Bowling by the Numbers

By Danny Speranza

            Back when I was working for the American Bowling Congress and the Women's International Bowling Congress, I helped design the CATS^TM (computer aided tracking system) equipment for them. At that time, we used this equipment to analyze a lot of bowlers with a full range of talent. We developed bowling profiles for the different average groups. The table below summarizes the results of the important variables that influence bowling based on bowling averages: 

            Ball velocity, rotation, and accuracy have a great impact on the ball path to the pins and your ability to score. There is no doubt that accuracy is the most important. This is measured by two variables:

           • the accuracy at hitting a target
           • the launch angle range

Both measure how much a bowler scatters their shots from the intended target.

            Rotation is also important. It affects entry angle, which has a great impact on pin carry. More entry angle usually creates a larger strike pocket. Velocity also has a big affect on the ball path. Slower ball speeds hook more and faster ball speeds hook less.

            There are also properties of the bowling ball which dramatically affect the ball path. The most significant ball property is friction between the ball and the lane. CATS^TM measures this property. The ball Rg also influences the ball path but to a smaller degree.

            At 900 Global, we developed a mathematical model of the ball path. This model takes into account the important bowler and ball properties which CATS^TM measures and some variables which CATS^TM does not directly measure. We can now take the results from CATS^TM and mathematically manipulate the results to determine what would happen if one variable is changed at a time.

            If we start with typical higher average bowlers' results from the chart above and typical friction and Rg values, we can adjust them to determine their impact on the ball path:

            The following assumptions will be used for a starting point:

           • Velocity = 18 MPH
           • Rotation = 270 RPM
           • Axis rotation angle = 45 degrees
           • Friction in oil = .0252
           • Friction on dry backend = .27
           • Launch angle = 0 degrees (straight down the boards)
           • Starting board location = 5^th board

           
            The following table shows the theoretical results from using the math model to measure the affect from changing the initial velocity on the ball path:

            Therefore, a 1 MPH (mile per hour) change in the velocity equates to 2 to 3 boards of hook and .2 to .3 degrees of entry angle. A 1 degree change in entry angle is huge. Two to three boards of hook is the difference between hitting the perfect strike pocket versus hitting straight on the head pin.

            The following chart shows the theoretical affect on the ball path from adjusting the rotation on the ball:

            An increase of 30 RPM results in 2 extra boards of hook and ½ degree more entry angle. This variable is not easy for the average bowler to vary. A typical bowler might be able to adjust their rotation by 30 RPM. It is not easy to learn to rotate the ball more. There are other ways that are easier to increase the amount the ball hooks. One of them is by increasing the axis rotation angle. The table below shows the theoretical importance of axis rotation angle:

            Axis rotation angle has one of the largest affects on total hook and entry angle. This variable is not directly measured by CATS^TM. Axis rotation is the measurement of the amount of side roll on the ball. If the bowler gets their hand to the side of the ball at the point of release, they will likely have a 90 degree axis rotation angle. Their axis point will be facing straight back at the bowler when they initially release the ball.

            If the bowler releases the ball with their hand directly behind the ball and keeps it there, they will have little side roll on the ball. They will have end-over-end roll. Their axis point will be at a small angle (such as 30 degrees), and it will be facing to the left side wall (for right handed bowlers). This will dramatically reduce the amount the ball can hook and the potential entry angle, as the table above shows. It is not that difficult for a bowler to learn to manipulate the axis rotation angle and get more, or less, hook. It just takes practice to learn to work the wrist at the point of release.

            Friction between the ball and lane has a big influence on the ball path. The following table shows mathematically how the friction in oil should affect the ball path:

            Small changes in the friction in the oil will affect how soon the ball hooks. This will have a large impact on the final ball location, but might not affect the entry angle. It can affect the entry angle if the ball has not reached roll out, but in this example, it did not show up. A change in the friction in the oil will be a result of the oil pattern, lane surface, ball cover stock, ball surface (sanded/ polished) or ball flare potential. A change from .02 to .05 will theoretically create 7 more boards of hook, which is a big difference. This is why we spend a lot of research time on developing new shells. Particle shells increase the friction in the oil. Different particles in the shells will alter the friction for various reasons.     

            The friction on the dry backend of the lane is also important. It is normal for the friction on a clean, dry backend of the lane to be 5 to 12 times greater then the friction in the oiled area of the lane. The table below shows how the friction on the dry backend affects the ball path:

            The friction on the dry backend needs a larger change to equal the same effect as a smaller change in the friction in the oil.  A polyester shell will have about a .15 friction on the backend. A urethane shell will have about a .20 friction on the backend.  And a reactive shell or particle shell will have about .25-.30 friction on a clean backend. The unique property about particle shells is that they have a larger difference in the friction in oil than on the backend of the lane. The friction of a reactive ball and a particle ball on the backend will not be very different.

            The core of the ball has an effect on the ball path. The Rg is one of the primary properties of the core. The table below shows how the ball Rg affects the ball path:

            Changes in the ball Rg have more effect on the entry angle than on the amount of hook. A ball with a low Rg is a center-heavy ball where the weight is concentrated close to the center of the ball. These balls hook sooner and have less potential entry angle. They normally are good oil balls. Balls with higher Rg have the weight concentrated closer to the outside shell. They hook later and have more potential entry angle. They normally work better for a drier condition. A lot of times, these balls are sold as less-hooking balls. But when they get on a really dry condition, they can generate a really strong turn on the backend as the chart shows. ABC ball specifications allow the Rg to range from 2.40 to 2.80 inches.

           That was a mathematical analysis of our sport of bowling. Hopefully it was not too confusing. Bowlers might have known some of the end results, like a ball thrown slower will hook more than a ball thrown faster. But now they have an understanding of how much each variable can alter the ball path.  Bowling is a sport which combines bowling talent, knowledge of the equipment, and an understanding of how the environment is constantly changing due to bowling activity. Bowling is a thinking man's game, which makes it so great.

            You can use the Ball Path Simulator on the internet by joining My 300 Club. Click the link to go there: http://www.my300club.com/ . This is a club to help bowlers improve their game and win a new reactive ball for shooting certain scores.