Wednesday, June 21, 2006

This year's NBA championship series is now over, with the Miami Heat defeating the Dallas Mavericks 4 games to 2. There were several instances of streakiness in the series, not least Miami's coming back from 2-0 down (and in great danger in Game 3) to take four straight. Each of the teams, as well as individual players, also went through periods of hotness and coldness, of course. Once the Heat began to turn the series around, Dwyane Wade went through stretches where it looked like he couldn't miss (and rarely did). At the other end of the spectrum, the Mavs' outside shooting during the second half of Game 6 seemed to disappear.

What I'd like to focus on here, though, is the dreadful free throw shooting of Miami center Shaquille O'Neal, whose statistics are available here. As all NBA fans know, even under the best of circumstances, Shaq is terrible from the stripe, making only 52.8% of free throws for his career (based on nearly 10,000 attempts!).

This past regular season, O'Neal slipped to 46.9% on free throws, then to 37.4% for the play-offs (68 of 182). In the finals against Dallas, Shaq's FT shooting was particularly hideous, 29.2% (14 of 48). In three of the games against the Mavs, he shot 1 of 9, 1 of 7, and 2 of 12.

Before possibly examining the depths of O'Neal's woes vs. Dallas, I think it's worth testing initially whether the roughly 10% drop in his FT percentage from the regular season to the play-offs overall is statistically significant. With a dichotomous outcome such as hit or miss on a free throw, a statistical technique known as the binomial probability (for which there's an online calculator in my links section, to the right) is very useful. It answers the question of how likely a given pattern is (i.e., a certain number of hits within some number of attempts), given some prior baseline percentage of success.

In Shaq's case, how likely is it that he would have made 68 (or fewer) free throws out of 182, assuming a baserate of .469 (corresponding to his FT percentage in the regular season)? Using the aformentioned calculator, this probability is .006, sufficiently small to be considered statistically significant (cut-offs of .05 or .01 are commonly used).

Thus, even when we take Shaq's play-off FT performance as a whole (not focusing merely on his horrible time in the final round), his fall-off from the regular season is more than would have been expected from ordinary fluctuation. Fatigue is a possibility, especially since his worst round in the play-offs was the last one. However, Shaq and the Heat had a six-day rest from the end of the Detroit series (June 2) to the start of the Dallas series (June 8), and he still went 1 for 9 from the line in the opener against the Mavs.

If anyone would like to conduct statistical analyses of other players in the Miami-Dallas series, please do so. You can provide a brief write-up of what you found in the comments section below.

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