> Minimizing loss over aggregates is what a statistical model is designed to do, so if you evaluate human judgment against statistical predictions in aggregate on data similar to what the model was trained on, then you should expect statistical prediction to win
This reminds me of the many years machine translation was evaluated on BLEU towards reference translations, because they didn't know any better ways. Turns out that if you measure translation quality by n-gram precision towards a reference translation, then methods based on n-gram precision (such as the old pre-NMT Google translate) were really hard to beat.
> There are a few ways to look at this from the standpoint of information that is available to the decision-maker. One is that human knowledge is valuable for guiding developing the model, but once you have a statistical model, it’s a better aggregator of the information. This is echoed by research on judgmental bootstrapping (https://gwern.net/doc/statistics/decision/1974-dawes.pdf), where a statistical model trained on a human expert’s past judgments will tend to outperform that expert.
By the way, note that this applies to LLMs too. One of the biggest pons asinorums that people get hung up on is the idea that "it just imitates the data, therefore, it can never be better than the average datapoint (or at least, best datapoint); how could it possibly be better?"
Well, we know from a long history that this is not that hard: humans make random errors all the time, and even a linear model with a few parameters or a little flowchart can outperform them. So it shouldn't be surprising or a mystery if some much more complicated AI system could too.
> One of the biggest pons asinorums that people get hung up on is the idea that "it just imitates the data, therefore, it can never be better than the average datapoint (or at least, best datapoint); how could it possibly be better?"
Hmm - the phrasing that perhaps holds more water is that LLMs just imitate the data, which means that novel ideas / code tends to be smashed against the force of averaging when fed into an LLM. E.g. NotebookLM summaries/podcasts are good infotainment but they tend to flatten unconventional paragraphs into platitudes or common wisdom. Obviously this is very subjective and hard to benchmark.
> Obviously this is very subjective and hard to benchmark.
I agree, but it also feels very obvious once you've been exposed to it enough times. The internet is filled of written or spoken AI slop that can generally be spotted with ease by trained eyes and ears.
Using a simple average of past performance to predict future performance is also a technique that is often disturbingly effective vs. standard practice. I suppose technically that is a linear model, but really deserves its own class.
Up to a point where the prediction runs afoul of the time horizon and changing unmodelled circumstances.
They do not have sufficient explicit risk or variance management. Makes them highly fragile. There are more robust versions of the estimators... Still have a problem.
Remember 2008? That market ran on these easy models.
I was going to say that it doesn't have to be a statistical model. Notable that statistical models are already seen as less than complete analytical models, for many people. (I think that is almost certainly a poor way of wording it? Largely just trying to say that F=ma and such are also models that don't have conditional answers.)
At any rate, I'm curious on some of the readings this post brings up. I'm also vaguely remembering that human's can have some odd behaviors where requiring justification or reasoning of decisions can sometimes provide more predictable decisions; but at a cost that you may not fully explore viable decisions.
User "Anoneuoid" from the source's own comment thread:
There is another aspect here where those averaged outcomes are also the output of statistical models. So it is kind of like asking whether statistical models are better at agreeing with other statistical models than humans.
You need to compare on both different variables and additionally produce actual error estimates on the comparison.
Say, suppose you're measuring successful treatments. You would have to both use the count, perhaps signed even (subtracting abject failures such as deaths), cost (financial or number of visits), then verify these numbers with a follow up.
See, the definition of success is critical here. OR and NNT are not evaluating side effects negatively, for example.
So it may turn out that you're comparing completely different ideas of better instead of matching models.
As a matter of practicality, it seems that you professionally now want to be firmly in the tails of the data distribution for your field, e.g. expert in those things that happen rarely.
Or maybe even be in a domain which, for whatever reason, is poorly represented by a statistical model, something where data points are hard to get.
OTOH. The blog mentions that humans excel at novel situations. Such as when there is little training data, when envisioning alternate outcomes, or when recognizing the data is wrong.
