Dr. Hartman here. A normal person might think that it's about time for a surgery to go wrong after 20 successes. A mathematician doesn't think so because every surgery is an independent event, so it doesn't matter if the surgeries before went well. A scientists assumes that this doctor is actually exceptionally good at performing this surgery, so the chances of survival are actually pretty high with this one.
20 successes in row signal trend so, yeah, either this surgeon and his team is really good or the process was finally debugged, optimized, whatever so that it works without fail
The scientist knows he's the only other person on earth who performs this surgery, and all his patients died, so the doctor actually bats 100% on this.
I apply something similar to product reviews. I don't care if a product has 4.8 stars with over 10,000 reviews. If the past 2 years of reviews are all less than four stars, it means it's become a shit product. You can apply the opposite if the inverse is true.
Not only that, but when looking at Ho and Ha and running a quick test it’s a good place to question the original 50% rate. Seems like it’s unlikely due to chance alone and therefore the risk isn’t as high as is being quoted
mm right but that's the weird thing with statistics.
if you flip a coin 20 times and seek an outcome of heads only, the odds of it being heads 20 times in a row is (1/2)20
but if you've already flipped a coin 20 times and they all turned out as heads, those previous flips should have no relevancy on your next flip as it's a 50/50 chance of heads or tails.
it's a very weird Schrodinger's box situation imo. cause depending how you look at the data, both are true and the determination of the next outcome is not set in stone until it is "observed".
(maybe im wrong or misinterpreting but that's how i view it)
like a 1% chance doesnt mean that "out of every 100 events 1 is selected" is CERTAIN. it just means that with a large enough sample size, this is the trend for that statistic. anomalies and outliers always exist.
If you flip a coin 20 times and it’s all heads, you actually conclude that there is something very different about the coin. There is a 0.0001% chance that heads just happen to randomly turn up 20 times. So then the next flip you would expect not to be 50/50 because you conclude it’s not a normal coin. In this case, we can be literally 99.999% confident that the surgeon is different from the rest of the population conducting the suéter
Right...if you think like that...I hadn't thought that the surgery's success rate is across a range of doctors. Realistically, in such a case, the doctor would cite his success rate instead of saying it is 50%
Doctors usually cite the overall success rate published in medical literature, because (1) the sample size from one doctor is often too small to make a firm conclusion, and (2) there’s not always a guarantee that the doctor you think will do the surgery is the one who actually performs it.
right im just speaking strictly statistics. cause the odds of (1/2)20 power is very low and is an anomaly if it occurs, external factors or simply luck, regardless.
but as others have said, the coin doesnt remember its last flip. if you flipped a coin everyday without logging it, how would you know that you flipped heads every day? from your perspective the odds are always 50/50 every day.
hence why i said statistics is a very weird thing as the perspective you view the data can greatly change how you view the next outcome. both aren't necessarily wrong and you don't know which is really true until the next flip.
for this meme, it's obvious that something as complex and with multiple unquantifiable factors like a surgery simply suggest either the surgery methods have improved or this surgeons odds of success are not 50/50.
Strictly statistics, you would have to conclude that the coin is not a normal coin. That’s what statistical inference is. It’d be odd to continue to treat the coin as having purely 50/50 odds. From a Bayesian statistics perspective, you would also update the strength of your belief that the coin has an x% chance of producing heads. All that is statistics
I thought there’s also the fact that while each flip is independent, “in a row” places a dependency on each of the previous flips. while each flip is 50/50, the 10th head in a row requires 9 previous heads in 9 flips.
right, but there have been many many thought experiments playing with this theme.
sure, the odds of (1/2)20 is so miniscule that it is CONSIDERED zero simply because it is statistically IMPROBABLE. it doesnt mean that it is actually zero. and because it has already happened, it's safe to determine that the odds are 50/50 or that some other factor is at hand affecting the odds.
