After the awesome half-court (hook!) shot by the Miami Heat fan on Friday, my co-worker asked a bunch of us in a thread what the probability of a random NBA fan making this shot would be.
I doubt anyone actually keeps track of this, so what I did was look at the field goal percentage of NBA players shooting beyond half court, which was around 2.6%. He countered that the data wasn't representative because the players are being (loosely) guarded, under time-pressure, and that I looked at distances well beyond 47 feet. I countered that NBA players are much better shooters than the average fan, and that it more-or-less cancels out those misrepresentations. But he brings up a fair point.
I think he was just angry, because someone bet him he couldn't make 1 in 40 tries.
You guys are all smart, how would you solve this? Relatedly, which side of the bet should I take, assuming even odds?
Probability of a fan making a half-court shot
Re: Probability of a fan making a half-court shot
One person, even if he is verifiably "random", should make a higher % of 40 shots than 40 different random people would make. It's not something most people do very often, and after a few tries, you should be getting closer at least.
Aren't there a number of these contests around the league, for many years? Surely a given team would have a record of how many payouts they've made and how many shots have been attempted.
A hook shot might not be any worse than some other 50-footer. The Harlem Globetrotters or similar outfit would chuck up a few and sometimes make one. Mark Jackson hit one in the NBA Finals. And some head coach (George Karl, perhaps?) used to bet his players he'd hit one before they did.
Standard jump shots are a pushing motion that's difficult from that distance. Running toward the basket gives you some extra momentum. A baseball throw is hard on the shoulder and not accurate. The most ergonomic form might be to face away from the basket and throw with both hands; but you can't see your target.
Aren't there a number of these contests around the league, for many years? Surely a given team would have a record of how many payouts they've made and how many shots have been attempted.
A hook shot might not be any worse than some other 50-footer. The Harlem Globetrotters or similar outfit would chuck up a few and sometimes make one. Mark Jackson hit one in the NBA Finals. And some head coach (George Karl, perhaps?) used to bet his players he'd hit one before they did.
Standard jump shots are a pushing motion that's difficult from that distance. Running toward the basket gives you some extra momentum. A baseball throw is hard on the shoulder and not accurate. The most ergonomic form might be to face away from the basket and throw with both hands; but you can't see your target.
Re: Probability of a fan making a half-court shot
There was an ESPN the Magazine article within the last year or so interviewing a guy who sells insurance for promotions like that. I can't find the issue, but if someone else is able to it might have a number. I do remember that it varies on the circumstances, like if the guy gets one shot coming in cold or if it's part of the lay-up/free throw/half-court in X seconds situation.
Re: Probability of a fan making a half-court shot
Right, I recall reading an article decades ago about a local team (probably a college team, but maybe CBA) that had a fan hit the halfcourt basket -- and then in the next home game, another fan did it! The prize I think was a car, IIRC the president of the team simply shrugged his shoulders and said they had insurance that would pay for the cars.
Yeah, George Karl's favorite trick shot was to face away from the basket at midcourt and sink a shot. But he has huge advantages over an average fan being asked to make such a shot: he's a former NBA player, and clearly practices making that shot.
I had a friend of a friend who at halftime was selected to make a free throw. Obviously the prize was something small, like a free dinner at a local restaurant or something like that. Some of us would have a decent chance of making that free throw, but he hadn't touched a basketball in who knows how long. Result: airball.
But as for the original question about which way to bet on the probability of making a halfcourt shot: really tough to say, especially because the 2.6% and 1 in 40 figures are so close to each other. As others have said, the amount of practice that the shooter gets is a huge huge variable, so that needs to be nailed down. That'd be true even for NBA players. One story said that George Karl liked to end his practices with everyone shooting trick shots (I imagine that a factor here was that he could then unveil his trick-shooting ability). So former Nuggets and former Sonics might be better bets at making the halfcourt shot than other former NBA players.
Yeah, George Karl's favorite trick shot was to face away from the basket at midcourt and sink a shot. But he has huge advantages over an average fan being asked to make such a shot: he's a former NBA player, and clearly practices making that shot.
I had a friend of a friend who at halftime was selected to make a free throw. Obviously the prize was something small, like a free dinner at a local restaurant or something like that. Some of us would have a decent chance of making that free throw, but he hadn't touched a basketball in who knows how long. Result: airball.
But as for the original question about which way to bet on the probability of making a halfcourt shot: really tough to say, especially because the 2.6% and 1 in 40 figures are so close to each other. As others have said, the amount of practice that the shooter gets is a huge huge variable, so that needs to be nailed down. That'd be true even for NBA players. One story said that George Karl liked to end his practices with everyone shooting trick shots (I imagine that a factor here was that he could then unveil his trick-shooting ability). So former Nuggets and former Sonics might be better bets at making the halfcourt shot than other former NBA players.
Re: Probability of a fan making a half-court shot
Excellent, I found the ESPN Mag article on the googles, with the appropriate quote below:
http://espn.go.com/espn/page2/story/_/i ... n-magazine
http://espn.go.com/espn/page2/story/_/i ... n-magazine
Assuming independence across trials and assuming this 2% success is true, the probability of missing 40 in a row is (1-0.02)^40 = ~44.5%. But as you said Mike, independence might not hold, since the more you shoot, presumably the better (and warmer) you get. I guess it depends on how the experiment is conducted.Next he determined the probability of making the half-court shot is 50-1, or 2 percent.