Probability of missing 100 free throws

[boyznum1]

According to the law of infinite probability, if you were to take a good basketball player and have them shoot 100 free throws an infinite number of times (ignoring fatigue) is it possible for him to eventually miss all 100. I am an assistant coach and had an argument with the head coach over this. Thank you.

[hypervalent_iodine]

I'm not a math expert, but of course it's possible. The likelihood would (I imagine) be very small, but it's still within the realm of possibility.

[DrKrettin]

Let's say that the basketball player has a 1 in 3 success rate of throwing (the argument is the still the same even if its not exactly that)

 

So the probability of a hit for each throw is 1/3.

 

What you need to do is consider the probability of a miss = 2/3.

 

Suppose he takes 100 throws.

The probability of missing the 1st is 2/3

The probability of missing the 2nd is 2/3

 

and so on, so the probability of missing 100 throws is 2^100/3^100 = 2.4596544e-18

 

So as said above, in theory it is possible. This is true for any repitition of any event which has a probability of less than 1 (i.e. not certain)

Edited October 11, 2016 by DrKrettin

[Ophiolite]

I recall a study a couple of decades ago in which the analyst attributed the success of WW1 flying ace Baron von Richtofen to chance. (I believe he had somewhere around 70 'kills'.) I imagine my success as a salesman had much the same explanation.

[tar]

Let's say that the basketball player has a 1 in 3 success rate of throwing (the argument is the still the same even if its not exactly that)

 

So the probability of a hit for each throw is 1/3.

 

What you need to do is consider the probability of a miss = 2/3.

 

Suppose he takes 100 throws.

The probability of missing the 1st is 2/3

The probability of missing the 2nd is 2/3

 

and so on, so the probability of missing 100 throws is 2^100/3^100 = 2.4596544e-18

 

So as said above, in theory it is possible. This is true for any repitition of any event which has a probability of less than 1 (i.e. not certain)

so the 1 in three shooter should miss all 100, if it takes about 5 minutes to shoot a hundred, once every 2.3 trillion years

 

I think it safe to consider the event highly unlikely.

 

However, if the guy or girl has an unknown strain or pull or eyesight issue and his predictive motor simulator has him missing in the same manner each time, and he or she does not correct for the issue, you could get 100 misses the first time. Or if he or she had a bet for 10 bucks that he could miss 100 in a row, he or she could probably miss all 100 the first try.

 

Regards, TAR

Edited October 11, 2016 by tar

[DrKrettin]

so the 1 in three shooter should miss all 100, if it takes about 5 minutes to shoot a hundred, once every 2.3 trillion years

 

I think it safe to consider the event highly unlikely.

 

However, if the guy or girl has an unknown strain or pull or eyesight issue and his predictive motor simulator has him missing in the same manner each time, and he or she does not correct for the issue, you could get 100 misses the first time. Or if he or she had a bet for 10 bucks that he could miss 100 in a row, he or she could probably miss all 100 the first try.

 

Regards, TAR

 

Yes, but the probability of missing 100 times is always non-zero, even when ridiculously small, which is what the dispute was about.

[John Cuthber]

I'm probably a good basketball player, compared to Stephen Hawking.

I would quite possibly miss 100 in a row.

How do you define "good"?

But, in the end it doesn't mater- the odds are not zero.

[tar]

Thread,

 

But, within the scope of the debate, between two coaches that coach basketball players probably more adept at free throws than John Cuthber the once in 3 trillion year possibility of missing 100 in a row, is for all intents and purposes close enough to zero to grant the argument to the coach that thought it would not ever happen, on their watch.

 

However, if you were coaching 5 year olds that did not have the strength to reach the rim from the foul line, the odds would be pretty good, indeed.

 

So given the 1 in three shooter as the caliber of foul shooter the coaches are coaching, I would still say that neither will ever see a guy or gal without a handicap, that is trying to make each shot, miss 100 in a row.

 

Regards, TAR

It is possible that the shooter could miss 100 in a row, but it is also possible the gym could be torn down, before she missed 100 in a row. More possible, that the gym will be torn down, within 3 trillion years, than that she will miss 100 in a row.

Besides, anyone that could miss 100 in a row, needs a better coach.

However, I am not sure random chance is involved, because skill is involved and muscle memory and the predictive motor simulator, that knows which muscles to activate at what time and with what force to get the ball to follow a successful trajectory.

Reminds me of a sponge bob square pants episode where he accidently ties his shoes together and falls down EVERY step he takes, all the way home.

Once you learn to thread a needle, and have the right light and the right technique, you will get it. It is not a random chance operation.

so the idea that a foul shooter could miss 100 in a row, is similar to the idea that you would fall down every time you took a step, attempting to get from goal line to goal line on a football field

possible, but if you know how to walk, and you are not injured or impeded in some way, you are not going to fall down EVERY step

Edited October 11, 2016 by tar

[dimreepr]

but if you know how to walk, and you are not injured or impeded in some way, you are not going to fall down EVERY step

 

 

And yet people fall down.

[boyznum1]

Let's say that the basketball player has a 1 in 3 success rate of throwing (the argument is the still the same even if its not exactly that)

 

So the probability of a hit for each throw is 1/3.

 

What you need to do is consider the probability of a miss = 2/3.

 

Suppose he takes 100 throws.

The probability of missing the 1st is 2/3

The probability of missing the 2nd is 2/3

 

and so on, so the probability of missing 100 throws is 2^100/3^100 = 2.4596544e-18

 

So as said above, in theory it is possible. This is true for any repitition of any event which has a probability of less than 1 (i.e. not certain)

Probably should have clarified, an average free throw shooter is about 70% from the free throw line.

