During the 2015 NBA playoffs, the Wall Street Journal published this article detailing the difference in Steph Curry’s free throw percentage with his mouthguard both in and out of his mouth. According to the WSJ research team, Curry made 198 out of 214 free throws while his mouthguard was out of his mouth (a 92.5 FT%), while making 110 out of 123 with his mouthguard in his mouth (a 89.4 FT%).
The average sports fan can look at these numbers and assume that Curry should shoot with his mouthguard out at all times, given his higher success rate. Is there really evidence that Steph shoots better with his mouthguard out of his mouth though? Let’s use descriptive statistics to further scrutinize the data.
In statistics, one would use a two–proportion z–test to determine whether the hypothesized difference between population proportions differs significantly from the observed sample difference. In English, we’d use a specific test to see whether Steph objectively shoots better with his mouthguard out or if the difference in shooting percentages is negligible.
There’s two possible outcomes:
- Steph Curry does NOT shoot any better with his mouthguard out of his mouth than in his mouth. (What’s called in statistics the null hypothesis)
- Steph Curry statistically shoots better while chewing on his mouthguard than with it in his mouth. (The alternative hypothesis).
After putting the data into a calculator, we’re left with a somewhat confusing line of numbers. Population1 represents Curry’s shooting with his mouthguard out (198 successes out of 214 attempts). Population2 represents Curry’s shooting with his mouthguard in (110 success out of 123 attempts). When we subtract Population1 from Population2, our hypothesis test outputs a p-value of .1649 or about 16.5%. The p-value is the probability of obtaining a result equal to or more extreme than what was actually observed. Typically, a p-value of less than or equal to .05 (or the level of confidence of the hypothesis test) entails that there is enough evidence to reject the null hypothesis and accept the alternative hypothesis. In the case of Steph Curry, the p-value is significantly greater than .05, so we can say that there is NOT statistically significant evidence that Steph Curry shoots better while chewing on his mouthguard than he does with his mouthguard in his mouth.