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# Three-pointer vs free-throw probability

Our friend and Cleveland Cavalier, LeBron James, asks Sal if there's a high probability of making three free throws in a row or one three-pointer. Before solving the problem, jot down what you think the answer will be! Created by Sal Khan and LeBron James.

## Want to join the conversation?

• So what is causing the rise of the 3-point shot? Are players getting better at shooting or is there some other factors to consider?
• Yes, culture and tradition does come into it. When they added the 3-point shot, players were learning to shoot from there. Now children are practicing 3-points from a very young age.
• If Lebron's 3 point percentage is 33%, wouldn't that mean each 3 pointer he takes, on average, is worth 1/3 of three points, or 1 point. If his free throw percentage is 75%, one can reason that each free throw he takes has an average worth of .75 points. Yet, Sal just proved he has a higher chance of getting three free throws in a row than making one three pointer, which seems to imply his free throws are more valuable. Could someone explain where I'm mistaken?
• When a basketball shoots a free throw their their a 9 times out of 10 chance going to make it. Making a jumper is a good shoot to take because it will give you the ability to make farther distant shot. For example when i pull up from Half court or Mind court i gives me a boost to make it.

PS: Why do NBA players have to not jump when they take Free Throws?
• This is a pedantic question, but aren't free throws not independent events?
Won't the shooter's state of mind and maybe even fitness change as the number of free throws increase?
• Hello S,
You are introducing real world variables (psychology, fatigue, etc) into a math problem. You make valid points because, yes, it is more difficult to make a free throw when you are tired at the end of a game, or if you are in a high pressure situation like an NBA Finals game rather than at practice. If you could quantify those variables somehow, you could then figure out the "true" probabilities of success in a given situation.
For the purpose of these lessons, however, I think Sal is just using a real world example, minus the real world variables, to demonstrate how the math works in a more entertaining way.
Good observation though :-)
• yes free throw whould be better because it has a better chance of making it then a three pointer.
• free throws are easier because no one can block or foul you unlike 3 pointers which are also farther away
• what if you have a player like Stephen Curry? His free-throw percentage (in his best year) would be 90 and his 3-pt percentage (also in his best year) would be 47.
• If you apply the exact same method that Sal discussed in the video, you would find that Stephen Curry's chance of making 3 free throws in a row would be (0.9)^3, or 72.9%. This is higher than his 3 pointer percentage of 47%, so Curry would be more likely to make three free throws in a row than one three pointer.
• How are you able to calculate the percentages since they change all the time?