August 3, 2021 • 45 mins
In this episode of Stuff to Blow Your Mind, Robert and Joe discuss regression to the mean, a phenomenon that occurs when a random sampling point is an outlier -- with applications to everything from economics and sports to health, religion and disappointing sequels.
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Episode Transcript
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Speaker 1 (00:03):
Welcome to Stuff to Blow Your Mind, the production of
My Heart Radio. Hey, welcome to Stuff to Blow Your Mind.
My name is Robert Lamb, and I'm Joe McCormick. And
in today's episode, we are going to be focusing on
a topic that is already something that's very well known
(00:24):
to people who are familiar with quantitative research and statistics,
but less known to the general public. And uh and
I think that's a tragedy because it's an idea that
should really be part of everybody's basic critical thinking toolkit,
no matter what your job is. And so in order
to introduce this concept, I thought it would be best
(00:44):
to start with a with a direct illustration from the
real world of people reaching incorrect conclusions by not understanding
the subject of today's episode. And so the illustration I
want to start with is an interesting story told by
the psycholo, just Daniel Kaneman, that's about the illusory power
of screaming at pilots. Uh. So, the context of the
(01:07):
story is that Knemon says he was giving a lecture
about positive reinforcement to a group of flight instructures. I
think this was in the nineteen sixties, and Kaneman was
trying to inform them about what he believed at the
time was the best consensus of scientific research on learning
and reinforcement, which was at the time that if these
(01:29):
flight instructors wanted their students to have the best possible outcomes,
they should focus more on praising the students when they
did well than on chewing them out when they did
something wrong. And Kneman says that when he finished his talk,
one of the flight instructors that he had been giving
this lecture two got up and tried to dispute him.
He said, no, you're wrong, And so the direct quote
(01:52):
Economy gives from the instructor here is on many occasions,
I have praised flight cadets for clean execution of some
aero attic maneuver, and in general when they try it
again they do worse. On the other hand, I've often
screamed at cadets for bad execution, and in general they
do better the next time. So please don't tell us
(02:13):
that reinforcement works and punishment does not, because the opposite
is the case. So you might think he has a
good point here if you accept that this flight instructor
has had a lot of direct experience working with students,
and you trust him to remember the relative frequency of
these events pretty well, you might assume that he has
(02:33):
a meaningful rebuke to ekonom In. Here again, he says
that most of the time, after a cadet does something
bad and he screams at them, they do better the
next time. And after a cadet does something good and
he praises them, they actually do worse the next time.
So if he's remembering these experiences correctly, and he's had
a lot of them, it would really seem like evidence
(02:55):
that praise has a negative effect on learning, maybe by
making the student pilots soft and overconfident or something, and
getting chewed out is good for skill development. I think
it's quite easy to see the allure of this, this
false conclusion, right right, And it's and you can also
easily imagine how you kind of build upon this with
(03:15):
certain loosely backed up you know, folk ideas about how
you encourage people and how people learn, and you got
to stay on them if they if you tell them
they're doing a good job, they'll get lazy, right, folk wisdom,
tough guy mentality. Yeah, But Knemon saw something different in
this response, and he says that he immediately set up
an experiment on the spot to demonstrate the flaw in
(03:38):
the flight instructors thinking here, so I want to read
from Knomen's description, he says, I immediately arranged a demonstration
in which each participant tossed two coins at a target
behind his back without any feedback. We measured the distances
from the target and could see that those who had
done best the first time had mostly deteriorated their second try,
(04:01):
and vice versa. But I knew that this demonstration would
not undo the effects of lifelong exposure to a perverse contingency.
So to explain this, this experiment a little bit better, right,
he has people stand with their backs to a target
so they couldn't see it, and they would take two
attempts to throw a coin and hit the target without
(04:21):
any feedback of any kind. So they're not getting praised,
they're not getting chewed out, nothing. Uh. And after staging
a number of these, he found again what he suspected,
that the people who were the closest on the first
throw did worse on their second throw, and the people
who were farthest away on their first throw tended to
do better on the second throw. So what kandiment is
(04:43):
actually demonstrating here is something that doesn't really have anything
to do with learning or reinforcement, or really skills or
even human psychology. Instead, this demonstration is showing the effects
of chance, luck, and statistics. What he was showing is
the subject we're talking about today, regression to the mean. Uh.
(05:05):
You'll you'll see that phrase a lot in in scientific
literature and in statistics. But if it helps to put
it in more everyday terms, anytime you see regression to
the mean, you can translate it in your head as
trending toward the average, trending toward the average. So, to
make the coin tossing illustration even clearer, imagine you throw
(05:26):
the coin not twice, but that you throw the coin
a hundred times. So you stand there throwing the coin
a hundred times. And then let's say afterwards you average
together the distance from the target across all a hundred throws,
and you'll come up with some kind of average distance
from target. Uh, just to make up a number for
the sake of argument. Common doesn't give this. But let's
(05:47):
say the average distance from the target across all your
throws is nine centimeters. And remember that you're getting no
feedback at all. Here, so it's unlikely that you will
be getting much better as you go on. So even
that the average distance from the target is nine cimeters,
if you throw a coin once and it happens to
be two centimeters from the targets really close, is your
(06:09):
next throw likely to be about the same as that one,
better or worse. Obviously, it is overwhelmingly likely that your
next throw will be worse, just due to chance, probably
closer to the average of nine cimeters away. And the
same goes for throws that are really far off. If
you throw something three hundred centimeters off, your next random toss,
(06:32):
just by chance, is likely to be much better, much closer. So,
simply put, most of the time, if you're sampling something
in a series over time, if one sample produces an
extreme value, the next one in the series is more
likely to be closer to the average instead of extreme
(06:52):
in the same way. In my experience, Uh, this is
This is why it can sometimes be liberating to start
off a game of bowling with just a disastrous gutter ball,
because because I know that I'm good enough that that's
probably not gonna happen twice in a row, but it's
definitely going to happen at some point in the game
because I'm not that good, you know, I like playing
(07:14):
you know, once a year or even with less frequency
these days. Oh yeah. And it's also like why I
think a lot of us have intuitions that when you
try something for the first time and you do really
good on the first attempt, that makes you kind of
nervous because you just know you're probably not gonna live
up to that repeatedly. Yeah, like if you get you
get a strike that first time, then that that first
(07:35):
um what is it round? I can't even remember. This
is how frequently I bowl. Um, the first role. So
the first role first, the first column, you know. So
the tendency of regression to the mean or or trending
towards the average is pretty obvious when you're dealing with
something like lots of random coin tosses with no feedback,
(07:56):
But it becomes much more obscure when you're dealing with,
say a more a more limited numbers of outcomes. In
the series you're looking at and introducing possibly influential variables
like pilot skill and instructor feedback. After all, we would
expect that some variables having to do with instructor feedback
(08:16):
should have an effect on pilot skill, right, That's the
point of teaching is to have an effect over time.