It's not weird. Things that have happened have happened, future probability is in the future, and Schrodingers cat is a criticism making fun of the Copenhagen interpretation of quantum mechanics, not an explanation :)
i understand Schrodinger's cat is a criticism. many have pointed out the irony that his criticism has actually become the "standard" for how we sorta understand quantum mechanics today which is something he hated.
i was simply using the criticism as an analogy for how i view statistics.
like 20 successful events in a row (not talking surgery) is statistically improbable but not impossible. and if we are adding one more to the data set (or if our goal is 21), 1/221 power is even smaller than 1/220 power. it is also true that the coin doesnt remember its last toss however, so each individual event is still 50/50.
just depends on how you're viewing the data set and it's only really set in stone until the next piece of data is observed (hence why i used the analogy).
in either case, 20 successful surgeries with a 50/50 chance is anomalous, and means there is another factor at play (which brings the meme full circle)
So when you play roulette, and you look up at the little history board thing and saw that the last 20 rolls hit red, are you gonna bet your life savings on black?
That is the gambler's fallacy. You'd think the odds have to even out, but that is only true for very large numbers. A streak of 20 1:2 chance rolls can easily extend to a streak of 30. In fact, that is as likely as a streak of 10 the other way.
unfortunately youre mixing up the probability of a sequence with the probability of the next event.
youre correct that 20 successes in a row is unlikely before it happens if the odds are 50/50
however, once it’s happened, that calculation doesn’t tell you anything about the next outcome.
if the events are truly independent and the probability is fixed, the next outcome doesn’t “owe” a failure, even though your intuition might feel like it does
nothing at all about the previous coin flip can physically or otherwise influence the next. probabilities aren't a prescription, they're a description
Sorry, i know it sucks. gambling would be way more fun if it did! :)
however, once it’s happened, that calculation doesn’t tell you anything about the next outcome.
I know. Once it's happened is a big "IF". I am aware that the 21st surgery is independent of the first 20 (strictly mathematically speaking). They are independent, which is why we multiply 1/2 by itself 20 times over.
EDIT: You're right it could happen (looking at your example)
All good. you're answering the wrong question perfectly!
Multiplying (1/2)^20 answers the question “how unlikely was it to see 20 successes in a row before we saw them, assuming a 50/50 success rate?”
the counterintuitive part is that once those 20 successes are observed (however unlikely it may be) that question is no longer the useful one.
the relevant question becomes: “given that we observed 20 successes, what should we believe about the underlying success rate?”
independence means one outcome doesn’t influence the next... so we can't know the success rate is in advance (the next surgery). the streak doesn’t make failure more or less likely (from a probability standpoint), but it DOES make the statement “this doctor is unusually good” more likely to be true.
A normal person might think this means because the last 20 survived the odds somehow decrease, as if every survival means someone HAS to die. A mathematician knows that's not how statistics works and everyone just has an equal 50/50 chance. A scientist likely understands that the 50% is across everyone performing the procedure and that if the last 20 patience survived it means this surgeon is likely just incredibly good at his job.
Though honestly, at 20, which comes out to about 1 in a million, mathematicians, and even a lot of normal people, are gonna come to the same conclusion as the scientist
1- 50% sounds like an alarming mortality rate for a procedure you're about to go into and if the last 20 people lived it sounds like it's relatively time for a failure
2- regardless of other data, this procedure is an independent event from all prior surgeries meaning whether the last 20 lived or died is irrelevant and doesn't change the chances
3- Trial and error leads to successful practices. The last 20 people survived which means the doctor may have learned a new technique that is helping save lives with more consistency
A 'normal person' might look at the two amounts given (50% survival, last 20 survived) and come to an incorrect conclusion that "there has to be a lot of deaths soon, to 'catch up' to the 50% rate" and be concerned.
A mathematician knows that this is a fallacy, that there is no 'extra deaths to be made up', and that the survival rate can still be estimated at 50%.
The scientist (and statisticians and mathematicians as well) would look beyond the numbers for meaning.
For example, if a surgery has a 50% survival rate, but a particular surgeon has 20 survivors in a row, maybe that surgeon is looking at patients, and only doing surgery on patients that have high survival rate, as opposed to not operating on sicker patients or less appropriate patients.
On the other hand, a superior surgeon might have a 20% survival rate, and still be a better surgeon, because they are taking cases that are too difficult for most surgeons to treat.
I mean, technically if the last 20 survived, then unless the doctors been doing this for a very long time, it implies that they are skilled enough that the operation has an ABOVE 50% success rate.
