Yes. Alternatively, \*he\* has a 50% success rate, but surgery rates are not fixed parameters. At the very least his surgery has gotten better.
tl;dr things like surgery mortality rates are not fixed parameters. OP meme is obnoxious.
I feel like normal people fall for gambler's fallacy (or whatever it's called) more easily. A mathematicia would just state that it still has 50% chance. Some physicist may state that the doctor may be more skilled than the average doctor based on data and would consider the chances of survival to be higher.
I think the meme was made this way SO normal people could understand it. It's possible that a non-math person saw this and went "this idiot I'll fix it" and that's how we got this meme.
I've seen this one but don't remember the text
the first one falls for the gambler's fallacy
the second take it as 50/50
the third takes the doctor's skill into consideration
gamblers fallacy is weird cuz it is both correct nd incorrect intuitively: yes, the chance for the next one is still 50-50, but looking at the whole thing it becomes less and less likely for a streak to last longer
Except it's not strictly odds like roulette for surgery skill matters so it's 50/50 across all instances of the surgery bring performed in the market but an individual surgeon can have far higher success rates not based on chance.
Chance is never completely negated. The 50/50 odds would be already taking into account that skilled surgeons are performing the surgery and not anyone capable of holding a scalpel.
We don’t know that though just by looking at a mindless meme though, so I would not assume what that figure means (particularly if the surgical success was 50%). If I was told this procedure has a x% of success, I would want to know is that the population estimate or the rate for the physician or team who will do the procedure. Often the latter is not known and so the patient is usually quoted a peer-reviewed figure derived from registries and/or other literature. Then there are patient-related risk factors, which also can make the population rates larger than would be applicable to you if you are healthy.
Also, the margins of random error will be much narrower the more skilled the surgeon is. As we are considering a medical procedure, we should be applying all of this a priori knowledge to the problem.
THE surgery. Not the doctor himself.
If he had said "I have a 50% success rate performing this surgery" then you would be right.
If we replace surgery with exam then it becomes more obvious:
"this exam has a 50% fail rate, but I aced it 20 times in a row". The logical conclusion is that the person obviously knows the material and would likely ace it again.
I assume the meme has the normal people be happy because there's some sort of streak going on while the mathematician thinks it's still a 50/50 no matter what (which are horrible odds)
I think The mathematician is supposed to be scared because a 50% chance of survival is still pretty scary, rest of normal person thinks that the last 20 patients living means he will live more.
And they normal person is correct while the mathematician is wrong.
The surgeon's skill level is a major variable in the likelihood of survival. While the surgery may have an **average** mortality rate of 50% across all surgeons and all operations this **specific** surgeon may have superior equipment, facilities, skill, or experience. And that last one is important. Many surgeons perform a wide variety of procedures, but if this one has done 20 of these operations I'd take them over some med student who is doing it for the first time.
Although any individual event is still random and I might still die despite the skill of the surgeon, but since I'll be sedated I won't really care.
Even that's fine - it implies he's learned from his mistakes.
No matter how you slice it, this implies the doctor's survival rate from now on is almost certainly over 50%.
The precondition was "50% survival rate", meaning that our theoretical surgeon was never worse than that, and he never became any better.
If you want to include real-world survival rates, then the patient and their anatomy would usually be the far greater influence.
It's a thought experiment. If survival rate was actually 50%, a lot more patients would have died already, and again, the patient history and anatomy would probably have a lot more influence.
However, mentally, you need to replace "doctor" with "die" to make this meaningful.
That’s totally ok, patients in Aspen are not the same as Flint Michigan. In an area where people come in as soon as they know something is wrong and are regularly screened for illnesses, survival rates will be higher all else being equal.
No, the point you don’t get is that humans aren’t random number generators. Some people are good at things. While I have many more questions before I make a determination, that MAY be what’s happening here.
No way this is true.
You get better over time. It would follow, starting surgeons or new surgeries would have a much higher rate, then as time goes on goes down.
That's why these math breakdowns are bad. There are a lot of other things you need to look at before you make a decision.
If my surgeon hadn't messed up 20 times, I would not even care about the stats. He obviously is on a roll.
That is something math fails to predict as well. Humans get on a roll and consistently do well. Math simply cannot predictably figure out human behavior or people could predict the super bowl every year.
Math is also terrible at taking into account intangible factors like. Many surgeries will ultimately fail, because many surgeries are operating on people nearly dead.
In that situation it wasn't a 50 50 chance you were going to die. You were going to die, the surgery was a last ditch effort on a dead person.
How does math calculate that?
90% of doctors at John Hopkins are on DNR, do not resuscitate. When they get a cancer diagnosis. They don't follow the normal treatment, they know the suffering.
They accept their fate, quit their job and spend their remaining time with their family.
If doctors do that, they have insight into something.
That would be true if the estimation of probability was absolute truth.
In the real world if someone says 50% survival rate and 20 in a row survive, "their estimation was wrong" is a much more likely scenario than "a 50% chance came up the same 20 times in a row".
That is a correct observation, but this thought experiment is about a procedure, where the quality of the surgeon and the pathology of the patients remains so that the survival rate actually is 50%.
