So I’ve been out shooting free throws on my new bball hoop. I’ve been aiming for 70% in clumps of 20 shots. Sidenote: I suck at free throws. I actually made it once yesterday (for the first time). I actually made 16/22.
The real question is, statistically speaking, how often will someone that has a “real” accuracy pct of, say, 50% hit 14/20? I’m sure there is a statistical formula to figure it out…
2 responses to “Free throw shooting”
DISCLAIMER: MATH ALMOST CERTAINLY INCORRECT
Your free-throw shooting follows a binomial distribution with a fixed probability of 50%.
The formula for calculating k successful shots in n attempts given a fixed probability of p is:
nCk * p^k * (1-p)^n-k.
20 Choose 14 is 38760 combinations of successful , so the answer should be 3.6%. This is to hit exactly 14, you can sum the probability of hitting 15, 16, 17, 18, 19, and 20 using the same method to find the probability of hitting AT LEAST 14.
after some discussion, i believe that the excel function
1-BINOMDIST(13,20,0.5,TRUE)
gives you the probability of having more than 13 correct