The statistical likelihood of Steph Curry's ridiculous shooting streak

The best 3-point shooters in the NBA hit around 40% of their attempts with Kyle Korver leading the way at nearly 50%. An oft-forgotten detail is that these numbers occur against NBA level defenses. What would these guys shoot under little or no pressure, ie what would they shoot in practice?

This is a hard number to get at since we don't generally have access to practice statistics of professional basketball players. However, there is some recent anecdotal evidence that we can use to give an estimate for one of NBA's best shooters, Stephen Curry. It was reported that Steph recently hit 77 3-pointers in a row and 94 out of 100 total. We're going to estimate his 3-point shooting percentage in two different ways: the easy, wrong way, and the not-so-easy right way.


The wrong way

Calculating Steph's likely shooting percentage is kind of tricky but we can first make an estimate assuming (incorrectly) that he didn't shoot 100 3s a day, but instead stopped at 77 (if this kind of simplification bothers you then don't become a physicist). In this case his one-day probability is \({p_3}^{77}\), where \(p_3\) is his 3-point shooting percentage. Let's assume for the moment that he shoots the same percentage in practice as in an actual NBA game. Looking at his stats, in 2015 this stands at 44%. Plugging this into our equation we get:

\(p_3 = {0.44}^{77} = 3.51*10^{-28}\).

Clearly Steph shoots a bit better than that in practice. How much better? Steph has been a professional basketball player for 6 seasons. Let's say he does this shooting drill every day he practices over those 6 seasons and that adds up to a total of 1000 days. We also have to assume that this would be newsworthy, i.e. this is not something he pulls off everyday.