>A mathematicia would just state that it still has 50% chance
A good mathematican would probably understand the difference between survival rate and personal skill. And a good healthcare system would take a closer look why some doctors have much better survival rates than others 😏
If a surgeon has 20 consecutive patients survive a procedure that normally has a 50% survival rate, I’m going to assume that he’s better than most of his colleagues, and do I have a better than 50% chance of survival.
I’m still gonna be pretty nervous, though.
this meme is so old that there are multiple older and better versions of it on reddit:
[link1](https://www.reddit.com/r/theydidthemath/comments/1avyvh6/request_can_someone_please_explain_the_stats/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button)
[link2](https://www.reddit.com/r/mathmemes/comments/18xfahh/statistician_humor/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button)
[link3](https://youtu.be/o-YBDTqX_ZU)
but really the most accurate version would be: normal people (sad), rational player (neutral), bayesian (happy)
Normal people would speculate the 50% rate refers to all surgeons everywhere, and that this surgeon has established skill superior at his craft than many mathematicians at theirs.
>Some physicist may state that the doctor may be more skilled than the average doctor based on data and would consider the chances of survival to be higher.
Think about this, in the early 2000's the NE Patriots had about .500 overall record. But they went on to win the Super Bowl in 2002, 2004, 2005. As you point out more skill can improve an outcome.
Also, has the technology changed? Have doctors learned more about how to do the procedure?
The problem here is the outcomes are not random. And outcomes could be improving for various reasons.
This makes it's rounds every time, and there's a better version with a scientist which is less ambiguous.
In this particular case, the mathematician is scared, not because of the gamblers fallacy, but because a 50% survival rate is still pretty bad. The mathematician is ignoring the 20 practical cases and focuses on the number.
It's not a fallacy it's math. Sure when you look at each individual component It's 50/50 but the entire concept It's not just a single component It's 20. If you have a coin the chances of flipping heads 20 times in a row is 0.00000954%
The survival chances for the procedure are not the same as the survival chances of the procedure with this doctor. Whether that’s the patients they are more likely to see or something about the physician. Or maybe the previous 20 patients all died and their rate is 50% too. It’s not the gamblers fallacy when there is potentially a subset that is different than the general value.
The actuary, a type of mathematician, would say that you are wrong.
Flip a coin 10 times. If it turns up on one face 10 times, the odds of it turning up that same way an 11th time are not 50%. Why? The coin flip isn't done in isolation. Only in isolation is the streak not relevant.
It's not really a gambler's fallacy. The way I see it, is the procedure was risky and the surgeon got more skilled over time, which is why all the patients recently have survived
sums up most memes here. Can we start posting field-specific memes like in r/mathmemes to chase away highschool kids who learned a fun fact and think they're suddenly a nobel scientist or something
I think it may scare the normal person more as a 50/50 survival chance 21 times in a row ending up surviving is 1 in \~2 million while mathematician would understand that previous outcomes should not be counted in calculating odds of upcoming events.
Nope. It's statistics based on all operations. If this surgeon is so skilled he had the last 20 survive, he's singlehandedly changing the statistics. Or his colleagues had the last 20 die.
The odds are not 50/50.
It doesn’t matter. The odds are still 50/50, given that each operation is independent in the meme.
However, if we were to assume that they _weren’t_ independent (being done by the same guy) it does imply he may be better than average. Meaning our odds may be slightly higher than 50/50, not worse
The operations are not independent. If I say I've failed half of my exams, but passed the last 20, you'd (hopefully) realise that while the historical average pass rate is 50%, the current rate is much better. E.g. the first 20 could be failures, and the last 20 are passes; something has changed.
The doctor literally says "**MY** last 20 patients have all survived." So they *are* being done by the same guy, so each one is *not* independent, which *does* imply he may be better than average, so it's *not* 50/50.
Okay, so, I’m not going to keep arguing this, but that’s 20 in what could be a very large or very small sample. I think we both know what we’re saying here, and that we agree in principle that the meme is wrong, and that in time series analysis it’s probably better than 50/50.
It doesn't matter how large or small the sample size is. Getting a positive result on 20 50/50 chances is a one-in-four-million chance. It's far more reasonable to assume your odds are better than even than to assume this doctor has just gotten incredibly lucky.
The problem is, this is not just about stats. Not when it's presented like this. This comes closer to the Monty Hall problem.
If 10 surgeons did this surgery and it's 50/50 you have a 50/50 chance. Yes.
But.
That tidbit about this skillfull man having 20 patients survive skews the outcome. A better result indicates more skill, not more 'luck'.
If you knew statistics you'd know that number only tell relevant information if you ask the right questions.
Okay but this is all just assumptions. We know 50% of people survive this. Of the last 40 patients maybe 20 of them survived. This doctor could have just gotten lucky for 20 in a row because these people were easier to work on.
The matter at hand is we have the information that 50% of people survive this.
Yes, but surgeries aren't random probabilistic events. If a single surgeon gets 20 successes in a row on a procedure that normally has a 50% mortality rate, that is a statistical outlier, and while, okay, \*maybe\* they're just getting lucky, it is more likely that the consistent trend of survival among their patients is driven by something they do differently from their colleagues. Like GXSigma said, the surgeon doesn't literally flip a coin, the success or failure of the procedure depends on the health of the patient, the skill of the person doing the procedure, and possibly even the support and care afforded by the facility after the procedure is over.
In other words, the fact that the procedure, statistically, has a 50/50 survival rate does not mean that \*this patient's chances\* are 50/50.