The most recent example I can think of is "Frank". In 2021, JPMorgan Chase acquired Frank, a startup founded by Charlie Javice, for $175 million. Frank claimed to simplify the FAFSA process for students. Javice asserted the platform had over 4 million users, but in reality, it had fewer than 300,000. To support her claim, she allegedly hired a data science professor to generate synthetic data, creating fake user profiles. JPMorgan later discovered the discrepancy when a marketing campaign revealed a high rate of undeliverable emails. In March 2025, Javice was convicted of defrauding JPMorgan.
IMO an data expert could have recognized the fake user profiles through the fact he has seen e.g., how messy real data is, know the demographics of would be users of a service like Frank (wealthy, time stressed families), know tell tale signs of fake data (clusters of data that follow obvious "first principles").
> an data expert could have recognized the fake user profiles through the fact he has seen e.g., how messy real data is, know the demographics of would be users of a service like Frank (wealthy, time stressed families), know tell tale signs of fake data
perhaps the data science professor who generated the fake data was quite well versed in all this and put effort into deliberately adding messiness and skew etc?
If there is not a human-explainable reason a model has made a prediction - and it's just a statistical blob in multi-dimensional feature space (which we cannot introspect) perceived improvement over humans is simply overfitting. It will be extremely good at finding the median issue, or following a decision tree in a more exacting way than a human. What a human can do is expand the degrees of freedom of their internal model at-will, integrate out of sample data, and have a natural human-bias to the individual at the expense of the median. I'd rather have that...
> why it’s often hard to demonstrate the value of human knowledge once you have a decent statistical model.
This seems to be a near restatement of the bitter lesson. It's not just that large enough statistical models outperform algorithms built from human expertise, they also outperform human expertise directly.
This is not a takedown of that statement, but the reason we've trouble with this idea is that it works in the lab and not always in real life.
To set up a clean experiment, you have define what success looks like before you conduct the experiment - that the output variable is defined.
Once you know what to measure ahead of time to determine success, then statistical models tend to not be as random as a group of humans in achieving that target.
The variance is bad in an experiment, but variance jitter is needed in an ever changing world even if most variants are worse off.
For example, if you can predict someone's earning potential from their birth zipcode, it is not wrong and often more right than otherwise.
And then if you base student loans and business loan interest rates on the basis of birth zipcodes, the original prediction does become more right.
The experimental version that's a win, but in real life that's a terrible loss to society.
Ah yes, the self fulfilling prophecies or hallucinations based on models trained on models.
Overfitting. Ending up in an evolutionary dead end...
Type 4 error of not asking a question one should also exists.
So thing is, suppose you're handling the common cases right - you have software that's say 95% correct.
The important bit is how critical the remaining 5% failures are.
If one of them happens to be "I give up my computer and data to the exploit" or "everything is destroyed" or "a lot of people die", then the extra 1% better average is no good to any inside observer.
It so happens that a lot of people believe themselves to be outside observers, especially rich.
(What's the success bonus for someone getting treated nicely?)
THANK YOU. It's mildly infuriating how often people forget that one of the things most human experts are good at is knowing when they are looking at something that is likely in distribution vs. out of distribution (and thus, updating their priors).
It's unfortunate how under appreciated is statistics, in nearly all (spare academic) positions that I occupied, mostly in the technical domain interacting with non-technical stakeholders, anectodal evidence always take priority compared to statistical backed data, for decision making. It's absurd sometimes.
Anecdotally, the way I've heard many stats related tools described is as follows: if the tool confirms something that we already knew then it's a waste of time or money because it doesn't tell us anything new, and if it doesn't agree with what we already know then it's obviously wrong.
I don't think it's a trivial problem though. It's notoriously easy to twist stats to sell any narrative. And Goodhart's Law all but guarantees that any meaningful metric will get hacked.
At least when humans are wrong we own it. Statistical models can be wrong 100% of the times you used them and the claim is ‘oh this is how statistics work, you did not query the model infinite times’.
My point is that in many occasions being right on average is less important than being right on the tail.