And after all, in this one scenario, the Konomen describes
the the instructor believed that his verbal abuse of the
students was so motivating that it made them instantly better
on the stick. And you can't necessarily rule that out,
(08:36):
but it's unlikely. I think. I'm convinced that regression to
the mean could more easily explain this flight instructor's belief
that screaming at pilots for screw ups made them better
at planes, because, again, on average, even in the absence
of any feedback at all, if a pilot in training
executes a maneuver perfectly, the random fluctuation from one execut
(09:00):
usian to the next will tend to mean that their
next attempt probably won't be as good as that really
good when the last time. And likewise, if they make
a major error totally botcha maneuver, they're more likely to
do better the next time just by chance. Both of
these tendencies are regression towards the mean. But then Conomon
actually draws a really interesting observation about about about our
(09:21):
psychology and about culture from this fact, so, to quote
him directly, this was a joyous moment in which I
understood an important truth about the world. Because we tend
to reward others when they do well and punish them
when they do badly, and because there is regression to
the mean, it is part of the human condition that
(09:43):
we are statistically punished for rewarding others and rewarded for
punishing them. And that was one of those things that
when I read it, I was just like, oh my god,
that's so true. Um, yeah, yeah, And in this specific instance,
it makes me think about the special fact of reversion
to the mean, fallacies on motivating belief in the effectiveness
(10:04):
of of not just screaming at pilots in this one case,
but all kinds of punishment behaviors, for example, corporal punishment.
Thankfully you hear this less often these days, but I
remember when I was younger, I used to hear people
who would defend the parental practice of spanking children by saying,
you know, I don't I don't care what the site
scientists say. I don't care what the research says. I
(10:26):
know from experience that it works to the extent that
comments like this were based on any real experience and
observation and not just sort of a free form, self
justifying statement that had nothing to do with experience. I
bet a lot of it was fallacious inference of causation
actually based on regression to the mean, just like in
this commument example. But anyway, I thought it would be
(10:49):
interesting to talk a bit more about regression to the
mean today because it's one of those things that, again,
once you see it, it's it's pretty simple, it's actually
actually pretty clear. But understanding it can help you have
a better sense of how good science works and help
keep you from drawing hasty inferences in everyday life. Yeah,
because it is. It is interesting how kind of an
(11:12):
insidious the results can be, the idea that that again,
praise is ultimately punished because there's going to be a
regression to the mean, to to to to the mean,
and then likewise there can be this illusion, uh that
uh that's screaming at pilots and so forth is going
to be the successful way to go about things. Um So, yeah,
(11:33):
this is I think this is an important episode to
cover because it's the kind of thing that it's the
kind of tool you kind of need tucked in your
back pocket, even if you're just doing something like like
scanning science headlines on a you know, a news server
or social media message board. Yeah, because of course, understanding
regression to the mean is extremely important in what scientists
(11:54):
do when they design good experiments. If you don't take
into account regression to the mean, you can incorrectly believe
you have discovered some kind of tiger repellent or something. Uh.
This concern plays a huge role in the history of medicine.
It's part of the design of good medical research, or
really any field that seeks to find remedies for problems.
(12:15):
So consider a very basic hypothetical, uh patent medicine, say
from a hundred years ago. So you know, you have
you have a foot pain that you've never really had before. Uh.
You know, you want it to go away. So you
go to the store and you buy a bottle of
Doctor Field Grades No Fail Pantasy for tumors, ulcers, cramps,
and rooms, and you you pull the cork out, you
(12:37):
chug it, and then the next day your foot feels better.
Now you can conclude from this that the Doctor Field
Grades cured you. But how do you know actually that
the feelings in your foot didn't just regress to the mean,
because the average is a low amount or no amount
of foot pain. And if you don't have a medication
that's tested with control groups and and randomized allocation into
(13:00):
the groups, then how do you know that that the
medicine actually did anything at all? Yeah? Yeah, So many
of the examples you see for this and the applications,
you're dealing with some sort of situation in the world
where there is fluctuation and or change happening, often separately
from whatever is being tested. So in this case, yeah,
the Doctor Field Greats could have just been like just water,
(13:22):
It just just you know, but there is the illusion
that it worked because things got better. But if you
don't have a control group and to you know, to
drive home what that is, that would be like if
you had a had like three different groups and a
study of Doctor Field Greats elixir. Here, one group was
taking Doctor Feel Greats elixer, another group was taking I
don't know, let's say a half dose of Feel Grade
(13:44):
or maybe a competitor's tonic. And then one group, the
control group was taking nothing was or was taking you know,
just water or something to that effect something completely innate. Uh.
And that would be that would be a a group
that you would judge the results of the other categories by, right,
And you would need to randomly sort the people into
(14:06):
those groups. So it wasn't just that, you know, the
only the people with real severe foot pain. We're taking
the doctor field grades, because the more extreme their pain
to begin with, probably the more likely they are to
have that pain be lessened or go away over time,
just naturally. Right. And uh. And I'm going to have
a more specific example of this a little later in
(14:27):
the podcast. So if you if you still don't get it,
just hang on. We'll we'll have another example in a bit.
I was looking at an article in the British Medical
Journal from nine that was just a collection of different
examples of regression to the mean in real life medical research.
(14:48):
This was by j Martin Bland and Douglas J. Altman
called statistics notes some examples of regression towards the mean,
and they point out a very common type of example,
so the this will be similar to what we just
talked about. The author's right. In clinical practice, there are
many measurements such as weight, serum cholesterol concentration, or blood pressure,
(15:10):
for which particularly high or low values are signs of
underlying disease or risk factors for disease. People with extreme
values of the measurements, such as high blood pressure may
be treated to bring their values closer to the mean.
If they are measured again, we will observe that the
mean of the extreme group is now closer to the
(15:30):
mean of the whole population. That is, it is reduced.
This should not be interpreted as showing the effect of
the treatment. Even if subjects are not treated, the mean
blood pressure will go down owing to regression towards the means.
So again, something starts with an extreme value in certain
types of cases, you would just expect it to have
a less extreme value the next time due to random fluctuation.
(15:55):
Uh So again, you know this could fill you with
despair because you might wonder, well, then how could you
ever know if a treatment was effective or not. But again,
this is where the standard practices of science based medicine
come to play. Instead of just taking people with some
extreme measurement and giving them a treatment, you randomize them
into test groups and control groups like we were just
(16:15):
talking about. So if you have a large enough sample,
you properly randomize the groups. People with the extreme starting
conditions will somewhat regress toward the mean, but they will
all regress toward the mean on average the same rate
whether they're receiving a real potential treatment or they're in
the placebo group. But if the treatment actually does something helpful,
this effect will manifest as the difference between the two groups.
(16:38):
So good scientific research good medical research has methods for
excluding the effects of reversion to the mean on their findings.
We have the tools, but we can still fall into
the trap of regression to the mean fallacies, especially in
our day to day lives drawing inferences the way that
that the pilot and in common story did, or or
(16:59):
even science if we're not careful and deliberate about designing experiments.
And in addition to just a methodology design that has
you know, randomized groups and control groups, there are also
ways of trying to counteract regression to the mean, just
through statistical methods that are maybe less reliable, But there
are statistical methods people can use to try to apply
(17:21):
sort of modifiers to data in order to estimate regression
to the mean and UH and counteract its effects. So
again we have tools within scientific research to to figure
this out, and it's a lot of what science does
is trying to sort out the difference between regression to
the mean and actual effects of interventions. But in our
(17:41):
day to day lives, we still fall for regression to
the mean fallacies all the time. Yeah, and it's important
to realize too that it's not just a situation where
regression towards the mean could create an illusion of something
working when it doesn't. Uh, you know, sometimes it can
just potentially overstate um the effects something. For an example
(18:02):
of that that I was looking at was that regression
towards the mean or the failure to account for it
can also overstate the effectiveness of something like traffic light cameras.
