Technical Advisor, United States Bowling Congress

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Presentation transcript:

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

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.

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

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

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 1900 1960 1980 1990 2000 Coverstock Evolution Core Rubber Polyester Polyurethane Reactive Particle Resin Enhanced Resin Pancake Dynamic Multi-Density

Bowling Through the Years 1970 - 2003 Changes in Ball Motion Through Technology

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

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.

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

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

The Original Ball Motion Study Illustrating Ball Motion

The Original Ball Motion Study Illustrating Ball Motion

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

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.

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

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

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

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.

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 -16.77 16.04 -1.05 0.307 Cover -0.5500 0.5689 -0.97 0.344 1.5 COF -52.21 27.84 -1.88 0.074 2.6 Oil Absorb -0.007392 0.007386 -1.00 0.328 2.0 RG 16.554 7.095 2.33 0.029 1.8 Total Diff 133.43 47.23 2.83 0.010 2.3 i-Diff -28.9 164.1 -0.18 0.862 64.4 Ratio -0.592 7.626 -0.08 0.939 62.1 Spin Time -0.1176 0.1012 -1.16 0.258 1.7 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 -17.19 14.79 -1.16 0.257 Cover -0.5360 0.5277 -1.02 0.320 1.4 COF -51.79 26.71 -1.94 0.065 2.5 Oil Absorb -0.007291 0.007110 -1.03 0.316 2.0 RG 16.620 6.891 2.41 0.024 1.8 Total Diff 136.12 31.51 4.32 0.000 1.1 i-Diff -41.44 27.22 -1.52 0.142 1.9 Spin Time -0.11703 0.09873 -1.19 0.248 1.7 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

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

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

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

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

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

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)

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

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

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 5.125 ounces Maximum static weight shared evenly between axes is 3 ounces

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

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

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

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.

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

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!

Questions and Discussion Bowl With US