The Basketball Calculator

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A jock filled world of basketball players who make million dollars off nothing they learned from a classroom may ironically be evolved by the classroom. It has longed been known that a players past success rate when shooting a basketball can be measured in percentages. However, the use of math to predict the future success of bank shots is an untapped market that may show enough promise to reshape the preparation of a pro basketball player in the future. This area of analysis can be depicted in 3 ways: how math is already used to calculate bank shot success, how the Pythagorean Theorem can predict bank shot success, and the effect of different angles on the success on the bank shot. By exploring these 3 concepts, the experiment can determine what variables should be manipulated.

First off, mathematical strategies are already applied to the art of shooting a basketball. According to the WIRED 2011 article called “Optimizing a basketball shot”, the equation of projectile motion in the x and y directions can applied to the task of making a shot. In this scenario, the angle the player must shoot the basketball with has to have its final position and the center of the basket to create a smooth shot. This does serve as a guide for angles the players may have to shoot relative to the floor. Another example of mathematical consideration in the context of basketball is the use of velocity. In the weebly article, “The Physics of Basketball”, velocity and force are huge factors in making a basketball shot as the force applied can influence the velocity of the shot immensely creating a response that may be enough to keep the basketball out of the hoop. To summarize math is already to have an established correlation with basketball shots.

Second off, the Pythagorean Theorem can be key to unlocking a basketball calculator or an equation that truly predicts the shot success. According to 2006 book called “The physics of Basketball” by John Fontenella, bank shots are easier to apply mathematical concepts to because air resistance is negligible as the success of the shot depends on the position the ball hits on the backboard relative to the hoop. The rebound caused by Newton’s third law creates triangles that can be solved using Pythagorean Theorems and trigonometry. The prospect of such an application can tie directly into the experiment. In addition, a Science Daily 2011 article called “optimal aim points for bank shots” indicates that a v shape created by hitting certain points of the backboard and the end of the “v” can convey the ball position when entering the rim. Knowing this piece of information, we can devise a way to calculate the success of a bank shot with actually going into a gym and shooting a basketball.

Finally, to make this experiment worthwhile, it should be designed to expand on the research done by others in this topic. According to a Science Daily 2015 article called “Mathematical proof for hot hand shooting in basketball”, there is shown to be strong relationship between the angle at which you shoot the basketball and the trajectory it may take after impact with backboard. The project proposed for science fair should take the trajectory of the rebound force of basketball and see the probability of getting a ball with distinct dimensions inside a hoop. This will allow the manipulation of angles to see variation in shot success.

In conclusion, mathematical analysis of shot selection in basketball is a definite but primitive topic area where it has not been used to improve the performance of basketball players. This is seen in the established research in the use of velocity, angle and the creation of a v shape to determine where the ball may end up However, it is also proven there is no conclusive research on it determination on shot success. This what the project presented hopes to accomplish. This science fair experiment will use calculated trajectory to find how often the ball can fit within the dimensions of a simulated hoop. This can have numerous benefits for the world of basketball as it can guide athletes in taking better shots to win more and swing the multimillion dollar industry to invest in mathematicians.

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The Basketball Calculator. (2020, Feb 06). Retrieved from

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