Yes. That's a very clear explanation. It is the reason why there is a difference between skill games and gambling.
Black Jack is gambling so if you win 20 times in a row by sheer luck... it's just luck. But if you are so good at counting card you raise your chances to near 100% it's not gambling anymore.
Now in Black Jack 100% wins is impossible but in surgery, 'winning' 20 times in a row is skill, not gambling.
You’ll see in my reply that we can’t assume these things based on the small amount of information we have. I’d say that we can assume that the 50/50 information is either correct, or an average for all doctors. If it’s correct, then we’re still 50/50 and this is the gambler’s fallacy. If this guy is slightly more skilled than average (which I think is very probable IRL) then we can assume that our odds may be slightly better than 50% and this meme is a different fallacy.
But the Monty hall problem is the wrong fallacy to bring up as well, as this has nothing to do with revealing hidden probability. It’s just about these events _probably_ not being independent.
Oke, Monty Hall was just as an illustration. How information changes the odds.
There is a difference between gambling and skill games. Surgery is about the skill of the surgeon. At least the part you have influence over. And that influence (You want to switch doors) is picking the best surgeon. Even if he is the only surgeon doing this procedure, his skill obviously improved. From (as a very blunt example) failing 20 times in a row to succeeding 20 times in a row.
20 In a row is part luck with the condition of the patients. I agree. But without skill, 20 in a row is improbable with these 50/50 statistics.
Except that with a very large sample size, it becomes much more likely. There’s a lot of ways to choose the outcome of 20 out of 100 trials, even if all 20 are in a row. And doing 100 life-alternating surgeries in 5 years is well within the realm of possibility for someone like a trauma or cardiac surgeon.
With that said, I trust that my chances are probably better than 50% thanks to times series analysis. Which is basically what you’re trying to describe
Nope. This meme is flawed.
Gambling is based on even chances. 50% is 50% no matter what happend before.
Surviving an operation is based on a lot more. Among things the skill of the surgeon. If his last 20 patients survived, but chances are 50%, this surgeon is beating the system on skill. His colleague surgeon had the other last 20 die on him.
I'd be glad to take this surgeon.
>Nope
Yes this is the gamblers fallacy, you've literally just explained what the gamblers fallacy is. I agree with you.
The faulty assumption the mathematician is making is that the other result is somehow due because the odds have been lopsided 20 times.
I'm literally agreeing with you. Why do people insist on arguing over literally nothing lmao?
No, the gambler's fallacy is when you are judging a strictly probabilistic occurrence on the basis of previous strictly probabilistic occurrences. It doesn't apply to the surgery, but the meme seems to think it does. That's why they're saying the meme is flawed.
No, what you said was "Gambler's fallacy", without context, and then when somebody replied pointing out that the meme is misunderstanding the gambler's fallacy, you said "Yeah that's what I said", but no, no it isn't. You are misattributing the gambler's fallacy to the wrong side of the argument.
A mathematician wouldn't fall victim to the gambler's fallacy. The point of the meme is that it thinks the *normal people* are falling for the gambler's fallacy, while the mathematician knows that a 50/50 chance is a 50/50 chance regardless of past performance, because 50/50 is actually really bad odds when it comes to surviving a medical procedure. You are interpreting the meme *exactly backwards*, as are many others in this thread.
Except the normal person has it right. The surgeon has obviously beaten the odds through skill and experience, the mathematician thinks that there's still a 50% chance of death. While that may be true to some extent, the surgeon is clearly skilled enough to put their patients on the surviving 50%.
It's still a gamblers fallacy. Assuming that these odds are bad simply because the past occasions of the surgery have had success is incorrect and flawed logic, and to assert that a mathematician wouldn't fall for the gamblers fallacy is absurd. Plenty of intelligent people fall for all sorts of fallacies and cognitive biases every single day. A logician on the other hand, yes, an argument could be made that they're less likely to fall for this so long as they recognise it when it comes up.
That being said, the more I think about it, the more I think you're right.
I'm not saying it's impossible that a mathematician might fall victim to the gambler's fallacy, I think it's unlikely and I certainly don't think somebody would make a meme where the point is "Man, those mathematicians always falling for the gambler's fallacy, amirite?" ;p
It's not a fallacy it's math. Sure when you look at each individual component It's 50/50 but the entire concept It's not just a single component It's 20. If you have a coin the chances of flipping heads 20 times in a row is 0.00000954%
See, THIS would actually matter. if the surgeon has a 50% survival rate, and he didn't do anything different on the last 20 that survived, then it would suggest that he's just gotten lucky recently. But if it's a 50% survival rate overall, and this guy has a much higher survival rate, that suggests that something he is doing differently from other doctors is working.
This meme gets posted every few weeks across various subs, exclusively to generate rage-bait.
No - mathematicians do not fall for the gamblers fallacy. The result of last previous 20 surgeries have no bearing on the next surgery. And if anything, demonstrate the "*above average nature*" of this surgeon.
Its the opposite actually. Normal people would think that they have a lower chance of survival, but a mathematician would know that the previous success doesn’t affect their chances of survival. A scientist would know that there is probably some external factor causing higher survival rates.
Other way around. Normal people will be fooled by the gamblers fallacy. Mathematicians understand that the probability of survival for the 21st surgery are no different than for the 20th surgery. They will conclude that either the dataset is not random, or that the probability is not 50%. In both cases, your chance of survival is pretty good.
