A basketball game is almost over and there is time for only one shot. The team with the ball is behind by two points. Its best 3-point shooter averages 30%, while its best 2-point shooter averages 50%. Who do you have take the last shot? The 2-point player to tie and go to overtime, or the 3-point player for the win?
It probably goes without saying that you should vote before reading any responses. Thanks!
30% is abysmal for a team’s best three point shooter. Even in the 80s.
Taking your percentages, you win with probability 30% if you take the 3 point shot and you win with probability 0.5*(prob win in overtime) with the two point shot. You have to have a win probability in overtime of better than 60% to come out ahead by taking the two point shot. As you are apparently about equally good teams since you’re nearly tied, I’d opt for the 3 point shot barring other information (like the other team’s top three players have fouled out and won’t be available for overtime).
This. I assumed a 50% win chance in OT.
I’d probably opt for the two point shot. Higher chance of extending the game, where maybe the other team gets in foul trouble, or otherwise falls behind. The three pointer is an all or nothing shot that according to the OP only works 30% of the time.
Given the low % you gave for the 3pt shooter, I chose to go for the two, for not all 2-pt goals are alike: a 15-footer might go in 50% of the time, but a shot from below the basket has a 60+% chance of going in.
http://courtvisionanalytics.com/the-shooting-terrain-of-the-nba-mapping-field-goal-percentage/
This is at odds with the assumption others make that overtime is a 50-50 proposition. That seems like a reasonable assumption to me, but you seem to imply otherwise when you say that extending the game is desirable. Any particular reason why, or am I simply misinterpreting?
Conventional wisdom says go for the win on the road and the tie if you are at home.
Ah, yes, baseball logic. But this ain’t about baseball, is it?
Well, understand that I am very much not a math guru. My gut feeling is that I’d rather have an overtime period to win the game than risk everything on a single all or nothing shot that the odds suggest I will miss 2/3 of the time.
Okay, here’s my argument for taking the 3 point shot. And yes, it ignores certain things I didn’t say in the OP.
It is reasonable to assume that since the game in regulation time resulted in a near tie, that both teams are evenly matched. From this, one could surmise that the overtime would result in a similarly close game. Therefore, the odds that a given team would win in overtime are 50% each. If you take the 3 point shot, you have a 30% chance of winning. If you take the 2 point shot, your odds of making it, and then winning in overtime (50%), are .50x.50=.25, ie 25% chance.
.30 > .25 QED
Take the three pointer!
Who said anything about baseball?
But odds also suggest you lose 50% of the time with a 2-pt shot, not to mention you chance of losing in overtime even if you do make it. Thats not much better; actually it’s worse. Assuming its 50-50, as it sounds (if you’re tied after 48 minutes you’re pretty evenly matched), the higher ‘expected win value,’ if you will, comes with a 3-pointer.
You charge the basket and take the 2 once you get contact to draw the foul.
Make the 2 - freethrow to win
Miss the 2 - 2 freethrows to tie
Of course this assumes you can shoot a friggin’ freethrow.
No one, but I didn’t say anything about home or the road.
If I was on a late rush (say I had scored 80% of the last 20 points) then go for two but if I am on the receiving end of it I would go for the three.
Actually I would go for the basket and try and draw a foul for a three point play.
Thank you, Mr. Kryslewski, or whomever that coach was from Duke. But again, not in the OP. 
…uh I was responding to Oakminster’s post (#10), but someone has already explained it better (albeit somewhat differently).
Well, really, it does depend (seems to me) on where the open shot is, who’s open to take it, and how he’s been playing that game.
As may be, I voted for the three. Presumably there’s a good place to take it from.
But I’m no expert fan. Does the coach make such a decision, or is it up to the players?
Subtract everything from the equation. It does not matter what the coach thinks, what phase the moon is in, nor anything else. I like the idea of trying to draw a foul, but that’s not the point. 
Based purely on the info I presented, what do you do?
Take the 3 point shot!!