Tuesday, January 06, 2009

Happy New Year to everyone! Please pardon my lack of timeliness, but back on Christmas Day, Shaquille O'Neal recorded the dubious career milestone of missing 5,000 free throws. Wilt Chamberlain is the only other member of this club.

Though O'Neal has carried a well-deserved reputation throughout his career as a disaster at the stripe (detailed here), strange things can happen when one plays as many games as he has (somewhat over 1,000, coming into this season).

As stated on O'Neal's official NBA biography page, he "was a perfect 13-13 from the foul line against Denver on Apr. 17, establishing a career high for most free throws made in a game without a miss" in the 2000-01 season (this is the only perfect free-throw shooting game by O'Neal, with a large number of attempts, I'm aware of, but I can't rule out the existence of others; he also once had a 16-of-18 game ).

For his career, O'Neal has been around a 52% free-throw shooter. His probability of pulling off a perfect 13-for-13 free-throw performance purely by chance (i.e., under an independence model) can therefore be estimated by raising .52 to the 13th power, which yields .0002. This probability is somewhat smaller than O'Neal's (apparent) actual rate of flawless nights from the line -- once in roughly 1,000 games -- but not all that different. Phil Maymin comes up with some similar calculations here.

Maymin's article makes an important point regarding the symmetry of extreme tails on the normal, bell-shaped curve: "If Shaq takes, for simplicity, about ten free throw attempts per game, then it would take one thousand games before he either made or missed all ten" (my emphasis added). In fact, O'Neal once had an 0-for-11 free-throw game (again, I can't be sure that he hasn't had additional all-miss games from the stripe).

I hope readers will forgive me for not looking up box scores from all 1,000-plus O'Neal games and creating a frequency distribution of game-specific free-throw percentages to compare to the normal curve. Based on this cursory review, however, Shaq's free-throw shooting appears consistent with coin-tossing.


igor eduardo küpfer said...

Basketball-reference has a search engine for games played that makes checking on Shaq's FT ability easy. For example here is a query showing all of Shaq's 0-for-n games where n>=5.

alan said...

Wow! Thanks so much.