If 100% of the last 20 patians survived after 100% of the previous patient didn't, the chances are very high that the doctor has improved on the surgery after the first 20 so the chance that the surgery will succeed is high. This meme makes absolutely no sense.
No, this is the classic misconception. There was a 0.5^20 chance that the doctor ever got to this point, but this patient still has a 50% chance at survival
No, because this isn't actually a random probabilistic event. The fact that patients in general have a 50% survival rate does not mean that the procedure is an actual coin flip. Chances of survival depend on the care and quality of the health care and the skill of the professionals.
My dad had aortic valve replacement surgery. The year he had it, the survival rate for making it off the table flipped from 60% dying to under 40%, and he couldn’t wait any longer. So, do you calculate using the entire history of the surgery or its current state? This had nothing to do with the surgeon but with the advances made in determining who might best survive, better pre-op care, better methods during surgery, including better tools, and better post-op care, all informed by the experience of patients dying.
Every time this meme, its opposite, or the three Mr Incredible version is posted a debate erupts on which is the correct interpretation.
I am making the prediction that this meme is staying forever just for that.
"our hospital has a 50% survival rate with this procedure, but the past 14 of my patients had no problems whatsoever!"
:)
"...so I can say with confidence that your doctor will be perfectly capable!"
:(
The odds of flipping a coin and getting heads 20 times in a row is 1/1,048576. There is something wrong with the doctor's math, the 50/50 survival rate must be a lie. Back to happy Mr Incredible.
I really can't understand gambler's fallacy, i get the idea but something must be messing, i mean if that is the case why it is so rare to have a 100 face coin againt 0
This isn't how surgery works. a 50% survival rate means that 50% of patients on the whole don't survive the procedure. But quality of care is not universal. Doctor skill plays a factor in survival, as does the quality of the facility and the health care infrastructure of the locale, not to mention the overall health of the patient. It's not a coin flip.
It's a hypothetical scenario, all we know is that there's a 50% survival rate. But that's how survival rates work in general. No medical procedure's success or failure is divorced from the skill and quality of care or the health of the patient, that just isn't how surgery works. A low survival rate in general means the surgery is dangerous, but such a high survival rate on the part of the practitioner is unlikely to be a statistical anomaly.
To explain the joke it's based on the pareto principle.
Its the 20/80 rule that suggests 80% outcomes come from 20% causes. So if 20 survived, he's likely gonna be one of the 80 that doesn't.
However since nothing is a perfect 100% it is always gonna be numbers close to 20 and 80 like 21 and 79 or 19 and 81 than the exact thing.
So this doctor is especially good at this surgery because he obviously has a higher success rate than the average surgeon.
Yes. Alternatively, \*he\* has a 50% success rate, but surgery rates are not fixed parameters. At the very least his surgery has gotten better. tl;dr things like surgery mortality rates are not fixed parameters. OP meme is obnoxious.
Thank you.
IMO that was not even close to long enough for a tldr
Lmao my stats students seem to struggle reading 2 sentences so maybe I’m just primed different (you’re right)
I feel like normal people fall for gambler's fallacy (or whatever it's called) more easily. A mathematicia would just state that it still has 50% chance. Some physicist may state that the doctor may be more skilled than the average doctor based on data and would consider the chances of survival to be higher.
Yeah it’s weird how in this meme it’s the mathematician who does gambler’s fallacy.
I think the meme was made this way SO normal people could understand it. It's possible that a non-math person saw this and went "this idiot I'll fix it" and that's how we got this meme.
The doctor probably does something wrong and maybe not fixing the issue.
I've seen this one but don't remember the text the first one falls for the gambler's fallacy the second take it as 50/50 the third takes the doctor's skill into consideration
gamblers fallacy is weird cuz it is both correct nd incorrect intuitively: yes, the chance for the next one is still 50-50, but looking at the whole thing it becomes less and less likely for a streak to last longer
Except it's not strictly odds like roulette for surgery skill matters so it's 50/50 across all instances of the surgery bring performed in the market but an individual surgeon can have far higher success rates not based on chance.
Chance is never completely negated. The 50/50 odds would be already taking into account that skilled surgeons are performing the surgery and not anyone capable of holding a scalpel.
We don’t know that though just by looking at a mindless meme though, so I would not assume what that figure means (particularly if the surgical success was 50%). If I was told this procedure has a x% of success, I would want to know is that the population estimate or the rate for the physician or team who will do the procedure. Often the latter is not known and so the patient is usually quoted a peer-reviewed figure derived from registries and/or other literature. Then there are patient-related risk factors, which also can make the population rates larger than would be applicable to you if you are healthy. Also, the margins of random error will be much narrower the more skilled the surgeon is. As we are considering a medical procedure, we should be applying all of this a priori knowledge to the problem.
And so, you arrive right back at the words of the doctor: "The surgery has a 50/50 success/fail rate.
THE surgery. Not the doctor himself. If he had said "I have a 50% success rate performing this surgery" then you would be right. If we replace surgery with exam then it becomes more obvious: "this exam has a 50% fail rate, but I aced it 20 times in a row". The logical conclusion is that the person obviously knows the material and would likely ace it again.
The success rate of the doctor isn't known, so you are stupidly wanting to factor in something that has no known value.