Is it making a difference and cutting down on accidents perhaps,
but any actual effectiveness could potentially be overstated by failure
to account for just regression towards the mean. Oh yeah,
(18:23):
So where do you tend to install things like that?
High acts like problem areas? Right, So, if there's like
a stretch of road that has a lot of problems
on it, people really speeding a lot there or crashing
a lot there, that might be where you stage the intervention.
It's possible some things like that fluctuate naturally over time
(18:43):
in different locations. Yeah, and you put the cameras in place,
and it could have an effect, but maybe not as
much of an effect as it looks like it is
taking place. Again, if you don't factor regression towards the
mean into the study. Right now, While our TM is
a very important phenomenon to understand and take into account,
(19:04):
it certainly doesn't apply to every sequence of values you
could repeatedly sample, So you also have to be careful
not to apply it in situations where it isn't warranted.
I was you know, there are a million examples you
could cite. One that came to my mind is the
orbital decay of a satellite. Let's say you've got a
communication satellite in lower orbit and you get a reading
(19:26):
on its altitude and the reading is lower than the
satellites average altitude. Uh. Now, you might say, hey, I
think this means we need to program a reboost to
insert it back into the orbit where it's supposed to be.
And somebody could erroneously apply regression to the mean here
and say, no, we don't need to do that. The
satellite might just return to its average altitude. It doesn't
(19:49):
apply in this scenario, even though you are taking repeated
measurements of a value over time, because we know things
about the physical characteristics determining the orbit of satellites and
in lower thorbit uh and that due to factors like
atmospheric drag, their altitude tends to trend steadily downward over
time in a consistent direction down, down, down, So eventually
(20:12):
you will need a reboost in order to put it
back up to the correct distance. So regression to the
mean applies to certain kinds of data that are repeatedly
sampled data where there is natural random fluctuation back and forth,
not a steady trend in the data in one direction
on the relevant time scale. The other thing that's important
(20:33):
to understand is that systems where you expect to find
regression to the mean are systems in which the repeated
data values you're sampling are to some degree determined by
luck or chance. If a series of values is influenced
almost entirely by deterministic influence, like in the satellite example,
by like the laws of physics, or by some extremely
(20:56):
reliable skill with little room for variation, values don't really
regress towards the mean in the same way, because there's
just less random fluctuation back and forth to begin with.
The more chance and random variation plays a role in
the outcome, the more you will tend to observe regression
towards the mean after an extreme sample in in whatever
(21:17):
it is you're looking at. Yeah, I've read that the
progression towards the mean is is not to be confused
with the law of large numbers. For example, Uh, this
is the the law that that states as a sample
size becomes larger, the sample mean gets closer to the
expected value. So a coin flipping example is key here.
Flip a coin and the random results are going to
(21:39):
ultimately average out to a point five proportion. But if
you only flip the coin ten times, you might not
see this breakdown. Um. And this also applies to say,
even odds on the rolling of a of a D
six of a six sided die. Uh So for example,
too regular people, that's just to die. That is nerves
like us, it's a D six. Yeah, D six is
(22:01):
what I could get my hands on because I was like, well,
I'm gonna do an example. I'm gonna try it myself.
So while I was putting together notes for this, I
went ahead and rolled ten times, and I got even
even odd even odd even even even even odd. So
that's that's seven to three in favor of even. So
it might make you wonder, well, is this die broken?
Does this D six need to go away? Because it
(22:22):
can't be trusted to roll? Uh? You know a balanced
array of odd and even numbers. Well, no, that's not
the case. Uh. And if I were to roll this,
say another hundred times, another thousand times, I would see
things even out even more to where we would see this, uh,
this point five proportion of odd versus even. Right. So
(22:45):
these are not exactly the same thing, regression to the
mean and the law of large numbers, but they are
closely related. Both observations require you to think about statistical
tendencies over time, over a time period of repeated sampling,
and both are prim ust on the knowledge that repeated
samples will tend towards the average. But regression to the
mean has to do with the idea that if you
(23:08):
start with an extreme observation and there is some role
of chance or luck in determining the value of this observation,
the next time you sample it, it's more likely to
be closer to the average. The law of large numbers
is that if in the real world, the more times
you run something, the closer your outcomes in the real
world will will be to the sort of perfect mathematical
(23:29):
average that you would estimate just given the chances to
begin with. Now, I want to come back to regression
towards the mean in um in medical studies because I
found a really interesting one that came out earlier this year.
Uh So, a lot of a lot of the examples
you find involving regression to the mean involved sports or economics,
and I found this one discussed in a New York
(23:51):
Times article again from earlier this year titled Intense strength
training does not ease knee pain, study finds by Gina Colada.
Uh this referring to a study published in JAMMA that
entailed an eighteen month clinical trial involving three seventy seven participants. Okay,
so the basic situation, the setup for this paper is
that a lot of people have knee osteoarthritis and one
(24:15):
of the go to treatment recommendations has long been strength training.
So in this study they decided to look into it
with three basic groups, one that received intense strength training,
another that received moderate strength training, and another that received
counseling on healthy living. So that third group, that's the
(24:36):
control group, They did not have any amount of strength training,
just uh, you know, some positive counseling about healthy living. Sure,
so the researchers here apparently actually expected to see the
intense strength training take the lead that they were looking
to identify what has been just sort of accepted wisdom,
um and and again that this has been the predominant
(24:58):
treatment idea. But in instead they found that the results
were the same for all three groups. Quote, everyone reported
slightly less pain, including those who had received only counseling.
Now why is that, Well, as Colotta points out, there's
there's always room for other effects, especially say the placebo effect.
Uh but regression to the mean is also a heavy
(25:20):
consideration here and certainly could work in congress with the
placebo effect. Right, So you don't necessarily have to assume
that the counseling actually helped to heal people's knees, though
it may have in in in some it may have
had some kind of mechanistic effect in in some way
a mind body kind of thing, But you would also
just expect over time, people who have an extreme starting position,
(25:41):
who are starting with a lot of knee pain, to
get gradually better over time. Yeah. So a Colatta rights
quote are the right, as symptoms tend to surge and subside,
and people tend to seek out treatments when the pain
is at its peak, when it declines, as it would
have anyway, they ascribed the improvement to the treatment. Uh.
So you know, this would this would roughly equate to
(26:03):
yelling at your knee when it's in pain, and it
really makes it certainly relates to many other health scenarios
as well, various medications and even things like prayer and
you know, supernatural um treatments and attempts to to deal
with pain, etcetera. Yeah, I mean it could apply to
to any intervention that is aimed at influencing something that
(26:24):
is naturally variable on its own, right. Yeah, and you
know something that's again any kind of system in which
change occurs, when fluctuation occurs. Uh, you know, you can
you can see this applying to not only physical pain,
but also uh, emotional distress things of that nature. You know.
So again, I think this is an important tool to
have in our our logic tool kit. Thank thank Now.
(26:52):
There are even cases where I'm tempted to think about
the application of regression to the mean, but where it's
probably a lot harder to quantify exactly what the effects are.
