We use three-dimensional optical tracking data on the 25-frames-per-second positional data of 2,400 free throw shots by the twenty players with at least twelve tracked makes and twelve tracked misses over the course of the 2010-2011 NBA season, fit each trajectory to a comprehensive physics model to find the implied backspin, initial launch height, velocity, angle, and left-right deviation, and examine the differences of those five factors between makes and misses for each player with sufficient attempts in our sample. We find that usually one or two factors are most responsible for a given player's misses, but the particular factors at fault differ across players. Thus, the causes of successes and failures in free throw shooting are idiosyncratic. This framework may also be useful in analyzing jump shots taken during the game.
Available on SSRN and on JQAS.
Citation: Maymin, Allan; Maymin, Philip Z.; Shen, Eugene (2012), "Individual Factors of Successful Free Throw Shooting," Journal of Quantitative Analysis in Sports 8:3, doi:10.1515/1559-0410.1414.
Data
The data used in this paper has been made publicly available. Download CSV.
The 2,400 rows after the header row each represent the best-fit parameters of a single free throw trajectory following the methodology described in the paper.
The columns are: Player Name, Backspin (w), Launch Height (z), Launch Velocity (v0), Launch Angle (a), Left-Right Deviation (lr), and Made/Missed (result; 1=make, 0=miss).
Media and Press
- Fox News: Study reveals why NBA players miss free throws
- Sina Sports: 3D手段能让魔兽不再尴尬？ 数据揭示罚球不中原因