> Minimizing loss over aggregates is what a statistical model is designed to do, so if you evaluate human judgment against statistical predictions in aggregate on data similar to what the model was trained on, then you should expect statistical prediction to win
This reminds me of the many years machine translation was evaluated on BLEU towards reference translations, because they didn't know any better ways. Turns out that if you measure translation quality by n-gram precision towards a reference translation, then methods based on n-gram precision (such as the old pre-NMT Google translate) were really hard to beat.
> There are a few ways to look at this from the standpoint of information that is available to the decision-maker. One is that human knowledge is valuable for guiding developing the model, but once you have a statistical model, it’s a better aggregator of the information. This is echoed by research on judgmental bootstrapping (https://gwern.net/doc/statistics/decision/1974-dawes.pdf), where a statistical model trained on a human expert’s past judgments will tend to outperform that expert.
By the way, note that this applies to LLMs too. One of the biggest pons asinorums that people get hung up on is the idea that "it just imitates the data, therefore, it can never be better than the average datapoint (or at least, best datapoint); how could it possibly be better?"
Well, we know from a long history that this is not that hard: humans make random errors all the time, and even a linear model with a few parameters or a little flowchart can outperform them. So it shouldn't be surprising or a mystery if some much more complicated AI system could too.
> One of the biggest pons asinorums that people get hung up on is the idea that "it just imitates the data, therefore, it can never be better than the average datapoint (or at least, best datapoint); how could it possibly be better?"
Hmm - the phrasing that perhaps holds more water is that LLMs just imitate the data, which means that novel ideas / code tends to be smashed against the force of averaging when fed into an LLM. E.g. NotebookLM summaries/podcasts are good infotainment but they tend to flatten unconventional paragraphs into platitudes or common wisdom. Obviously this is very subjective and hard to benchmark.
> Obviously this is very subjective and hard to benchmark.
I agree, but it also feels very obvious once you've been exposed to it enough times. The internet is filled of written or spoken AI slop that can generally be spotted with ease by trained eyes and ears.
The problem making a bear-proof trash can is that there's significant overlap between the smartest bears and the dumbest tourists.
> and even a linear model with a few parameters
Using a simple average of past performance to predict future performance is also a technique that is often disturbingly effective vs. standard practice. I suppose technically that is a linear model, but really deserves its own class.
Up to a point where the prediction runs afoul of the time horizon and changing unmodelled circumstances.
They do not have sufficient explicit risk or variance management. Makes them highly fragile. There are more robust versions of the estimators... Still have a problem.
Remember 2008? That market ran on these easy models.
You don't even need a statistical model. We make checklists because we know we'll fail to remember to check things.
Humans are tool users. If you make a statistical table to consult for some medical issue, you've using a tool.
I was going to say that it doesn't have to be a statistical model. Notable that statistical models are already seen as less than complete analytical models, for many people. (I think that is almost certainly a poor way of wording it? Largely just trying to say that F=ma and such are also models that don't have conditional answers.)
At any rate, I'm curious on some of the readings this post brings up. I'm also vaguely remembering that human's can have some odd behaviors where requiring justification or reasoning of decisions can sometimes provide more predictable decisions; but at a cost that you may not fully explore viable decisions.
User "Anoneuoid" from the source's own comment thread:
You need to compare on both different variables and additionally produce actual error estimates on the comparison.
Say, suppose you're measuring successful treatments. You would have to both use the count, perhaps signed even (subtracting abject failures such as deaths), cost (financial or number of visits), then verify these numbers with a follow up.
See, the definition of success is critical here. OR and NNT are not evaluating side effects negatively, for example.
So it may turn out that you're comparing completely different ideas of better instead of matching models.
As a matter of practicality, it seems that you professionally now want to be firmly in the tails of the data distribution for your field, e.g. expert in those things that happen rarely.
Or maybe even be in a domain which, for whatever reason, is poorly represented by a statistical model, something where data points are hard to get.
OTOH. The blog mentions that humans excel at novel situations. Such as when there is little training data, when envisioning alternate outcomes, or when recognizing the data is wrong.
