Zayna's Free Throw Analysis

For this project, I calculated the parabolas of three different free throws. The first free throw I looked at was WNBA player Elena Delle Donne. In 2015, she shot over 95% from the free throw line, the highest percentage in the WNBA and the NBA. I also looked at my own free throw shot to compare the parabola of an amateur to a professional free throw shooter. The last free throw I looked at was an underhand free throw from a professional basketball player. I used logger pro to graph the shape the shot forms and then I used Desmos to make equations that fit the data. By looking at the different data points of the graph, it is clear that the underhand free throw is released from further back (by about 1.5 units) and is also released from significantly lower than the over hand shot by about 2.25 units. The general shape of Delle Donne’s shot (black) and my shot (blue) are very similar, although it’s clear that my shot has a higher arc. Delle Donne’s shot has a vertex of (4.95, 5.232), my shot has a vertex of (5.055, 5.391), and the underhand shot has a vertex of (4.89, 4.967). The x-coordinate varies by 0.165 meters, or 16.5 centimeters. The y-coordinate, or how high above the ground the ball is, varies by 42.4 centimeters. It’s interesting that the vertex of the underhand shoot has a lowest x and y coordinate. This would make me think that underhand shot is a low-percentage shot because it would be having more force going forward than down when it reaches the basket. However, underhand free throws, despite their unpopularity in professional basketball, generally have a higher free throw percentage because there is less room for error when the ball is released. My shot and Delle Donne’s shot have a similar vertex with the x-coordinate varying by 10 centimeters and the y-coordinate varying by 15.9 centimeters. Another interesting difference between all three of them is how much (or little) the parabola is stretched by. The underhand free throw is stretched the most (by 0.225), which makes sense because it’s released further from the basket than the other two shots. Delle Donne’s shot and my shot vary significantly. My shot is stretched by 0.39 whereas her shot is stretched by 0.31. It makes sense that my shot is stretched less because my shot had a higher arc. If I shoot 16 centimeters lower and 10 centimeters less far, Elena Delle Donne needs to watch out! Growing another foot might also help.

MST, Division 3Emily NaitoDecember 7, 2020