The Terrible Tale of the Threes

Two weeks ago, BYU was better than more than 330 of the 345 Division 1 basketball teams in 3 point shooting. Over their first 20 games, BYU was making a very respectable 39.8% of their 3-point attempts. Then something happened. Something terrible. Something so unprobable that it led to the following use of oversized tables and graphs.

Over its last 4 games, BYU has only made 11 of 73 three point attempts, a mere 15.0%. Jimmer Fredette, over his last 4 games has made 11 of 17 NBA-length 3 point attempts; 56 fewer attempts than BYU, but the same number of makes.

Can this slump be blamed on the level of competition? Yes, and no. Loyola Marymount, Pepperdine, Virginia Tech and St. Mary’s rank 15th, 155th, 3rd and 246th respectively in 3 point percentage defense. That’s an average of 105th.

To try to get a rough feel for how unlikely the magnitude of this shooting slump is, let’s look at the math of the coin flip. In calculating the odds of getting a certain number of heads, an assumption is made that it doesn’t matter what has happened in the past as far as what will happen in the future. Now, intuition would have you believe that in the real world, it DOES matter how you have shot in the recent past when determining how likely you will make your next shot. In other words, if a team is hot, they will be more likely to make a shot than average and vice versa. However, statistical research into this very topic (feel free to Google a bit) has failed to substantiate that intuition.

So let’s assume that we have a coin that comes up heads 40% of the time; consistent with BYU’s 3 point accuracy for their first 20 games. If you flipped that lop-sided coin 73 times, how often would you expect to get heads 11 times or less? Well, I simulated this very thing 500,000 times in Excel. In only TWO simulations did Excel produce a result where there were 11 “heads” or less.

Take a look at the raw data and then the bar chart below.  I had to stretch the graph in Excel to be 350 rows high before I could even see the pixel representing BYU’s 11 for 73 likelihood.  Using this approximation, the odds against this severe of a slump is 250,000 to 1.  In reality the odds are most likely not anywhere that extreme, but even if you generously account for an increase in the level of competition and the psychological effects of being in a slump, it’s still safe to say that the magnitude of this slump is still quite remarkable.