Just a few weeks in the past, Sports Illustrated tweeted this video of Golden State Warriors level guard Steph Curry that instantly went viral. It reveals him taking a shot on the basket—from the far facet of the court docket. The ball goes in. OK, I can imagine that. He’s a famously nice shooter. But then he turns round and grabs one other ball and takes one other shot … and makes it. And then once more. And once more. And a fifth time.

So is it actual or faux? Let’s use statistics and physics to search out out.

Basic Probability

Physicists do not normally bounce proper into probably the most sophisticated model of an issue. Instead, they do a tough estimation, usually known as a “back of the envelope” calculation. So let’s make some approximations in regards to the likelihood of creating 5 full-court pictures in a row.

We can begin with a easy experiment you can attempt at house—you simply want a coin. Make a prediction: Will it land on head or tails? Unless you’ve got some psychic powers, you should have a 50 p.c probability of guessing proper. It’s finest to consider this as a fraction of 1, so this might be a likelihood of success with a price of 0.5.

What if you wish to predict the result of two coin flips in a row? In that case, you’ll have a likelihood of 0.5 for the primary flip and one other 0.5 for the second. The complete likelihood is the product of those two: 0.5 × 0.5 = 0.25. That’s a one-in-four probability of getting it proper. That is sensible, as a result of there are 4 attainable flipping outcomes: HH, HT, TH, TT.

But in case you needed to foretell 5 flips in a row? That could be (0.5)⁵ = 0.031. You have only a 3 p.c probability to appropriately predict the entire outcomes.

Do you see the place that is going? We can apply this similar thought to basketball. Suppose Steph Curry’s talent is such that he has a 50-50 probability of creating a full-court shot (which might already be wonderful). If that had been true, his probability of getting 5 in a row could be 3 out of 100. That’s really not too dangerous. If you needed to make a viral video, you can simply preserve tossing balls till you get 5 in a row. It would possibly take all day, however it ought to be attainable.

However, it will get a lot worse in case you assume a decrease probability of success for one shot. What in case you can hit simply 1 out of 20 of these full-court throws? (That could be 0.05.) In that case, the possibility of sinking 5 in a row could be 0.00003 p.c. Good luck with that.

Or how about this? Curry takes 5 pictures. What if he has a 50 p.c probability of creating all 5 in a row? He would want a success likelihood of 0.87 per shot to get (0.87)⁵ = 0.5. Just examine that to the likelihood of creating a free throw shot—which is way simpler as a result of the participant is standing a lot nearer to the ring—at somewhere between 0.7 and 0.8.