Statistically significant results (p = less than 0.05). Obviously it's somewhat flawed, but I think that's the logic they are going for with the use of the number 20. Scientists - please correct me if I'm wrong.
The number twenty is not tied to 0.05 here. 1/20 = 0.05 is just coincidence. Although we can use p-values to reason whether 50% is the correct estimation to the actual success rate.
Statistical significance means "how surprising is it to obtain the observed result assuming the underlying assumptions are true?" That is, take something that actually has a 50% success rate, say flipping a coin and having tails. Then do many runs of 20 flips in a row. How often will you get perfect runs of 20/20 tails? That will be your p-value. If flips are independent, this is 1/220 approximately 1 out of a million runs you can get this lucky. Although you're correct to notice that 0.05 > 1/million, but it's multiple orders of magnitude difference
The meme implies that with this crazy p-value we can safely assume that whoever said it was 50% were just completely wrong
A child born at 22 weeks has a 14-20% chance of survival, and if they do, they have a high risk of significant developmental delay or other life long issues. But at this hospital, with a level 4 NICU, almost all kids survive and quite often come out with relatively few "compared to expected" life long issues.
Nobody is going to come out and say that the hospital has a 90% success rate, as it's included in the national average - which also includes natural/free births (ugh) and unfortunately areas that don't have the support required to handle this sort of birth weight and the post birth care that is required to even ensure the survival of the child.
Who look like crazy little cat/bird aliens with black eyes at birth, I might add.
If you flip a coin 20 times and call heads, and you hypothetically get heads every single time, your success rate is still 50% even if you succeed every time.
Normal people probably assume that the more patients they survive the worse their own chances are.
Mathematicians know that every patient has a 50 percent chance in isolation to each other, and no patents chances have an impact on any others.
Scientists know that a doctor who treats 20 patients with a 50 percent survival rate should have statistically lost one by now, so clearly knows what they are doing.
I would argue that the explanation provided by many people below, about the expectation of failure versus the likelihood of one event versus another versus the real world skill of this doctor, are all likely correct, but that the images chosen to depict each understanding are probably not in line with this if you have a 50/50 chance of surviving the surgery, that mathematician should absolutely not be calm.
Dr. Hartman here. A normal person might think that it's about time for a surgery to go wrong after 20 successes. A mathematician doesn't think so because every surgery is an independent event, so it doesn't matter if the surgeries before went well. A scientists assumes that this doctor is actually exceptionally good at performing this surgery, so the chances of survival are actually pretty high with this one.
20 successes in row signal trend so, yeah, either this surgeon and his team is really good or the process was finally debugged, optimized, whatever so that it works without fail
God I hate when I get a buggy surgery, now when I pinch my left nipple, my right eye blinks.
As a CS major: Don't blame us, blame the AI companies are replacing us with.
We want to fix it, trust me.
dw I think the Devs are patching that out
Let me test that out. For science
Whenever I fart and sneeze at the Same time, I Take a Screenshot.
If you put your phone down while you do that, it won’t 😆
Without fail yet. I think it's fair to say that it's almost certainly much greater than a 50% survival rate but assuming 100% is a bit of a stretch.
Or there's one guy who keeps fucking it up and bringing the average down.
The scientist knows he's the only other person on earth who performs this surgery, and all his patients died, so the doctor actually bats 100% on this.
Me a gambler: it’s 50% cause it either happens or it doesn’t
I apply something similar to product reviews. I don't care if a product has 4.8 stars with over 10,000 reviews. If the past 2 years of reviews are all less than four stars, it means it's become a shit product. You can apply the opposite if the inverse is true.
Bayesian, right?
drop the act
Not only that, but when looking at Ho and Ha and running a quick test it’s a good place to question the original 50% rate. Seems like it’s unlikely due to chance alone and therefore the risk isn’t as high as is being quoted
Yeah, but 50% is still really bad odds lmao. Maybe they should've used: 90% survival rate, last 1000 patients have been fine.
