A couple of weeks in the past, Sports activities 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 consider that. He’s a famously nice shooter. However then he turns round and grabs one other ball and takes one other shot … and makes it. After which once more. And once more. And a fifth time.
So is it actual or pretend? Let’s use statistics and physics to search out out.
Fundamental Chance
Physicists do not often leap proper into probably the most difficult model of an issue. As a substitute, they do a tough estimation, typically referred to as a “back of the envelope” calculation. So let’s make some approximations in regards to the likelihood of creating 5 full-court photographs in a row.
We will begin with a easy experiment which you can strive at residence—you simply want a coin. Make a prediction: Will it land on head or tails? Except you have got some psychic powers, you’ll have a 50 p.c probability of guessing proper. It is best to consider this as a fraction of 1, so this could 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’d have a likelihood of 0.5 for the primary flip and one other 0.5 for the second. The overall likelihood is the product of those two: 0.5 × 0.5 = 0.25. That is a one-in-four probability of getting it proper. That is sensible, as a result of there are 4 potential flipping outcomes: HH, HT, TH, TT.
However if you happen to wished to foretell 5 flips in a row? That will be (0.5)5 = 0.031. You will have only a 3 p.c probability to appropriately predict the entire outcomes.
Do you see the place that is going? We will apply this identical 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 superb). If that have been true, his probability of getting 5 in a row could be 3 out of 100. That is truly not too unhealthy. If you happen to wished to make a viral video, you can simply maintain tossing balls till you get 5 in a row. It would take all day, however it needs to be potential.
Nevertheless, it will get a lot worse if you happen to assume a decrease probability of success for one shot. What if you happen to can hit simply 1 out of 20 of these full-court throws? (That will be 0.05.) In that case, the prospect of sinking 5 in a row could be 0.00003 p.c. Good luck with that.
Or how about this? Curry takes 5 photographs. What if he has a 50 p.c probability of creating all 5 in a row? He would wish successful likelihood of 0.87 per shot to get (0.87)5 = 0.5. Simply 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.