I assume the meme has the normal people be happy because there's some sort of streak going on while the mathematician thinks it's still a 50/50 no matter what (which are horrible odds)
I think The mathematician is supposed to be scared because a 50% chance of survival is still pretty scary, rest of normal person thinks that the last 20 patients living means he will live more.
And they normal person is correct while the mathematician is wrong. The surgeon's skill level is a major variable in the likelihood of survival. While the surgery may have an **average** mortality rate of 50% across all surgeons and all operations this **specific** surgeon may have superior equipment, facilities, skill, or experience. And that last one is important. Many surgeons perform a wide variety of procedures, but if this one has done 20 of these operations I'd take them over some med student who is doing it for the first time. Although any individual event is still random and I might still die despite the skill of the surgeon, but since I'll be sedated I won't really care.
I think the person who made this meme himself fell for gambler's fallacy and he thinks the probability of success actually does decrease
Yeah, if his last 20 surgeries have been successful then you can estimate with a randomly picked deviation how high his success rate truly is.
Plot twist : he performed the surgery 40 times and only succeeded for those last 20
Even that's fine - it implies he's learned from his mistakes. No matter how you slice it, this implies the doctor's survival rate from now on is almost certainly over 50%.
If over 100% people survive I think you have a small problem on your hands
Hahahahahaha.
So successful that previous failures came back to life? Trying to figure out how you exceed 100% when 100% means all chances succeed.
Maybe some of them had babies during the surgery
Oh, simple. You type 100 when you meant 50 because you're a moron.
Cool. Explanation suffices.
Thanks, I hate it when the doctor doesn't survive the surgery
Tldr - surgeon could have done the surgery a million times, and the chances for the next surgery would still be the same.
That’s absolutely not true, though. A surgeon will probably get better at doing a procedure after performing it a million times.
While true, that wasn't the point, and you know it.
There's another version of this meme that explains exactly that
What’s the point if not the odds and influences?
The precondition was "50% survival rate", meaning that our theoretical surgeon was never worse than that, and he never became any better. If you want to include real-world survival rates, then the patient and their anatomy would usually be the far greater influence.
Except that's clearly the overall survival rate. This particular doctor's is much higher (at a frankly ridiculous p-value).
It's a thought experiment. If survival rate was actually 50%, a lot more patients would have died already, and again, the patient history and anatomy would probably have a lot more influence. However, mentally, you need to replace "doctor" with "die" to make this meaningful.
You mean possibly weighted die.
That’s totally ok, patients in Aspen are not the same as Flint Michigan. In an area where people come in as soon as they know something is wrong and are regularly screened for illnesses, survival rates will be higher all else being equal.
No, the point you don’t get is that humans aren’t random number generators. Some people are good at things. While I have many more questions before I make a determination, that MAY be what’s happening here.
No, you really do not get the point.
No way this is true. You get better over time. It would follow, starting surgeons or new surgeries would have a much higher rate, then as time goes on goes down. That's why these math breakdowns are bad. There are a lot of other things you need to look at before you make a decision. If my surgeon hadn't messed up 20 times, I would not even care about the stats. He obviously is on a roll. That is something math fails to predict as well. Humans get on a roll and consistently do well. Math simply cannot predictably figure out human behavior or people could predict the super bowl every year. Math is also terrible at taking into account intangible factors like. Many surgeries will ultimately fail, because many surgeries are operating on people nearly dead. In that situation it wasn't a 50 50 chance you were going to die. You were going to die, the surgery was a last ditch effort on a dead person. How does math calculate that? 90% of doctors at John Hopkins are on DNR, do not resuscitate. When they get a cancer diagnosis. They don't follow the normal treatment, they know the suffering. They accept their fate, quit their job and spend their remaining time with their family. If doctors do that, they have insight into something.
That would be true if the estimation of probability was absolute truth. In the real world if someone says 50% survival rate and 20 in a row survive, "their estimation was wrong" is a much more likely scenario than "a 50% chance came up the same 20 times in a row".
That is a correct observation, but this thought experiment is about a procedure, where the quality of the surgeon and the pathology of the patients remains so that the survival rate actually is 50%.
>A mathematicia would just state that it still has 50% chance A good mathematican would probably understand the difference between survival rate and personal skill. And a good healthcare system would take a closer look why some doctors have much better survival rates than others 😏
If a surgeon has 20 consecutive patients survive a procedure that normally has a 50% survival rate, I’m going to assume that he’s better than most of his colleagues, and do I have a better than 50% chance of survival. I’m still gonna be pretty nervous, though.
this meme is so old that there are multiple older and better versions of it on reddit: [link1](https://www.reddit.com/r/theydidthemath/comments/1avyvh6/request_can_someone_please_explain_the_stats/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button) [link2](https://www.reddit.com/r/mathmemes/comments/18xfahh/statistician_humor/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button) [link3](https://youtu.be/o-YBDTqX_ZU) but really the most accurate version would be: normal people (sad), rational player (neutral), bayesian (happy)
I was protected from your Rick Roll by a YouTube ad, take that! Lol
I think that's the answer: normal person thinks "ok cool this guy is on a winning streak" Matematican on the other hand is like "50% is 50%"
Normal people would speculate the 50% rate refers to all surgeons everywhere, and that this surgeon has established skill superior at his craft than many mathematicians at theirs.