Odds of 20 independent surgeries a success: (1/2)20 ~= 0. It is a BS meme imo
mm right but that's the weird thing with statistics.
if you flip a coin 20 times and seek an outcome of heads only, the odds of it being heads 20 times in a row is (1/2)20
but if you've already flipped a coin 20 times and they all turned out as heads, those previous flips should have no relevancy on your next flip as it's a 50/50 chance of heads or tails.
it's a very weird Schrodinger's box situation imo. cause depending how you look at the data, both are true and the determination of the next outcome is not set in stone until it is "observed".
(maybe im wrong or misinterpreting but that's how i view it)
like a 1% chance doesnt mean that "out of every 100 events 1 is selected" is CERTAIN. it just means that with a large enough sample size, this is the trend for that statistic. anomalies and outliers always exist.
If you flip a coin 20 times and it’s all heads, you actually conclude that there is something very different about the coin. There is a 0.0001% chance that heads just happen to randomly turn up 20 times. So then the next flip you would expect not to be 50/50 because you conclude it’s not a normal coin. In this case, we can be literally 99.999% confident that the surgeon is different from the rest of the population conducting the suéter
Right...if you think like that...I hadn't thought that the surgery's success rate is across a range of doctors. Realistically, in such a case, the doctor would cite his success rate instead of saying it is 50%
Well I think a social scientist would look at this and say all the other doctors need to come learn how to do surgery from this guy.
No $hit!
Doctors usually cite the overall success rate published in medical literature, because (1) the sample size from one doctor is often too small to make a firm conclusion, and (2) there’s not always a guarantee that the doctor you think will do the surgery is the one who actually performs it.
right im just speaking strictly statistics. cause the odds of (1/2)20 power is very low and is an anomaly if it occurs, external factors or simply luck, regardless.
but as others have said, the coin doesnt remember its last flip. if you flipped a coin everyday without logging it, how would you know that you flipped heads every day? from your perspective the odds are always 50/50 every day.
hence why i said statistics is a very weird thing as the perspective you view the data can greatly change how you view the next outcome. both aren't necessarily wrong and you don't know which is really true until the next flip.
for this meme, it's obvious that something as complex and with multiple unquantifiable factors like a surgery simply suggest either the surgery methods have improved or this surgeons odds of success are not 50/50.
Strictly statistics, you would have to conclude that the coin is not a normal coin. That’s what statistical inference is. It’d be odd to continue to treat the coin as having purely 50/50 odds. From a Bayesian statistics perspective, you would also update the strength of your belief that the coin has an x% chance of producing heads. All that is statistics
I thought there’s also the fact that while each flip is independent, “in a row” places a dependency on each of the previous flips. while each flip is 50/50, the 10th head in a row requires 9 previous heads in 9 flips.
You're right in that the 21st surgery has a 50% success rate, but the chances of all prev ones being a success are 0.
right, but there have been many many thought experiments playing with this theme.
sure, the odds of (1/2)20 is so miniscule that it is CONSIDERED zero simply because it is statistically IMPROBABLE. it doesnt mean that it is actually zero. and because it has already happened, it's safe to determine that the odds are 50/50 or that some other factor is at hand affecting the odds.
Yes, odds of 1/2 20 being a success is literally 1 in a million. The hand is definitely at play here
im not talking abt the surgeon rn though. that is obviously some other factor at play.
im just talking abt how we view statistics as a whole.
ive already conceded in the previous comment that the odds are AT LEAST 50/50 but likely higher due to other factors.
It's not weird. Things that have happened have happened, future probability is in the future, and Schrodingers cat is a criticism making fun of the Copenhagen interpretation of quantum mechanics, not an explanation :)
i understand Schrodinger's cat is a criticism. many have pointed out the irony that his criticism has actually become the "standard" for how we sorta understand quantum mechanics today which is something he hated.
i was simply using the criticism as an analogy for how i view statistics.
like 20 successful events in a row (not talking surgery) is statistically improbable but not impossible. and if we are adding one more to the data set (or if our goal is 21), 1/221 power is even smaller than 1/220 power. it is also true that the coin doesnt remember its last toss however, so each individual event is still 50/50.
just depends on how you're viewing the data set and it's only really set in stone until the next piece of data is observed (hence why i used the analogy).
in either case, 20 successful surgeries with a 50/50 chance is anomalous, and means there is another factor at play (which brings the meme full circle)
So when you play roulette, and you look up at the little history board thing and saw that the last 20 rolls hit red, are you gonna bet your life savings on black?