It's cases where it can be difficult to separate out,
say the effects of some kind of deterministic influence like
skill versus how how strong the effect of chance or
(27:15):
luck is. But I think about things even in the
world of the arts, like I think about, you know,
the sophomore album by by a band that has like
a really stellar debut album. Uh, you know, often that
is perceived is disappointing, and you have to wonder, like, Okay,
is it is that often true? Because I don't know
(27:35):
if people get famous and it goes to their heads
and then they you know, they get full of themselves
and make something dumb, or is it because when somebody
has a debut album that's really well received, to some extent,
it's so good partially because of luck or chance, and
that's an outlier that you're as you're starting sample, yeah, yeah,
And certainly this is an area that's there's a lot
(27:56):
more subjectivity here and and so it's not the kind
of thing you can that's really have a control group
for anything. But but I think it is quite interesting,
and I did find as I was looking around for
some jazzy or examples or possible examples of aggression to
the mean. Um, I found one that that actually gets
into a little bit into the idea of you know,
(28:16):
first and second album. But also uh, the idea of
follow up films and Hollywood sequels has pointed out both
good Yeah has pointed out by Joanna Deong in two
thousand eighteen on the blogs scientifically sound movie sequels are
potentially a great example of aggression to the mean. Quote,
Hollywood sequels are only made if the original film is
(28:39):
a quote unquote high quality success. But the average quality
of sequels will be closer to the mean than average
quality of originals of sequels because of regression to the means,
So sequels tend to be of lower quality than the original. Now,
I might somewhat dispute the premise here that Hollywood sequels
are only made to films that are high quality to
(29:00):
begin with. Um, right, But but I still think this
is onto something because there is a movie that gets
a sequel tends to have something about it something that
people are responding to, whether it's a movie that I
would like or not. Right, I mean, sometimes obviously the
situation is the film just made a lot of money.
I mean, I guess that's the key thing. It didn't
(29:21):
make a lot of money. If so, producers are going
to be more inclined to say, let's do that again,
Let's have that experience again of all that money coming in.
And sometimes this this certainly matches up with a quality film.
You have something that really captures people's imagination and is
of high quality. And uh and you know, so it's
really firing on all cylinders. But you know, and yes,
(29:45):
certainly in some cases it's just the right film at
the right time. Or or maybe it has nothing to
do with the film itself. Maybe it's who's in it,
or I don't know what's going on in the zeitgeist
during that particular era. Well, the way I would think
about this is, and I think that again, this is
onto something. It highlights that when we experience confusion where
we say, like, wow, you know, the Exorcist is such
(30:07):
a great horror movie and the Exorcist too is so bad?
How could that be the case? You know, why is it.
Why is such a bad sequel to such a great movie.
It's because of the comparison of the original to the
sequel that we're experiencing this confusion. Another way you could
just look at it is most horror movies are direc
(30:28):
most movies are bad, and it is only by comparing
the The Exorcist Too to The Exorcist that you notice
this steep drop off where Another way of looking at
it is that The Exorcist Too is bad like most
horror movies are, and the first one was an outlier
at the beginning. It was a first film in a
series that happened to be really good to cut above. Yeah, absolutely, like, yeah,
(30:53):
I think this is the correct way to look at it,
and also keeping in mind it just how amazing it
is that any film gets completed, like even bad film,
Like a lot of people probably work pretty hard to
make that happen, even if the end results don't really
please anyone at all. But but yeah, I think this
is also an interesting inversion of the opening example of
yelling at pilots as well, because most of the time,
(31:15):
if a flawed movie comes out, people are not clamoring
for the sequel. Um sequels are rarely guaranteed, so you're
not often going to hear things like, oh, well that
wasn't great. I hope the next one is an improvement.
I mean some people say that, some people I've said
things like that before, where it will be like, oh,
really flawed film, but maybe there's like a cool idea.
(31:35):
I kind of wish it would they would remake it,
even though there's no like logical reason that there would
be like a there would be money behind that idea. Well,
I guess it's kind of different when you're talking about
a one off creative project versus something. I mean, we
live in a kind of different era now because we
were at the height of this you know, cinematic universe
thing with a huge number of the big budget movies
(31:59):
that come out, the big event movies are not one
off creative products, but they are a product that exists
within some kind of franchise or universe or something. So
you just know automatically that there's gonna be another one,
whether this one is good or not. Yeah, like either
it's an established film universe where like, you know, they
put out another Marvel movie and it's just terrible. Well,
(32:22):
obviously there's enough momentum, they're not going to stop. They're
not gonna be like, oh, well, lesson learned, Well we'll
stop them. No, no, there's gonna be another. Another example
of this might be a successful franchise in another medium,
say a book series, so like the Harry Potter books
for example, or I don't know, Lord of the Rings,
where you know that once they make the Fellowship of
the Rings, there's going to be a follow up, They're
(32:44):
gonna do another one. So in these ways, unless it's
the seventies and it's uh, that Lord of the Rings
movie that that ends with Helm's Deep, well, but they
picked that up eventually, but yeah, okay, but but yeah,
probably the Harry Hotter films are a better example. And
there may be spe specific you know things about how
(33:04):
that wasn't guaranteed either, uh, you know, the economic reality
can always come into play. But for the most part,
like those were when when that started, you knew they
were going to keep making these at least they were
going to make a follow up, so you could have
comments like, well, there that was this was kind of
flawed in some of the some of its execution. I
hope that they fixed that in the next film for
the most part. Yeah, with one offs, this is not
(33:25):
the case. It's like, if if this film fizzles, then
only you know, a few, like rare people are going
to be clamoring for a sequel or dreaming about what
the sequel would be. Yeah. I think this observation but
regression to the mean and movie sequels is actually very
on point, but more so for the films of yester year,
where the more the more common thing was you'd have
(33:46):
a an independent sort of creative product that it's its
own thing, and then if it resonated with somebody, if
it did well, there would be sequels. I think it's
a little it applies a little bit less today when
there's just you know, we're in the world of France,
Chises and extended universes and there's just sort of like
a guaranteed ongoing uh conveyor belt of of new stuff
(34:07):
within the Marvel world or the Star Wars world or whatever. Yeah,
but I think it it is a worthwhile way to
think about creative the creative process, and you know, as
opposed to some of these alternate sort of folk wisdomy
ways of thinking about it. For example, on Weird House, cinema.
We recently talked about Toby Hooper. Toby Hooper is one
of those directors who's often you'll often you'll see descriptions.
(34:29):
I think we've even read part of a review where
they they really they talk about, oh, well, you know
he put out Texas Chainsaw Mascre directed that film and
this was great. It was, you know, just a real
lightning bolt um to the cinematic world into horror itself
as a genre. And then the idea that well, he
was never able to capture that magic again, you know,
(34:50):
that is his career was just like one long slide
after that, which I don't think it is a fair assessment,
especially if you employ regression to the mean you the
idea being that, yeah, he did kind of get lightning
in a bottle with that with that first big film,
that that he was able to to really bring something
together that is an outlier, um, but that that that's
(35:13):
just going to happen. That's just the way these things work, right,
So most movies aren't that good. So you know, the
random chance of like how good his ideas and execution
are from one year to the next is going to
set in and you might have a different idea about
his career. If you were to say, like randomly chronologically
reorder all his movies, right, you know, like if you
(35:33):
were to put the worst ones earlier on or something,
people might feel differently about it. Yeah, well then they
would talk about, well, okay, TCM was peak Toby Hooper,
like this was his peak output. Because this is the
kind of the kind of view of an artist's you know,
creative trajectory that we tend to want to um to
follow along, you know, because it's more story shaped, the
(35:55):
idea of ascent and then eventually decent that there's gonna
be h is going to be a period of high
noon in their creative out output, and sometimes that does
match up with the reality. But I don't know even
then we I think we tend to overlook the dogs
in the filmographies of people we love, you know. Oh
yeah uh. But then again, I mean, this is interesting
because in talking about regression to the mean applying to
(36:19):
creative products like movies, we are acknowledging that the creative
process is not purely a product of talent and skill,
that there is a significant amount of chance and luck
involved in something like how good a movie turns out?