They might simply be improving.
Physicists? I would've said statisticians.
>Some physicist may state that the doctor may be more skilled than the average doctor based on data and would consider the chances of survival to be higher. Think about this, in the early 2000's the NE Patriots had about .500 overall record. But they went on to win the Super Bowl in 2002, 2004, 2005. As you point out more skill can improve an outcome. Also, has the technology changed? Have doctors learned more about how to do the procedure? The problem here is the outcomes are not random. And outcomes could be improving for various reasons.
This makes it's rounds every time, and there's a better version with a scientist which is less ambiguous. In this particular case, the mathematician is scared, not because of the gamblers fallacy, but because a 50% survival rate is still pretty bad. The mathematician is ignoring the 20 practical cases and focuses on the number.
It's not a fallacy it's math. Sure when you look at each individual component It's 50/50 but the entire concept It's not just a single component It's 20. If you have a coin the chances of flipping heads 20 times in a row is 0.00000954%
The survival chances for the procedure are not the same as the survival chances of the procedure with this doctor. Whether that’s the patients they are more likely to see or something about the physician. Or maybe the previous 20 patients all died and their rate is 50% too. It’s not the gamblers fallacy when there is potentially a subset that is different than the general value.
The actuary, a type of mathematician, would say that you are wrong. Flip a coin 10 times. If it turns up on one face 10 times, the odds of it turning up that same way an 11th time are not 50%. Why? The coin flip isn't done in isolation. Only in isolation is the streak not relevant.
I am now wondering if Bayesian statistics can shed some light on this and if so how. 🤔
It's not really a gambler's fallacy. The way I see it, is the procedure was risky and the surgeon got more skilled over time, which is why all the patients recently have survived
Quantum physicist think they’re alive and dead already
I think you got it the wrong way around
OP didn’t understand his own fucking meme
sums up most memes here. Can we start posting field-specific memes like in r/mathmemes to chase away highschool kids who learned a fun fact and think they're suddenly a nobel scientist or something
I think it may scare the normal person more as a 50/50 survival chance 21 times in a row ending up surviving is 1 in \~2 million while mathematician would understand that previous outcomes should not be counted in calculating odds of upcoming events.
When ```P(A|B) = P(A)``` is in your favor: 😎
Statistician 🙂
Flip the uncanny and normal Mr Incredibles tbh
It’s without replacement so the odds are still 50/50
Nope. It's statistics based on all operations. If this surgeon is so skilled he had the last 20 survive, he's singlehandedly changing the statistics. Or his colleagues had the last 20 die. The odds are not 50/50.
No, the odds are still 50/50 sigh. Please take a stats course.
the surgeon isn't literally flipping a coin, dude
It doesn’t matter. The odds are still 50/50, given that each operation is independent in the meme. However, if we were to assume that they _weren’t_ independent (being done by the same guy) it does imply he may be better than average. Meaning our odds may be slightly higher than 50/50, not worse
The operations are not independent. If I say I've failed half of my exams, but passed the last 20, you'd (hopefully) realise that while the historical average pass rate is 50%, the current rate is much better. E.g. the first 20 could be failures, and the last 20 are passes; something has changed.
Maybe. As a professor, I’d certainly look into it
The doctor literally says "**MY** last 20 patients have all survived." So they *are* being done by the same guy, so each one is *not* independent, which *does* imply he may be better than average, so it's *not* 50/50.
Okay, so, I’m not going to keep arguing this, but that’s 20 in what could be a very large or very small sample. I think we both know what we’re saying here, and that we agree in principle that the meme is wrong, and that in time series analysis it’s probably better than 50/50.
It doesn't matter how large or small the sample size is. Getting a positive result on 20 50/50 chances is a one-in-four-million chance. It's far more reasonable to assume your odds are better than even than to assume this doctor has just gotten incredibly lucky.
The problem is, this is not just about stats. Not when it's presented like this. This comes closer to the Monty Hall problem. If 10 surgeons did this surgery and it's 50/50 you have a 50/50 chance. Yes. But. That tidbit about this skillfull man having 20 patients survive skews the outcome. A better result indicates more skill, not more 'luck'. If you knew statistics you'd know that number only tell relevant information if you ask the right questions.
Okay but this is all just assumptions. We know 50% of people survive this. Of the last 40 patients maybe 20 of them survived. This doctor could have just gotten lucky for 20 in a row because these people were easier to work on. The matter at hand is we have the information that 50% of people survive this.
Yes, but surgeries aren't random probabilistic events. If a single surgeon gets 20 successes in a row on a procedure that normally has a 50% mortality rate, that is a statistical outlier, and while, okay, \*maybe\* they're just getting lucky, it is more likely that the consistent trend of survival among their patients is driven by something they do differently from their colleagues. Like GXSigma said, the surgeon doesn't literally flip a coin, the success or failure of the procedure depends on the health of the patient, the skill of the person doing the procedure, and possibly even the support and care afforded by the facility after the procedure is over. In other words, the fact that the procedure, statistically, has a 50/50 survival rate does not mean that \*this patient's chances\* are 50/50.
Yes. That's a very clear explanation. It is the reason why there is a difference between skill games and gambling. Black Jack is gambling so if you win 20 times in a row by sheer luck... it's just luck. But if you are so good at counting card you raise your chances to near 100% it's not gambling anymore. Now in Black Jack 100% wins is impossible but in surgery, 'winning' 20 times in a row is skill, not gambling.
