A few weeks ago, Sports Illustrated tweeted this video of Golden State Warriors point guard Steph Curry that instantly went viral.It shows him taking a shot at the basket—from the far side of the court. The ball goes in. OK, I can believe that. He’s a famously great shooter. But then he turns around and grabs another ball and takes another shot … and makes it. And then again. And again. And a fifth time.
So is it real or fake? Let’s use statistics and physics to find out.
Physicists don’t usually jump right into the most complicated version of a problem. Instead, they do a rough estimation, often called a “back of the envelope” calculation. So let’s make some approximations about the probability of making five full-court shots in a row.
We can start with a simple experiment that you can try at home—you just need a coin. Make a prediction: Will it land on head or tails? Unless you have some psychic powers, you will have a 50 percent chance of guessing right. It’s best to think of this as a fraction of 1, so this would be a probability of success with a value of 0.5.
What if you want to predict the outcome of two coin flips in a row? In that case, you would have a probability of 0.5 for the first flip and another 0.5 for the second. The total probability is the product of these two: 0.5 × 0.5 = 0.25. That’s a one-in-four chance of getting it right. That makes sense, because there are four possible flipping outcomes: HH, HT, TH, TT.
But if you wanted to predict five flips in a row? That would be (0.5)5 = 0.031. You have just a 3 percent chance to correctly predict all of the results.
Do you see where this is going? We can apply this same idea to basketball. Suppose Steph Curry’s skill is such that he has a 50-50 chance of making a full-court shot (which would already be amazing). If that were true , his chance of getting five in a row would be 3 out of 100. That’s actually not too bad. If you wanted to make a viral video, you could just keep tossing balls until you get five in a row. It might take all day , but it should be possible.
However, it gets much worse if you assume a lower chance of success for one shot. What if you can hit just 1 out of 20 of those full-court throws? (That would be 0.05.) In that case, the chance of sinking five in a row would be 0.00003 percent. Good luck with that.
Or how about this? Curry takes five shots. What if he has a 50 percent chance of making? all five in a row? He would need a hit probability of 0.87 per shot to get (0.87)5 = 0.5. Just compare that to the probability of making a free throw shot—which is much easier because the player is standing much closer to the hoop—at somewhere between 0.7 and 0.8.