To be um, and it's hard to know exactly how
to like how to picture that influence of chance and luck.
(36:39):
You know, like, what what is that in the creative process.
It's obviously true because there are people who can be
incredibly skilled in one instance and then I don't know,
things just don't go right the next time, and to
make something that nobody really likes. But uh, but that's
that's just not often how people like to think about
creative talents and people like to think about the creative
(37:00):
process like it is much more strictly deterministic. Yeah, yeah,
Or or you look at things like the Star Wars
films and you kind of like fall into this idea
of thinking, this is stuff that is mind out of
the mythic earth, and then you know, it just makes
sense that things would accumulate and get better. So um,
but really looking back on it, especially if you actually
(37:20):
like watch documentaries, and there's some great ones about the
production of those films, like it's it's amazing that Star Wars,
the first one in New Hope was as good as
it was, and then it's nothing short of I mean,
it's it's just a pure miracle that the second one
was so much better and like really nailed it. Like
if if the second film had had floundered, I mean,
(37:43):
just imagine how different the cinematical landscape would have been
for decades to come. Yeah, So it's it's amazing if
the first film in a series is good, and it's
super amazing if the second one is good. And and
this is why I think we often find too that
if if part one in part two, if something are
of high quality, then you've got to look out for
(38:04):
that part three because that part three, that part three
may be coming to get you. But likewise, if a
part two is rubbish, um, you know, subjectively, then then
part three might pick it up and uh and get
things back on track. So you certainly see that that
kind of fluctuation as well. I have a question I
actually don't know the answer to, but this would be
interesting in terms of I don't know the high performing output,
(38:29):
whether that is in whether that is a creative endeavor
like you know, writing books or creating movies, or whether
that's something even like athletics, like athletic performance, do you
expect to see more random fluctuation in the performance of
collaborative output versus individual output? So say, um, do you
expect more influence of random chance and fluctuation in the
(38:52):
quality of uh books written by a single author versus
you know, movies that have the input of hundreds of
thousands of people? Uh? Or in in the realm of
say sports, like, do you expect more random variation in
the output of an individual athletes like you know, an
individual gymnast or something, or in team sports? Yeah? I
(39:14):
can see it going both ways, because yeah, if you
think too hard to about even just like the film analogy,
you can easily get into discussions of like, Okay, well
was it the same cast and crew that are producing
the sequel? Uh? You know, what happens when the budget
is different, what happens when there are other constraints, what
happens when suddenly there are a whole bunch of producers
that have their ideas about what things should be. I mean,
there's so many different factors to take into place. Uh.
(39:36):
You know, with this example that you know, perhaps doesn't
bear too close of scrutiny, but but but it's but
it's still I think serves as a nice um illustration
of the overall trend that we're talking about here. Well,
it does bring up the fact that since I mentioned
athletes that, you know, I don't know a lot about sports.
I'm not a big sports fan. But but clearly, but
regression to the mean is something that has widely been
(39:57):
applied to the world of sports. Uh for example, in
the observation that often after having a really stellar season,
either an individual athlete or a sports team will be
perceived to underperform the next season. And again that very
well could have something to do with regression to the mean. Like,
you know, the fact that they're observed having an amazing
(40:19):
season is actually an outlier. You're starting your expectations then
and saying like, Okay, now they're going to be the
best forever. Just by random fluctuation over time, you would
expect their next season to probably be not as good
as the first. I wonder to what an extent this
can be applied to, say, the world of the culinary arts,
or even just like various food crops, like say the
(40:41):
selecting a cantalope at the grocery store, that sort of thing.
I mean, I guess it would apply to pretty much
anything where you're sampling in a series over time. There's
plenty of random fluctuation in what you're sampling and the
first thing you sample is an outlier in some way
really good or really bad. If those things true, then
you can probably expect you're going to see some regression
(41:04):
one way or the other. Yeah. Yeah. By the way,
I was looking around for like really stellar examples of
a sequel film that is widely believed to be uh rubbish,
and I think The Exorcist Too is the primary example.
Like you get into some of the other examples that
pop up, I feel like there's room for disagreement. Um.
For instance, Texas Chainsaw Masker two is one which I
(41:26):
saw popping up on some of these lists for disappointing sequels.
But I think that's entirely based on who you ask.
I think if you ask us, we will agree that
that that t c M two is is actually a
great film. It's different from the first one perhaps if
you go into if you go into part two with
the expectations you had for part one, you may see
it as a dip in quality. But depending on what
(41:48):
else you're bringing to the table, you might see it
as an increase in in quality or at least or
something that maybe is different but on par with the original.
I mean it's certainly not for everybody. I mean, it
is a it is a gross, disgusting film in in
a way like the first one, probably even grosser, but
also a sort of satirical masterpiece. Um. But I just
had another thought when you said that The Exorcist Too
(42:09):
is regarded as like one of the best examples of
a sequel. That's really rubbish. I mean, it makes me
also wonder about the pretty high estimation critics generally have
of The Exorcist three. Makes me wonder if the effect
of the Exorcist to being so bad actually makes people
sort of over you know, they're like they're ready to
be impressed by the Exorcist three. Yeah. Yeah, I wonder
(42:31):
if that's the case too with it with especially when
you have a situation with a part three coming back
and restoring uh some I don't know, some level of
quality to a franchise. I mean there's also like the
Star Trek h example, right, I mean that was long
the Long held up as an example of like, okay,
you have you even Star Treks and your odd Star Treks, right. Uh.
And I think you've made a similar case for the
(42:55):
Faster and Furious movies, right, I mean once you get
to a certain point in the series, I think it's
pretty much all uh, you know, a nitrous boosted brain.
It's it gets you know, it's all like we're driving
cars in space now and flying and all that. But um,
but for the earlier ones, yeah, i'd say the odd
ones are better, Like, uh, three is the first one
(43:15):
where it really starts getting ludicrously weird. Four is kind
of a uh, and then five starts. Five is when
the rock shows up, and then but by seven year
Golden All right, well, we're gonna go ahead and close
this one out here. But we'd obviously love to hear
from everyone about this about regression towards the mean, just
(43:36):
in our daily lives, in various scientific studies. Perhaps you
have thoughts about how this applies to something we've discussed
on the show in the past, because I know we've
we've mentioned regression to the mean in passing before, but
certainly we've never taken the opportunity to really dive into
it and explain it like we did today. Yeah, I
know it's come up in passing, just in us making
(43:58):
comments here and there about like the import of of
randomized trials and control groups and all that. In the meantime,
if you would like to listen to other episodes of
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I Heart Radio. For more podcasts for my heart Radio,
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listening to your favorite shows.
Welcome to Stuff to Blow Your Mind, the production of
My Heart Radio. Hey, welcome to Stuff to Blow Your Mind.