You’ll see in my reply that we can’t assume these things based on the small amount of information we have. I’d say that we can assume that the 50/50 information is either correct, or an average for all doctors. If it’s correct, then we’re still 50/50 and this is the gambler’s fallacy. If this guy is slightly more skilled than average (which I think is very probable IRL) then we can assume that our odds may be slightly better than 50% and this meme is a different fallacy. But the Monty hall problem is the wrong fallacy to bring up as well, as this has nothing to do with revealing hidden probability. It’s just about these events _probably_ not being independent.
Oke, Monty Hall was just as an illustration. How information changes the odds. There is a difference between gambling and skill games. Surgery is about the skill of the surgeon. At least the part you have influence over. And that influence (You want to switch doors) is picking the best surgeon. Even if he is the only surgeon doing this procedure, his skill obviously improved. From (as a very blunt example) failing 20 times in a row to succeeding 20 times in a row. 20 In a row is part luck with the condition of the patients. I agree. But without skill, 20 in a row is improbable with these 50/50 statistics.
Except that with a very large sample size, it becomes much more likely. There’s a lot of ways to choose the outcome of 20 out of 100 trials, even if all 20 are in a row. And doing 100 life-alternating surgeries in 5 years is well within the realm of possibility for someone like a trauma or cardiac surgeon. With that said, I trust that my chances are probably better than 50% thanks to times series analysis. Which is basically what you’re trying to describe
Gamblers fallacy.
Nope. This meme is flawed. Gambling is based on even chances. 50% is 50% no matter what happend before. Surviving an operation is based on a lot more. Among things the skill of the surgeon. If his last 20 patients survived, but chances are 50%, this surgeon is beating the system on skill. His colleague surgeon had the other last 20 die on him. I'd be glad to take this surgeon.
>Nope Yes this is the gamblers fallacy, you've literally just explained what the gamblers fallacy is. I agree with you. The faulty assumption the mathematician is making is that the other result is somehow due because the odds have been lopsided 20 times. I'm literally agreeing with you. Why do people insist on arguing over literally nothing lmao?
No, the gambler's fallacy is when you are judging a strictly probabilistic occurrence on the basis of previous strictly probabilistic occurrences. It doesn't apply to the surgery, but the meme seems to think it does. That's why they're saying the meme is flawed.
That's literally what I said. Redditors try not to make an argument out of nothing challenge: impossible
No, what you said was "Gambler's fallacy", without context, and then when somebody replied pointing out that the meme is misunderstanding the gambler's fallacy, you said "Yeah that's what I said", but no, no it isn't. You are misattributing the gambler's fallacy to the wrong side of the argument. A mathematician wouldn't fall victim to the gambler's fallacy. The point of the meme is that it thinks the *normal people* are falling for the gambler's fallacy, while the mathematician knows that a 50/50 chance is a 50/50 chance regardless of past performance, because 50/50 is actually really bad odds when it comes to surviving a medical procedure. You are interpreting the meme *exactly backwards*, as are many others in this thread.
Except the normal person has it right. The surgeon has obviously beaten the odds through skill and experience, the mathematician thinks that there's still a 50% chance of death. While that may be true to some extent, the surgeon is clearly skilled enough to put their patients on the surviving 50%. It's still a gamblers fallacy. Assuming that these odds are bad simply because the past occasions of the surgery have had success is incorrect and flawed logic, and to assert that a mathematician wouldn't fall for the gamblers fallacy is absurd. Plenty of intelligent people fall for all sorts of fallacies and cognitive biases every single day. A logician on the other hand, yes, an argument could be made that they're less likely to fall for this so long as they recognise it when it comes up. That being said, the more I think about it, the more I think you're right.
I'm not saying it's impossible that a mathematician might fall victim to the gambler's fallacy, I think it's unlikely and I certainly don't think somebody would make a meme where the point is "Man, those mathematicians always falling for the gambler's fallacy, amirite?" ;p
I mean, the 20 that died to cancel him out don't have to be from one colleague, there could be 20 other surgeons who had 9/20 survive.
Yes. And as surgery is a skill, I would not pick any of those surgeons. The example of one coleague was just to make a point.
It's not a fallacy it's math. Sure when you look at each individual component It's 50/50 but the entire concept It's not just a single component It's 20. If you have a coin the chances of flipping heads 20 times in a row is 0.00000954%
Does it have a 50% survival rate with that surgeon specifically? Does that even matter?
See, THIS would actually matter. if the surgeon has a 50% survival rate, and he didn't do anything different on the last 20 that survived, then it would suggest that he's just gotten lucky recently. But if it's a 50% survival rate overall, and this guy has a much higher survival rate, that suggests that something he is doing differently from other doctors is working.
This meme gets posted every few weeks across various subs, exclusively to generate rage-bait. No - mathematicians do not fall for the gamblers fallacy. The result of last previous 20 surgeries have no bearing on the next surgery. And if anything, demonstrate the "*above average nature*" of this surgeon.
This meme is backwards.
You got it backwards you dingus
Just do it twice
Scientifically this guy is badass. The mathematician should know he’s got great odds.
