Phase I DOE
Realm of Unknown
Current Specifications

28. Static Weight Study
The Second DOE
The second DOE utilized static weight limits that were determined by the maximum top weight specification and the presence of a weight hole.
Weight holes are allowed by USBC to create static weights within specifications, or to bring a drilled ball into specification for static weights
The DOE was designed based on the following potentials:
Allow the three ounces of top weight to be distributed anywhere in the ball, based on the drilling
Limit the size of the balance hole
Maximum static weight on any axis is ounces
Maximum static weight shared evenly between axes is 3 ounces

29. Static Weight Study
The Second DOE
The second DOE was a response surface central composite design.
Captures the non-linear effects
Allows for modeling
Evaluates both the axial points (static weights all on one axis) and the corner points (static weights shared between axes)
Captures the center point

30. Static Weight Study The results of the DOE were very insightful:
Phase II Results
The results of the DOE were very insightful:
Non-linear effects were significant on some ball motion variables
Interactions were significant on some ball motion variables
4th phase of ball motion was present on two of the fifteen runs, and was still not in a consistent direction
The order of importance of the static weights was identical to the original ball motion study

31. Static Weight Study The results of the DOE were very insightful:
Phase II Results
The results of the DOE were very insightful:
Contour plots allowed visualization of the effects of static weights on ball motion within the entire inference space of the DOE
Contour plots also showed that ball motion is minimally affected within the current specifications for static weights

32. Static Weight Study
Phase II Results
As an example, side weight, which is the most significant influencer, has the following effect on the ball motion variables which are most readily recognized by the bowler:
Intended path at 60 feet (total board of hook) – 4.06 boards
Entry angle into the pins – 0.16 degrees
With the DOE testing taking place on a lighter volume oil pattern with a low ball speed, the typical bowler will see less of an impact.

33. Static Weight Study
Final Conclusions
USBC will make no changes to the static weight specification for bowling balls.
Eliminating or expanding the specification could lead to:
An unanticipated 4th phase of ball motion, which could be problematic for the bowler, the pro shop operator, and /or the ball manufacturers
An intentional 4th phase of ball motion, which could artificially increase the skill of the bowler
Potential damage to the ball return and lane substructure

34. Andy Veripapa Trick Shots
Final Thoughts
Andy Veripapa Trick Shots
For several decades starting in the 1940s, Andy Veripapa—an accomplished and multi-titled professional bowler, often performed trick shots in front of an amazed audience. Now we know how these were done—with illegal static weights!

35. Questions and Discussion
Bowl With US