My name is Robert Lamb, and I'm Joe McCormick. And
in today's episode, we are going to be focusing on
a topic that is already something that's very well known
(00:24):
to people who are familiar with quantitative research and statistics,
but less known to the general public. And uh and
I think that's a tragedy because it's an idea that
should really be part of everybody's basic critical thinking toolkit,
no matter what your job is. And so in order
to introduce this concept, I thought it would be best
(00:44):
to start with a with a direct illustration from the
real world of people reaching incorrect conclusions by not understanding
the subject of today's episode. And so the illustration I
want to start with is an interesting story told by
the psycholo, just Daniel Kaneman, that's about the illusory power
of screaming at pilots. Uh. So, the context of the
(01:07):
story is that Knemon says he was giving a lecture
about positive reinforcement to a group of flight instructures. I
think this was in the nineteen sixties, and Kaneman was
trying to inform them about what he believed at the
time was the best consensus of scientific research on learning
and reinforcement, which was at the time that if these
(01:29):
flight instructors wanted their students to have the best possible outcomes,
they should focus more on praising the students when they
did well than on chewing them out when they did
something wrong. And Kneman says that when he finished his talk,
one of the flight instructors that he had been giving
this lecture two got up and tried to dispute him.
He said, no, you're wrong, And so the direct quote
(01:52):
Economy gives from the instructor here is on many occasions,
I have praised flight cadets for clean execution of some
aero attic maneuver, and in general when they try it
again they do worse. On the other hand, I've often
screamed at cadets for bad execution, and in general they
do better the next time. So please don't tell us
(02:13):
that reinforcement works and punishment does not, because the opposite
is the case. So you might think he has a
good point here if you accept that this flight instructor
has had a lot of direct experience working with students,
and you trust him to remember the relative frequency of
these events pretty well, you might assume that he has
(02:33):
a meaningful rebuke to ekonom In. Here again, he says
that most of the time, after a cadet does something
bad and he screams at them, they do better the
next time. And after a cadet does something good and
he praises them, they actually do worse the next time.
So if he's remembering these experiences correctly, and he's had
a lot of them, it would really seem like evidence
(02:55):
that praise has a negative effect on learning, maybe by
making the student pilots soft and overconfident or something, and
getting chewed out is good for skill development. I think
it's quite easy to see the allure of this, this
false conclusion, right right, And it's and you can also
easily imagine how you kind of build upon this with
(03:15):
certain loosely backed up you know, folk ideas about how
you encourage people and how people learn, and you got
to stay on them if they if you tell them
they're doing a good job, they'll get lazy, right, folk wisdom,
tough guy mentality. Yeah, But Knemon saw something different in
this response, and he says that he immediately set up
an experiment on the spot to demonstrate the flaw in
(03:38):
the flight instructors thinking here, so I want to read
from Knomen's description, he says, I immediately arranged a demonstration
in which each participant tossed two coins at a target
behind his back without any feedback. We measured the distances
from the target and could see that those who had
done best the first time had mostly deteriorated their second try,
(04:01):
and vice versa. But I knew that this demonstration would
not undo the effects of lifelong exposure to a perverse contingency.
So to explain this, this experiment a little bit better, right,
he has people stand with their backs to a target
so they couldn't see it, and they would take two
attempts to throw a coin and hit the target without
(04:21):
any feedback of any kind. So they're not getting praised,
they're not getting chewed out, nothing. Uh. And after staging
a number of these, he found again what he suspected,
that the people who were the closest on the first
throw did worse on their second throw, and the people
who were farthest away on their first throw tended to
do better on the second throw. So what kandiment is
(04:43):
actually demonstrating here is something that doesn't really have anything
to do with learning or reinforcement, or really skills or
even human psychology. Instead, this demonstration is showing the effects
of chance, luck, and statistics. What he was showing is
the subject we're talking about today, regression to the mean. Uh.
(05:05):
You'll you'll see that phrase a lot in in scientific
literature and in statistics. But if it helps to put
it in more everyday terms, anytime you see regression to
the mean, you can translate it in your head as
trending toward the average, trending toward the average. So, to
make the coin tossing illustration even clearer, imagine you throw
(05:26):
the coin not twice, but that you throw the coin
a hundred times. So you stand there throwing the coin
a hundred times. And then let's say afterwards you average
together the distance from the target across all a hundred throws,
and you'll come up with some kind of average distance
from target. Uh, just to make up a number for
the sake of argument. Common doesn't give this. But let's
(05:47):
say the average distance from the target across all your
throws is nine centimeters. And remember that you're getting no
feedback at all. Here, so it's unlikely that you will
be getting much better as you go on. So even
that the average distance from the target is nine cimeters,
if you throw a coin once and it happens to
be two centimeters from the targets really close, is your
(06:09):
next throw likely to be about the same as that one,
better or worse. Obviously, it is overwhelmingly likely that your
next throw will be worse, just due to chance, probably
closer to the average of nine cimeters away. And the
same goes for throws that are really far off. If
you throw something three hundred centimeters off, your next random toss,
(06:32):
just by chance, is likely to be much better, much closer. So,
simply put, most of the time, if you're sampling something
in a series over time, if one sample produces an
extreme value, the next one in the series is more
likely to be closer to the average instead of extreme
(06:52):
in the same way. In my experience, Uh, this is
This is why it can sometimes be liberating to start
off a game of bowling with just a disastrous gutter ball,
because because I know that I'm good enough that that's
probably not gonna happen twice in a row, but it's
definitely going to happen at some point in the game
because I'm not that good, you know, I like playing
(07:14):
you know, once a year or even with less frequency
these days. Oh yeah. And it's also like why I
think a lot of us have intuitions that when you
try something for the first time and you do really
good on the first attempt, that makes you kind of
nervous because you just know you're probably not gonna live
up to that repeatedly. Yeah, like if you get you
get a strike that first time, then that that first
(07:35):
um what is it round? I can't even remember. This
is how frequently I bowl. Um, the first role. So
the first role first, the first column, you know. So
the tendency of regression to the mean or or trending
towards the average is pretty obvious when you're dealing with
something like lots of random coin tosses with no feedback,
(07:56):
But it becomes much more obscure when you're dealing with,
say a more a more limited numbers of outcomes. In
the series you're looking at and introducing possibly influential variables
like pilot skill and instructor feedback. After all, we would
expect that some variables having to do with instructor feedback
(08:16):
should have an effect on pilot skill, right, That's the
point of teaching is to have an effect over time.
And after all, in this one scenario, the Konomen describes
the the instructor believed that his verbal abuse of the
students was so motivating that it made them instantly better
on the stick. And you can't necessarily rule that out,
(08:36):
but it's unlikely. I think. I'm convinced that regression to
the mean could more easily explain this flight instructor's belief
that screaming at pilots for screw ups made them better
at planes, because, again, on average, even in the absence
of any feedback at all, if a pilot in training
executes a maneuver perfectly, the random fluctuation from one execut
(09:00):
usian to the next will tend to mean that their
next attempt probably won't be as good as that really
good when the last time. And likewise, if they make
a major error totally botcha maneuver, they're more likely to
do better the next time just by chance. Both of
these tendencies are regression towards the mean. But then Conomon
actually draws a really interesting observation about about about our
(09:21):
psychology and about culture from this fact, so, to quote
him directly, this was a joyous moment in which I
understood an important truth about the world. Because we tend
to reward others when they do well and punish them
when they do badly, and because there is regression to
the mean, it is part of the human condition that
(09:43):
we are statistically punished for rewarding others and rewarded for
punishing them. And that was one of those things that
when I read it, I was just like, oh my god,
that's so true. Um, yeah, yeah, And in this specific instance,
it makes me think about the special fact of reversion
to the mean, fallacies on motivating belief in the effectiveness
(10:04):
of of not just screaming at pilots in this one case,
but all kinds of punishment behaviors, for example, corporal punishment.