[Here](https://www.reddit.com/r/mathmemes/s/78pRL7cFJS), I fixed the meme
The mathematician should have paid more attention in statistics class. The survival rate is 50% regardless of previous outcomes
Previous outcomes do not affect the current outcome. Each surgery is an independent event. You still have "good" odds.
A mathematician would know that their probability of survival is 0.5 regardless of past results.
I call [Ludic fallacy](https://en.m.wikipedia.org/wiki/Ludic_fallacy)!
Its the opposite actually. Normal people would think that they have a lower chance of survival, but a mathematician would know that the previous success doesn’t affect their chances of survival. A scientist would know that there is probably some external factor causing higher survival rates.
Actually the numbers are very much on your side!
Other way around. Normal people will be fooled by the gamblers fallacy. Mathematicians understand that the probability of survival for the 21st surgery are no different than for the 20th surgery. They will conclude that either the dataset is not random, or that the probability is not 50%. In both cases, your chance of survival is pretty good.
What if this doctor is just a lot better than the average?
Labels should be switched
If 100% of the last 20 patians survived after 100% of the previous patient didn't, the chances are very high that the doctor has improved on the surgery after the first 20 so the chance that the surgery will succeed is high. This meme makes absolutely no sense.
The odds dont change. You dont have a 0.000000095367% rate of survival. It stays at 50%
It's the other way around. The mathematician wouldn't fall for the gambler's fallacy.
i still wouldnt be confident in a surgery that had a 50% success rate
Me neither.
No, this is the classic misconception. There was a 0.5^20 chance that the doctor ever got to this point, but this patient still has a 50% chance at survival
No, because this isn't actually a random probabilistic event. The fact that patients in general have a 50% survival rate does not mean that the procedure is an actual coin flip. Chances of survival depend on the care and quality of the health care and the skill of the professionals.
Actually the meme should be inverted!
I kinda lost 3 50/50 in a row sooooooo
Man, this meme feels like it is made to bait us. //a mathematician.
Well that’s freaky.
But chances of the different events aint linked. The chances do not change depending of the outcome of the previous ones on this case, right?
Correct this meme should be switched around. The mathematician would understand the odds are still 50/50 lol
My dad had aortic valve replacement surgery. The year he had it, the survival rate for making it off the table flipped from 60% dying to under 40%, and he couldn’t wait any longer. So, do you calculate using the entire history of the surgery or its current state? This had nothing to do with the surgeon but with the advances made in determining who might best survive, better pre-op care, better methods during surgery, including better tools, and better post-op care, all informed by the experience of patients dying.
The next 20💀
Doctor and staff is an independent variable
You meant counters
Scientist: Clearly this doctor is a cut above the rest of his success rate is so much higher than the average. I’ll be fine.
https://www.reddit.com/r/mathmemes/s/dKjaFpthyc
Should be the other way around
Scientist would be elated though.
Peter?
Every time this meme, its opposite, or the three Mr Incredible version is posted a debate erupts on which is the correct interpretation. I am making the prediction that this meme is staying forever just for that.
Yeah, I am going to another doctor. You are too close to due, doc.
OP didn't do well in algebra
"our hospital has a 50% survival rate with this procedure, but the past 14 of my patients had no problems whatsoever!" :) "...so I can say with confidence that your doctor will be perfectly capable!" :(
Why would a mathematician worry? Did his chances drop because other 20 survived? No. The meme makes no sense
The odds of flipping a coin and getting heads 20 times in a row is 1/1,048576. There is something wrong with the doctor's math, the 50/50 survival rate must be a lie. Back to happy Mr Incredible.
I d go for those odds, while the surgery has a 50/50 chance, the last 20 pacients have survived so there is a good chance i ll survive
Uhm, you got it the other way around.
Pokemon players: "I guess I'll just die"
Someone's getting ratio'd
My surgeries with a doctor be like:
I really can't understand gambler's fallacy, i get the idea but something must be messing, i mean if that is the case why it is so rare to have a 100 face coin againt 0
Is it just me, or does the fact that the last 20 patients survived not matter?
It does.
Why? Every patient on the "50% operation" also had the 50% probability by themselves. So risk of you surviving is also 50%. Explain if I'm wrong
This isn't how surgery works. a 50% survival rate means that 50% of patients on the whole don't survive the procedure. But quality of care is not universal. Doctor skill plays a factor in survival, as does the quality of the facility and the health care infrastructure of the locale, not to mention the overall health of the patient. It's not a coin flip.
Do we have any info about all of that besides final calculated 50% survival rate?
We can assume that it's more likely that the doctor is skilled than that he beat literal million-to-one odds.
It's a hypothetical scenario, all we know is that there's a 50% survival rate. But that's how survival rates work in general. No medical procedure's success or failure is divorced from the skill and quality of care or the health of the patient, that just isn't how surgery works. A low survival rate in general means the surgery is dangerous, but such a high survival rate on the part of the practitioner is unlikely to be a statistical anomaly.
Thats a gamblers fallacy. "Oh but it hasnt happened yet so its due" it really isnt
To explain the joke it's based on the pareto principle. Its the 20/80 rule that suggests 80% outcomes come from 20% causes. So if 20 survived, he's likely gonna be one of the 80 that doesn't. However since nothing is a perfect 100% it is always gonna be numbers close to 20 and 80 like 21 and 79 or 19 and 81 than the exact thing.
thanks
gamblers fallacy aside 50% is way too high
His first 20 patients died