If the surgeons been successful the last 20 times, then they’re probably doing something different or much better at it than the pool of surgeons the data was pulled from.
You’re only looking at the last 20 and not all of the the surgeries. Imagine the surgeon has had 10020 surgeries and the first 10000 are an even 50/50 split, but the last 20 are all successful. Would you really think you have a higher chance because the last 20 were successful?
Yeah. The odds of 20 coinflips coming up heads is 1 / 2^20, 1 in 1048576. Meaning, it would take over one million tries of 20 coinflips to get one that comes up all heads on average. Our surgeon has done the surgery 10000 times, you say. That’s 500 runs of 20 coinflips. The surgeon could do 2000 times the amount of surgery they’ve already done and not expect a given run of 20 surgeries to succeed. Granted, odds are slightly higher looking for a string of 20 successes in one run of 10000 than looking for one successful run of 20 in 500 runs of 20, but I don’t believe those odds are higher by one or more orders of magnitude. I don’t remember enough of my statistics class to calculate it though and I’m too lazy to look it up. In any case, either that last 20 is an INSANELY lucky run, or the surgeon has improved drastically, and it’s far far farore likely the surgeon has improved or found a way to improve the procedure.
The difference between this and the gambler’s fallacy being it’s not using past results to justify the next, we’re using past results to make a hypothesis that the conditions have changed. If you have a slot machine with a 1% chance to pay out, going 200 or 300 pulls without winning wouldn’t really be unusual. If it didn’t happen for enough tries that you reach the same odds as the surgeon hitting that 20 coinflips run, I’d say your 1% chance slot machine is broken or faulty – you’re so far out of the normal distribution your data points is in a different zip code
I’m pretty sure somewhere your math is going wrong, but that’s not really relevant because I don’t think the hard probabilities are particularly relevant to my point anyway. We’ve established that if the surgeon does 10000 surgeries with 50% success but then does 20 with 100% success then that’s not luck, that’s skill. Just for a second I’m going to bend the original statement.
Instead of the last 20 being 100% the surgeon some point has done 20 successful surgeries in a row. Let’s say he did 5000 surgeries with 50% success, then did 20 with 100% success and then did the next 5000 with 50% success. Would you still call that skill or is it now luck? I think it would be misleading to call it skill because their success rate didn’t change after the 20 surgery streak.
But when we put those 20 to the end it becomes skill? So just because we don’t know the success rate of future surgeries we’re supposed to believe he’s better than 50%? Call me a skeptic but it doesn’t really matter how probable or improbable those 20 surgeries are, I wouldn’t consider that an indication of skill. If someone flipped tails 20 times in a row I wouldn’t go “wow, what a skilled coin flipper”
Gamblers fallacy does go both ways. There’s also a thing in gambling, not part of the gamblers fallacy, more of a superstition thing, that there can be runs of, what is more or less luck. The gamblers fallacy would have you believe that after 20 successes, a failure is “due to happen”. According to math, that’s not the case, and in the event of something that requires skill to execute, almost nothing is just luck or statistics.
So the last one isn’t so much the gamblers fallacy, if anything it would be the superstition that the run of successes will continue; however scientists will look at this more as a game of skill. While 50% of all patients who have the procedure do not survive, or whatever, the last 20 of this doctors patients have survived. Clearly their skill for the procedure is above average. Even from a statistics perspective the rate might be 50% but you’re in the hands of a doctor pushing that number up to 50%, rather than dragging it down to 50%. So on all fronts, if you hear this, bluntly, you have an unknown risk level, somewhere between 50% and 0%.
Nope.
Gambler’s fallacy goes both ways. Just because the last 20 were successful doesn’t mean the actual success rate is higher.
EDIT: Or you might actually be right and whoever made this is wrong.
If the surgeons been successful the last 20 times, then they’re probably doing something different or much better at it than the pool of surgeons the data was pulled from.
You’re only looking at the last 20 and not all of the the surgeries. Imagine the surgeon has had 10020 surgeries and the first 10000 are an even 50/50 split, but the last 20 are all successful. Would you really think you have a higher chance because the last 20 were successful?
Yeah. The odds of 20 coinflips coming up heads is 1 / 2^20, 1 in 1048576. Meaning, it would take over one million tries of 20 coinflips to get one that comes up all heads on average. Our surgeon has done the surgery 10000 times, you say. That’s 500 runs of 20 coinflips. The surgeon could do 2000 times the amount of surgery they’ve already done and not expect a given run of 20 surgeries to succeed. Granted, odds are slightly higher looking for a string of 20 successes in one run of 10000 than looking for one successful run of 20 in 500 runs of 20, but I don’t believe those odds are higher by one or more orders of magnitude. I don’t remember enough of my statistics class to calculate it though and I’m too lazy to look it up. In any case, either that last 20 is an INSANELY lucky run, or the surgeon has improved drastically, and it’s far far farore likely the surgeon has improved or found a way to improve the procedure.
The difference between this and the gambler’s fallacy being it’s not using past results to justify the next, we’re using past results to make a hypothesis that the conditions have changed. If you have a slot machine with a 1% chance to pay out, going 200 or 300 pulls without winning wouldn’t really be unusual. If it didn’t happen for enough tries that you reach the same odds as the surgeon hitting that 20 coinflips run, I’d say your 1% chance slot machine is broken or faulty – you’re so far out of the normal distribution your data points is in a different zip code
I’m pretty sure somewhere your math is going wrong, but that’s not really relevant because I don’t think the hard probabilities are particularly relevant to my point anyway. We’ve established that if the surgeon does 10000 surgeries with 50% success but then does 20 with 100% success then that’s not luck, that’s skill. Just for a second I’m going to bend the original statement.
Instead of the last 20 being 100% the surgeon some point has done 20 successful surgeries in a row. Let’s say he did 5000 surgeries with 50% success, then did 20 with 100% success and then did the next 5000 with 50% success. Would you still call that skill or is it now luck? I think it would be misleading to call it skill because their success rate didn’t change after the 20 surgery streak.
But when we put those 20 to the end it becomes skill? So just because we don’t know the success rate of future surgeries we’re supposed to believe he’s better than 50%? Call me a skeptic but it doesn’t really matter how probable or improbable those 20 surgeries are, I wouldn’t consider that an indication of skill. If someone flipped tails 20 times in a row I wouldn’t go “wow, what a skilled coin flipper”
Gamblers fallacy does go both ways. There’s also a thing in gambling, not part of the gamblers fallacy, more of a superstition thing, that there can be runs of, what is more or less luck. The gamblers fallacy would have you believe that after 20 successes, a failure is “due to happen”. According to math, that’s not the case, and in the event of something that requires skill to execute, almost nothing is just luck or statistics.
So the last one isn’t so much the gamblers fallacy, if anything it would be the superstition that the run of successes will continue; however scientists will look at this more as a game of skill. While 50% of all patients who have the procedure do not survive, or whatever, the last 20 of this doctors patients have survived. Clearly their skill for the procedure is above average. Even from a statistics perspective the rate might be 50% but you’re in the hands of a doctor pushing that number up to 50%, rather than dragging it down to 50%. So on all fronts, if you hear this, bluntly, you have an unknown risk level, somewhere between 50% and 0%.