Thankfully you hear this less often these days, but I
remember when I was younger, I used to hear people
who would defend the parental practice of spanking children by saying,
you know, I don't I don't care what the site
scientists say. I don't care what the research says. I
(10:26):
know from experience that it works to the extent that
comments like this were based on any real experience and
observation and not just sort of a free form, self
justifying statement that had nothing to do with experience. I
bet a lot of it was fallacious inference of causation
actually based on regression to the mean, just like in
this commument example. But anyway, I thought it would be
(10:49):
interesting to talk a bit more about regression to the
mean today because it's one of those things that, again,
once you see it, it's it's pretty simple, it's actually
actually pretty clear. But understanding it can help you have
a better sense of how good science works and help
keep you from drawing hasty inferences in everyday life. Yeah,
because it is. It is interesting how kind of an
(11:12):
insidious the results can be, the idea that that again,
praise is ultimately punished because there's going to be a
regression to the mean, to to to to the mean,
and then likewise there can be this illusion, uh that
uh that's screaming at pilots and so forth is going
to be the successful way to go about things. Um So, yeah,
(11:33):
this is I think this is an important episode to
cover because it's the kind of thing that it's the
kind of tool you kind of need tucked in your
back pocket, even if you're just doing something like like
scanning science headlines on a you know, a news server
or social media message board. Yeah, because of course, understanding
regression to the mean is extremely important in what scientists
(11:54):
do when they design good experiments. If you don't take
into account regression to the mean, you can incorrectly believe
you have discovered some kind of tiger repellent or something. Uh.
This concern plays a huge role in the history of medicine.
It's part of the design of good medical research, or
really any field that seeks to find remedies for problems.
(12:15):
So consider a very basic hypothetical, uh patent medicine, say
from a hundred years ago. So you know, you have
you have a foot pain that you've never really had before. Uh.
You know, you want it to go away. So you
go to the store and you buy a bottle of
Doctor Field Grades No Fail Pantasy for tumors, ulcers, cramps,
and rooms, and you you pull the cork out, you
(12:37):
chug it, and then the next day your foot feels better.
Now you can conclude from this that the Doctor Field
Grades cured you. But how do you know actually that
the feelings in your foot didn't just regress to the mean,
because the average is a low amount or no amount
of foot pain. And if you don't have a medication
that's tested with control groups and and randomized allocation into
(13:00):
the groups, then how do you know that that the
medicine actually did anything at all? Yeah? Yeah, So many
of the examples you see for this and the applications,
you're dealing with some sort of situation in the world
where there is fluctuation and or change happening, often separately
from whatever is being tested. So in this case, yeah,
the Doctor Field Greats could have just been like just water,
(13:22):
It just just you know, but there is the illusion
that it worked because things got better. But if you
don't have a control group and to you know, to
drive home what that is, that would be like if
you had a had like three different groups and a
study of Doctor Field Greats elixir. Here, one group was
taking Doctor Feel Greats elixer, another group was taking I
don't know, let's say a half dose of Feel Grade
(13:44):
or maybe a competitor's tonic. And then one group, the
control group was taking nothing was or was taking you know,
just water or something to that effect something completely innate. Uh.
And that would be that would be a a group
that you would judge the results of the other categories by, right,
And you would need to randomly sort the people into
(14:06):
those groups. So it wasn't just that, you know, the
only the people with real severe foot pain. We're taking
the doctor field grades, because the more extreme their pain
to begin with, probably the more likely they are to
have that pain be lessened or go away over time,
just naturally. Right. And uh. And I'm going to have
a more specific example of this a little later in
(14:27):
the podcast. So if you if you still don't get it,
just hang on. We'll we'll have another example in a bit.
I was looking at an article in the British Medical
Journal from nine that was just a collection of different
examples of regression to the mean in real life medical research.
(14:48):
This was by j Martin Bland and Douglas J. Altman
called statistics notes some examples of regression towards the mean,
and they point out a very common type of example,
so the this will be similar to what we just
talked about. The author's right. In clinical practice, there are
many measurements such as weight, serum cholesterol concentration, or blood pressure,
(15:10):
for which particularly high or low values are signs of
underlying disease or risk factors for disease. People with extreme
values of the measurements, such as high blood pressure may
be treated to bring their values closer to the mean.
If they are measured again, we will observe that the
mean of the extreme group is now closer to the
(15:30):
mean of the whole population. That is, it is reduced.
This should not be interpreted as showing the effect of
the treatment. Even if subjects are not treated, the mean
blood pressure will go down owing to regression towards the means.
So again, something starts with an extreme value in certain
types of cases, you would just expect it to have
a less extreme value the next time due to random fluctuation.
(15:55):
Uh So again, you know this could fill you with
despair because you might wonder, well, then how could you
ever know if a treatment was effective or not. But again,
this is where the standard practices of science based medicine
come to play. Instead of just taking people with some
extreme measurement and giving them a treatment, you randomize them
into test groups and control groups like we were just
(16:15):
talking about. So if you have a large enough sample,
you properly randomize the groups. People with the extreme starting
conditions will somewhat regress toward the mean, but they will
all regress toward the mean on average the same rate
whether they're receiving a real potential treatment or they're in
the placebo group. But if the treatment actually does something helpful,
this effect will manifest as the difference between the two groups.
(16:38):
So good scientific research good medical research has methods for
excluding the effects of reversion to the mean on their findings.
We have the tools, but we can still fall into
the trap of regression to the mean fallacies, especially in
our day to day lives drawing inferences the way that
that the pilot and in common story did, or or
(16:59):
even science if we're not careful and deliberate about designing experiments.
And in addition to just a methodology design that has
you know, randomized groups and control groups, there are also
ways of trying to counteract regression to the mean, just
through statistical methods that are maybe less reliable, But there
are statistical methods people can use to try to apply
(17:21):
sort of modifiers to data in order to estimate regression
to the mean and UH and counteract its effects. So
again we have tools within scientific research to to figure
this out, and it's a lot of what science does
is trying to sort out the difference between regression to
the mean and actual effects of interventions. But in our
(17:41):
day to day lives, we still fall for regression to
the mean fallacies all the time. Yeah, and it's important
to realize too that it's not just a situation where
regression towards the mean could create an illusion of something
working when it doesn't. Uh, you know, sometimes it can
just potentially overstate um the effects something. For an example
(18:02):
of that that I was looking at was that regression
towards the mean or the failure to account for it
can also overstate the effectiveness of something like traffic light cameras.
Is it making a difference and cutting down on accidents perhaps,
but any actual effectiveness could potentially be overstated by failure
to account for just regression towards the mean. Oh yeah,
(18:23):
So where do you tend to install things like that?
High acts like problem areas? Right, So, if there's like
a stretch of road that has a lot of problems
on it, people really speeding a lot there or crashing
a lot there, that might be where you stage the intervention.
It's possible some things like that fluctuate naturally over time
(18:43):
in different locations. Yeah, and you put the cameras in place,
and it could have an effect, but maybe not as
much of an effect as it looks like it is
taking place. Again, if you don't factor regression towards the
mean into the study. Right now, While our TM is
a very important phenomenon to understand and take into account,
(19:04):
it certainly doesn't apply to every sequence of values you
could repeatedly sample, So you also have to be careful
not to apply it in situations where it isn't warranted.
I was you know, there are a million examples you
could cite. One that came to my mind is the
orbital decay of a satellite. Let's say you've got a
communication satellite in lower orbit and you get a reading
(19:26):
on its altitude and the reading is lower than the
satellites average altitude. Uh. Now, you might say, hey, I
think this means we need to program a reboost to
insert it back into the orbit where it's supposed to be.