The most recent example I can think of is "Frank". In 2021, JPMorgan Chase acquired Frank, a startup founded by Charlie Javice, for $175 million. Frank claimed to simplify the FAFSA process for students. Javice asserted the platform had over 4 million users, but in reality, it had fewer than 300,000. To support her claim, she allegedly hired a data science professor to generate synthetic data, creating fake user profiles. JPMorgan later discovered the discrepancy when a marketing campaign revealed a high rate of undeliverable emails. In March 2025, Javice was convicted of defrauding JPMorgan.
IMO an data expert could have recognized the fake user profiles through the fact he has seen e.g., how messy real data is, know the demographics of would be users of a service like Frank (wealthy, time stressed families), know tell tale signs of fake data (clusters of data that follow obvious "first principles").
> an data expert could have recognized the fake user profiles through the fact he has seen e.g., how messy real data is, know the demographics of would be users of a service like Frank (wealthy, time stressed families), know tell tale signs of fake data
perhaps the data science professor who generated the fake data was quite well versed in all this and put effort into deliberately adding messiness and skew etc?
If there is not a human-explainable reason a model has made a prediction - and it's just a statistical blob in multi-dimensional feature space (which we cannot introspect) perceived improvement over humans is simply overfitting. It will be extremely good at finding the median issue, or following a decision tree in a more exacting way than a human. What a human can do is expand the degrees of freedom of their internal model at-will, integrate out of sample data, and have a natural human-bias to the individual at the expense of the median. I'd rather have that...
> why it’s often hard to demonstrate the value of human knowledge once you have a decent statistical model.
This seems to be a near restatement of the bitter lesson. It's not just that large enough statistical models outperform algorithms built from human expertise, they also outperform human expertise directly.
> they also outperform human expertise directly
When measured statistically.
This is not a takedown of that statement, but the reason we've trouble with this idea is that it works in the lab and not always in real life.
To set up a clean experiment, you have define what success looks like before you conduct the experiment - that the output variable is defined.
Once you know what to measure ahead of time to determine success, then statistical models tend to not be as random as a group of humans in achieving that target.
The variance is bad in an experiment, but variance jitter is needed in an ever changing world even if most variants are worse off.
For example, if you can predict someone's earning potential from their birth zipcode, it is not wrong and often more right than otherwise.
And then if you base student loans and business loan interest rates on the basis of birth zipcodes, the original prediction does become more right.
The experimental version that's a win, but in real life that's a terrible loss to society.
Ah yes, the self fulfilling prophecies or hallucinations based on models trained on models. Overfitting. Ending up in an evolutionary dead end...
Type 4 error of not asking a question one should also exists.
So thing is, suppose you're handling the common cases right - you have software that's say 95% correct. The important bit is how critical the remaining 5% failures are. If one of them happens to be "I give up my computer and data to the exploit" or "everything is destroyed" or "a lot of people die", then the extra 1% better average is no good to any inside observer.
It so happens that a lot of people believe themselves to be outside observers, especially rich.
(What's the success bonus for someone getting treated nicely?)
> > they also outperform human expertise directly
> When measured statistically.
THANK YOU. It's mildly infuriating how often people forget that one of the things most human experts are good at is knowing when they are looking at something that is likely in distribution vs. out of distribution (and thus, updating their priors).
The original article discusses this explicitly.
It's unfortunate how under appreciated is statistics, in nearly all (spare academic) positions that I occupied, mostly in the technical domain interacting with non-technical stakeholders, anectodal evidence always take priority compared to statistical backed data, for decision making. It's absurd sometimes.
Anecdotally, the way I've heard many stats related tools described is as follows: if the tool confirms something that we already knew then it's a waste of time or money because it doesn't tell us anything new, and if it doesn't agree with what we already know then it's obviously wrong.
I don't think it's a trivial problem though. It's notoriously easy to twist stats to sell any narrative. And Goodhart's Law all but guarantees that any meaningful metric will get hacked.
This is because the correct answer is rarely the politically palatable answer.
At least when humans are wrong we own it. Statistical models can be wrong 100% of the times you used them and the claim is ‘oh this is how statistics work, you did not query the model infinite times’.
My point is that in many occasions being right on average is less important than being right on the tail.