[DrKrettin]

is it possible for him to eventually miss all 100.

 

 

Ok, if you are insisting, I still say that the answer to the above question is yes.

[tar]

I think infinite probability theories miss the reality of the situation. Like the infinite number of monkeys typing out the works of Shakespeare. Most likley the typewriters would all be jammed or broken, long before any one monkey changed even one piece of paper following a flawlessly typed first page.

Edited October 11, 2016 by tar

[dimreepr]

I think infinite probability theories miss the reality of the situation. Like the infinite number of monkeys typing out the works of Shakespeare. Most likey the typewriters would all be jammed or broken, long before any one monkey changed even one piece of paper following a flawlessly typed first page.

 

 

If the probability of this event is once in a trillion years, we can't say it won't happen tomorrow.

[tar]

dimreepr,

 

sure people fall down, but not 100 times in a row, unless they are crippled or drunk or the field is iced

dimreepr,

 

equally possible it happened yesterday, and neither coach saw it, or will, for another 3 trillion years

 

Regards, TAR

Edited October 11, 2016 by tar

[dimreepr]

dimreepr,

 

equally possible it happened yesterday, and neither coach saw it, or will, for another 3 trillion years

 

Regards, TAR

 

So???

Even if it happened yesterday, It doesn't mean it won't happen tomorrow.

[tar]

so I am changing my answer

 

There are 500 million people in the world that play basketball. Most have probably taken 100 free throws, if not standing at the same foul line, without moving, at least one can consider any run of 100 foul shots they took. A one in a trillion possibility, given 500,000,000 people, would look more like a 1 in 2,000 possibility. Given that for our purposes we could take any string of 100 shots they took. Somebody, somewhere, at some point, could have missed 100 in a row. Might have already, might happen again.

of course after missing 99 in a row, one might have switched to another sport

Or, what is the probability of missing 100 free throws in a row, and staying on the team?

Edited October 11, 2016 by tar

[dimreepr]

so I am changing my answer

 

There are 500 million people in the world that play basketball. Most have probably taken 100 free throws, if not standing at the same foul line, without moving, at least one can consider any run of 100 foul shots they took. A one in a trillion possibility, given 500,000,000 people, would look more like a 1 in 2,000 possibility. Given that for our purposes we could take any string of 100 shots they took. Somebody, somewhere, at some point, could have missed 100 in a row. Might have already, might happen again.

of course after missing 99 in a row, one might have switched to another sport

Or, what is the probability of missing 100 free throws in a row, and staying on the team?

 

 

You miss the point; skill does change probability, but not what will happen tomorrow.

[tar]

dimreepr,

 

but if there is a 50 50 chance you are going to make the free throw, each time you make the attempt, there is still a 50 50 chance you are going to make it after you missed 76 in a row...and if you make it, the count starts again at zero

 

any shot, today, tomorrow or after 99 misses or 99 hits has a 50 percent chance of going in

 

earlier calculations on the thread were based on a 1 in 3 hit rate, and later it was acknowledged that 70 percent hit rate is more likely among good basketball players

 

the worst NBA foul shooters shoot better than 50 percent

 

what are the odds that a 50 percent foul shooter will miss 100 in row?

[dimreepr]

dimreepr,

 

but if there is a 50 50 chance you are going to make the free throw, each time you make the attempt, there is still a 50 50 chance you are going to make it after you missed 76 in a row...and if you make it, the count starts again at zero

 

any shot, today, tomorrow or after 99 misses or 99 hits has a 50 percent chance of going in

 

earlier calculations on the thread were based on a 1 in 3 hit rate, and later it was acknowledged that 70 percent hit rate is more likely among good basketball players

 

the worst NBA foul shooters shoot better than 50 percent

 

what are the odds that a 50 percent foul shooter will miss 100 in row?

 

 

How does that argue my point?

[tar]

probably close to the odds of flipping 100 heads in row

 

possible, but its not going to happen tomorrow, unless the coin is weighted to highly favor a head

dimreepr,

 

as to the thread question, it is possible for extremely long odds to hit, but the longer the odds, the less likely

 

At a certain point, the odds are so long, as to be considered close enough to zero, to be functionally zero.

[swansont]

!

Moderator Note

tar, stop hijacking the discussion. Bringing up needing a better coach, staying on the team, broken typewriters, etc. are all off-topic distractions.

Do not further hijack the thread by responding to this in the thread

[tar]

so what is the probability of missing 100 free throws in a row, if you are a 50 percent free throw shooter?

if you are a 50 percent free throw shooter, are the odds the same that you will miss 100 in a row, as that you will make 100 in a row?

 

if you are a 50 percent free throw shooter, are the odds of any particular streak of misses the same as the odds of that number of makes in a row?

[dimreepr]

Seven impossible things you can do before breakfast...

[tar]

does missing 99 in a row lower the percentage of free throw shooter you are below 50 percent, and make it a little more likely you are going to miss the next shot?

[DrKrettin]

so what is the probability of missing 100 free throws in a row, if you are a 50 percent free throw shooter?

if you are a 50 percent free throw shooter, are the odds the same that you will miss 100 in a row, as that you will make 100 in a row?

 

if you are a 50 percent free throw shooter, are the odds of any particular streak of misses the same as the odds of that number of makes in a row?

1. 0.5^100 = 7.8886091e-31

 

2. Yes

 

3. Yes