Just a few 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 aspect of the court docket. The ball goes in. OK, I can imagine 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 faux? Let’s use statistics and physics to search out out.
Fundamental Likelihood
Physicists do not often leap proper into essentially the most sophisticated model of an issue. As an alternative, they do a tough estimation, typically known as a “again of the envelope” calculation. So let’s make some approximations concerning the likelihood of constructing 5 full-court photographs in a row.
We are able to begin with a easy experiment which you could attempt at house—you simply want a coin. Make a prediction: Will it land on head or tails? Until you’ve gotten some psychic powers, you should have a 50 % probability of guessing proper. It is best to think about this as a fraction of 1, so this may be a likelihood of success with a worth of 0.5.
What if you wish to predict the end 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 attainable flipping outcomes: HH, HT, TH, TT.
However for those who wished to foretell 5 flips in a row? That may be (0.5)5 = 0.031. You may have only a 3 % probability to accurately predict all the outcomes.
Do you see the place that is going? We are able to apply this identical concept to basketball. Suppose Steph Curry’s talent is such that he has a 50-50 probability of constructing a full-court shot (which might already be superb). If that have been true, his probability of getting 5 in a row can be 3 out of 100. That is really not too unhealthy. If you happen to wished to make a viral video, you possibly can simply maintain tossing balls till you get 5 in a row. It’d take all day, nevertheless it must be attainable.
Nonetheless, it will get a lot worse for those who assume a decrease probability of success for one shot. What for those who can hit simply 1 out of 20 of these full-court throws? (That may be 0.05.) In that case, the possibility of sinking 5 in a row can be 0.00003 %. Good luck with that.
Or how about this? Curry takes 5 photographs. What if he has a 50 % probability of constructing all 5 in a row? He would want successful likelihood of 0.87 per shot to get (0.87)5 = 0.5. Simply evaluate that to the likelihood of constructing a free throw shot—which is far simpler as a result of the participant is standing a lot nearer to the ring—at somewhere between 0.7 and 0.8.
