Thursday, January 25, 2007

For an athlete to exhibit a "hot hand," say by making several basketball free throws in a row (which removes the elements of variation in shot distance and defense by the other team), one of the most rudimentary aspects would be his or her ability to remember, at some level, the motoric actions exhibited on previous successful shots and reproduce them (within some margin of error).

Short of videotaping athletes' repeated shots from different angles (and perhaps with some kinds of electrodes, computer microchips, or other detectors attached to their limbs), it would be helpful to have some type of easily recordable measure of shot intensity on repeated trials. From free throws, only the hit-or-miss outcome is easily obtainable, although trajectory and launch velocity could also be gleaned with greater effort.

One potentially informative solution to our problem comes from the annual National Hockey League All-Star SuperSkills Competition, held the night before the actual All-Star Game. Of particular interest to me is the hardest shot competition, where each of the eight participants gets to take two separate whacks at the puck, and the speeds in miles per hour (mph) are revealed instantly by the television crew.

Here we can get a quantitative look -- admittedly from a small sample of players, exhibiting a fairly basic technique -- at the reproducibility of a sports action. A video of the hardest-shot contest and a results page from all of the skills competitions are both available.

I plotted the correlation between the speeds of each player's two shots, as shown below.

The linear correlation is near perfect (.88, where 1.00 is the maximum), indicating that players who really sent the puck zipping along on one of their shots also did so on their other shot, whereas those with relatively slow-moving shots on one attempt also attained similar movement on their other shot.

On this crude test, with shots taken in quick succession, slapshot speed seems highly reproducible.

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