That is the gambler's fallacy. You'd think the odds have to even out, but that is only true for very large numbers. A streak of 20 1:2 chance rolls can easily extend to a streak of 30. In fact, that is as likely as a streak of 10 the other way.
Yeah, I know ;)
It never happens that way, that is the point! If it did happen, the odds weren't 50/50
unfortunately youre mixing up the probability of a sequence with the probability of the next event.
youre correct that 20 successes in a row is unlikely before it happens if the odds are 50/50
however, once it’s happened, that calculation doesn’t tell you anything about the next outcome.
if the events are truly independent and the probability is fixed, the next outcome doesn’t “owe” a failure, even though your intuition might feel like it does
nothing at all about the previous coin flip can physically or otherwise influence the next. probabilities aren't a prescription, they're a description
Sorry, i know it sucks. gambling would be way more fun if it did! :)
(P.S. there have been some crazy long streaks in roulette - here's one mentioning it hitting black 26 times in a row... so it does infact "happen that way" sometimes)
I know. Once it's happened is a big "IF". I am aware that the 21st surgery is independent of the first 20 (strictly mathematically speaking). They are independent, which is why we multiply 1/2 by itself 20 times over.
EDIT: You're right it could happen (looking at your example)
All good. you're answering the wrong question perfectly!
Multiplying (1/2)^20 answers the question “how unlikely was it to see 20 successes in a row before we saw them, assuming a 50/50 success rate?”
the counterintuitive part is that once those 20 successes are observed (however unlikely it may be) that question is no longer the useful one.
the relevant question becomes: “given that we observed 20 successes, what should we believe about the underlying success rate?”
independence means one outcome doesn’t influence the next... so we can't know the success rate is in advance (the next surgery). the streak doesn’t make failure more or less likely (from a probability standpoint), but it DOES make the statement “this doctor is unusually good” more likely to be true.
Same math. Different question.
That's exactly why we must conclude that the survival rate depends on the surgeon.
Yes - the way it is worded seems to imply that this doctor's success rate is 50% though (at least that is how I read it)
That's the joke... The probability is bogus so the scientist don't even worry about it..
A normal person might think this means because the last 20 survived the odds somehow decrease, as if every survival means someone HAS to die. A mathematician knows that's not how statistics works and everyone just has an equal 50/50 chance. A scientist likely understands that the 50% is across everyone performing the procedure and that if the last 20 patience survived it means this surgeon is likely just incredibly good at his job.
Though honestly, at 20, which comes out to about 1 in a million, mathematicians, and even a lot of normal people, are gonna come to the same conclusion as the scientist
A normal person would think they got experience and figured it out and not do the math
In this specific case probably but when it comes to pure random events like dice ot roulette a lot of normal people fall for the gambler's fallacy.
Fair analysis
Here ya go champ https://www.reddit.com/r/explainitpeter/s/D95du5Z1HL
Search is your friend and a lot quicker than waiting for a response
I'm 90% sure it's just bot accounts that keep posting this over and over.
I assume it's because
1- 50% sounds like an alarming mortality rate for a procedure you're about to go into and if the last 20 people lived it sounds like it's relatively time for a failure
2- regardless of other data, this procedure is an independent event from all prior surgeries meaning whether the last 20 lived or died is irrelevant and doesn't change the chances
3- Trial and error leads to successful practices. The last 20 people survived which means the doctor may have learned a new technique that is helping save lives with more consistency
A 'normal person' might look at the two amounts given (50% survival, last 20 survived) and come to an incorrect conclusion that "there has to be a lot of deaths soon, to 'catch up' to the 50% rate" and be concerned.
A mathematician knows that this is a fallacy, that there is no 'extra deaths to be made up', and that the survival rate can still be estimated at 50%.
The scientist (and statisticians and mathematicians as well) would look beyond the numbers for meaning.
For example, if a surgery has a 50% survival rate, but a particular surgeon has 20 survivors in a row, maybe that surgeon is looking at patients, and only doing surgery on patients that have high survival rate, as opposed to not operating on sicker patients or less appropriate patients.
