several weeks Previous, sports illustrated Golden State Warriors point guard Stephen Curry tweeted this video it went viral right awayIt shows him aiming at the basket from across the court. I got a ball. OK, I believe you. He’s a famous great shooter. But he turns around, grabs another ball, takes another shot…and makes it. and again. and again. And the 5th time.
So is it real or fake? Let’s find out using statistics and physics.
basic probability
Physicists usually don’t jump straight to the most complicated version of the problem. Instead, make a rough estimate, often called a “back of the envelope” calculation. Let’s make a rough estimate of the odds of him making five full-court shots in a row.
Let’s start with a simple experiment that you can do at home. All you need is coins. Make a prediction: Will it land on its head or tail? Unless you have psychic abilities, you have a 50% chance of guessing correctly. It’s better to think of this as a fraction of 1, so a value of 0.5 is the probability of success.
What if you want to predict the outcome of two consecutive coin tosses? Then the probability of the first flip is 0.5 and the probability of the second flip is 0.5. The total probability is the product of these two: 0.5 × 0.5 = 0.25. The probability of getting it right is 1 in 4. This makes sense because there are four possible reversal results: HH, HT, TH, TT.
But what if we want to predict 5 flips in a row?it will be (0.5)Five = 0.031. The probability of correctly predicting all outcomes is only 3%.
Can you see where this is going? This same idea can be applied to basketball. Suppose Stephen Curry’s skill is such that he has a 50-50 chance of making a full-court shot (which is already amazing). If that’s true, he has a 3 in 100 chance of winning his fifth straight. It’s actually not that bad. If you want to make a viral video, you can keep throwing 5 balls in a row.
However, assuming a single shot is unlikely to succeed, it’s even worse. What if he can only hit 1 out of 20 full-court throws? (That would be 0.05.) Then the chance of sinking 5 in a row would be 0.00003%. Please do your best.
or how about this? Curry has five shots. What if he has a 50% chance of succeeding? all five continue? To get (0.87) you need a hit probability of 0.87 per shot.Five = 0.5. Compare this to the probability of making a successful free throw shot (which is much easier since the player is standing closer to the hoop). Somewhere between 0.7 and 0.8.