On the other hand, a superior surgeon might have a 20% survival rate, and still be a better surgeon, because they are taking cases that are too difficult for most surgeons to treat.
Math is hard!
how many times is this going to get posted here
Every day. I called dibs tomorrow.
The same shitty explanations trigger me even more. This picture just does not make any fucking sense.
The joke is, you still have 50% chance, even after 20 patients.
the truth is, this surgeon is skilled. He fights against the odd and gives 20 of his patients 100% chance of survival.
50% chance is only in the book
A scientist would think there is publication worthy data here.
I mean, technically if the last 20 survived, then unless the doctors been doing this for a very long time, it implies that they are skilled enough that the operation has an ABOVE 50% success rate.
Or there's a lot of hacks in the field and they're the one keeping it from dropping below 50.
This gets posted weekly. Is Reddit getting that many new users each day?
Doctor: You only have 5% chance of survival.
Patient, a gacha game player: 5%? That's high, we have 1.5% SSR banners and I'd still do single roll thinking I'd win.
I love how often I see this exact picture on this sub
At least some stable point in our lives.
Statistically significant results (p = less than 0.05). Obviously it's somewhat flawed, but I think that's the logic they are going for with the use of the number 20. Scientists - please correct me if I'm wrong.
The number twenty is not tied to 0.05 here. 1/20 = 0.05 is just coincidence. Although we can use p-values to reason whether 50% is the correct estimation to the actual success rate.
Statistical significance means "how surprising is it to obtain the observed result assuming the underlying assumptions are true?" That is, take something that actually has a 50% success rate, say flipping a coin and having tails. Then do many runs of 20 flips in a row. How often will you get perfect runs of 20/20 tails? That will be your p-value. If flips are independent, this is 1/220 approximately 1 out of a million runs you can get this lucky. Although you're correct to notice that 0.05 > 1/million, but it's multiple orders of magnitude difference
The meme implies that with this crazy p-value we can safely assume that whoever said it was 50% were just completely wrong
Great answer! Thank you!
20% failure is across the board.
For example:
A child born at 22 weeks has a 14-20% chance of survival, and if they do, they have a high risk of significant developmental delay or other life long issues. But at this hospital, with a level 4 NICU, almost all kids survive and quite often come out with relatively few "compared to expected" life long issues.
Nobody is going to come out and say that the hospital has a 90% success rate, as it's included in the national average - which also includes natural/free births (ugh) and unfortunately areas that don't have the support required to handle this sort of birth weight and the post birth care that is required to even ensure the survival of the child.
Who look like crazy little cat/bird aliens with black eyes at birth, I might add.
Over-under guys, can we make it 2 days before this is reposted again? Taking bets, favor has "no"
The scientist knows the doctor is bad at math, but good at surgery.
I come from the planet of anti-induction, and I have every reason to be terrified
Goddammit how many time is this same meme going to be posted on this fucmking sub
If you flip a coin 20 times and call heads, and you hypothetically get heads every single time, your success rate is still 50% even if you succeed every time.
if success chance is 50% then just do it twice, lol
People think about numbers differently.
Normal people probably assume that the more patients they survive the worse their own chances are.
Mathematicians know that every patient has a 50 percent chance in isolation to each other, and no patents chances have an impact on any others.
Scientists know that a doctor who treats 20 patients with a 50 percent survival rate should have statistically lost one by now, so clearly knows what they are doing.
Normal people: he’s due to have a failed surgery
Math: Nah it is still 50/50 because the events are independent
Scientist: 20 50/50’s in a row is very improbable, the doctor needs to re-evaluate their odds (I think)
I would argue that the explanation provided by many people below, about the expectation of failure versus the likelihood of one event versus another versus the real world skill of this doctor, are all likely correct, but that the images chosen to depict each understanding are probably not in line with this if you have a 50/50 chance of surviving the surgery, that mathematician should absolutely not be calm.
This is just a katma farming sub now isnt it?
Wow thanks guys, I really appreciate the help! my friend is really into intelligent humor 😆
Say hi to your "friend".
99% bot