And somebody could erroneously apply regression to the mean here
and say, no, we don't need to do that. The
satellite might just return to its average altitude. It doesn't
(19:49):
apply in this scenario, even though you are taking repeated
measurements of a value over time, because we know things
about the physical characteristics determining the orbit of satellites and
in lower thorbit uh and that due to factors like
atmospheric drag, their altitude tends to trend steadily downward over
time in a consistent direction down, down, down, So eventually
(20:12):
you will need a reboost in order to put it
back up to the correct distance. So regression to the
mean applies to certain kinds of data that are repeatedly
sampled data where there is natural random fluctuation back and forth,
not a steady trend in the data in one direction
on the relevant time scale. The other thing that's important
(20:33):
to understand is that systems where you expect to find
regression to the mean are systems in which the repeated
data values you're sampling are to some degree determined by
luck or chance. If a series of values is influenced
almost entirely by deterministic influence, like in the satellite example,
by like the laws of physics, or by some extremely
(20:56):
reliable skill with little room for variation, values don't really
regress towards the mean in the same way, because there's
just less random fluctuation back and forth to begin with.
The more chance and random variation plays a role in
the outcome, the more you will tend to observe regression
towards the mean after an extreme sample in in whatever
(21:17):
it is you're looking at. Yeah, I've read that the
progression towards the mean is is not to be confused
with the law of large numbers. For example, Uh, this
is the the law that that states as a sample
size becomes larger, the sample mean gets closer to the
expected value. So a coin flipping example is key here.
Flip a coin and the random results are going to
(21:39):
ultimately average out to a point five proportion. But if
you only flip the coin ten times, you might not
see this breakdown. Um. And this also applies to say,
even odds on the rolling of a of a D
six of a six sided die. Uh So for example,
too regular people, that's just to die. That is nerves
like us, it's a D six. Yeah, D six is
(22:01):
what I could get my hands on because I was like, well,
I'm gonna do an example. I'm gonna try it myself.
So while I was putting together notes for this, I
went ahead and rolled ten times, and I got even
even odd even odd even even even even odd. So
that's that's seven to three in favor of even. So
it might make you wonder, well, is this die broken?
Does this D six need to go away? Because it
(22:22):
can't be trusted to roll? Uh? You know a balanced
array of odd and even numbers. Well, no, that's not
the case. Uh. And if I were to roll this,
say another hundred times, another thousand times, I would see
things even out even more to where we would see this, uh,
this point five proportion of odd versus even. Right. So
(22:45):
these are not exactly the same thing, regression to the
mean and the law of large numbers, but they are
closely related. Both observations require you to think about statistical
tendencies over time, over a time period of repeated sampling,
and both are prim ust on the knowledge that repeated
samples will tend towards the average. But regression to the
mean has to do with the idea that if you
(23:08):
start with an extreme observation and there is some role
of chance or luck in determining the value of this observation,
the next time you sample it, it's more likely to
be closer to the average. The law of large numbers
is that if in the real world, the more times
you run something, the closer your outcomes in the real
world will will be to the sort of perfect mathematical
(23:29):
average that you would estimate just given the chances to
begin with. Now, I want to come back to regression
towards the mean in um in medical studies because I
found a really interesting one that came out earlier this year.
Uh So, a lot of a lot of the examples
you find involving regression to the mean involved sports or economics,
and I found this one discussed in a New York
(23:51):
Times article again from earlier this year titled Intense strength
training does not ease knee pain, study finds by Gina Colada.
Uh this referring to a study published in JAMMA that
entailed an eighteen month clinical trial involving three seventy seven participants. Okay,
so the basic situation, the setup for this paper is
that a lot of people have knee osteoarthritis and one
(24:15):
of the go to treatment recommendations has long been strength training.
So in this study they decided to look into it
with three basic groups, one that received intense strength training,
another that received moderate strength training, and another that received
counseling on healthy living. So that third group, that's the
(24:36):
control group, They did not have any amount of strength training,
just uh, you know, some positive counseling about healthy living. Sure,
so the researchers here apparently actually expected to see the
intense strength training take the lead that they were looking
to identify what has been just sort of accepted wisdom,
um and and again that this has been the predominant
(24:58):
treatment idea. But in instead they found that the results
were the same for all three groups. Quote, everyone reported
slightly less pain, including those who had received only counseling.
Now why is that, Well, as Colotta points out, there's
there's always room for other effects, especially say the placebo effect.
Uh but regression to the mean is also a heavy
(25:20):
consideration here and certainly could work in congress with the
placebo effect. Right, So you don't necessarily have to assume
that the counseling actually helped to heal people's knees, though
it may have in in in some it may have
had some kind of mechanistic effect in in some way
a mind body kind of thing, But you would also
just expect over time, people who have an extreme starting position,
(25:41):
who are starting with a lot of knee pain, to
get gradually better over time. Yeah. So a Colatta rights
quote are the right, as symptoms tend to surge and subside,
and people tend to seek out treatments when the pain
is at its peak, when it declines, as it would
have anyway, they ascribed the improvement to the treatment. Uh.
So you know, this would this would roughly equate to
(26:03):
yelling at your knee when it's in pain, and it
really makes it certainly relates to many other health scenarios
as well, various medications and even things like prayer and
you know, supernatural um treatments and attempts to to deal
with pain, etcetera. Yeah, I mean it could apply to
to any intervention that is aimed at influencing something that
(26:24):
is naturally variable on its own, right. Yeah, and you
know something that's again any kind of system in which
change occurs, when fluctuation occurs. Uh, you know, you can
you can see this applying to not only physical pain,
but also uh, emotional distress things of that nature. You know.
So again, I think this is an important tool to
have in our our logic tool kit. Thank thank Now.
(26:52):
There are even cases where I'm tempted to think about
the application of regression to the mean, but where it's
probably a lot harder to quantify exactly what the effects are.
It's cases where it can be difficult to separate out,
say the effects of some kind of deterministic influence like
skill versus how how strong the effect of chance or
(27:15):
luck is. But I think about things even in the
world of the arts, like I think about, you know,
the sophomore album by by a band that has like
a really stellar debut album. Uh, you know, often that
is perceived is disappointing, and you have to wonder, like, Okay,
is it is that often true? Because I don't know
(27:35):
if people get famous and it goes to their heads
and then they you know, they get full of themselves
and make something dumb, or is it because when somebody
has a debut album that's really well received, to some extent,
it's so good partially because of luck or chance, and
that's an outlier that you're as you're starting sample, yeah, yeah,
And certainly this is an area that's there's a lot
(27:56):
more subjectivity here and and so it's not the kind
of thing you can that's really have a control group
for anything. But but I think it is quite interesting,
and I did find as I was looking around for
some jazzy or examples or possible examples of aggression to
the mean. Um, I found one that that actually gets
into a little bit into the idea of you know,
(28:16):
first and second album. But also uh, the idea of
follow up films and Hollywood sequels has pointed out both
good Yeah has pointed out by Joanna Deong in two
thousand eighteen on the blogs scientifically sound movie sequels are
potentially a great example of aggression to the mean. Quote,
Hollywood sequels are only made if the original film is
(28:39):
a quote unquote high quality success. But the average quality
of sequels will be closer to the mean than average
quality of originals of sequels because of regression to the means,
So sequels tend to be of lower quality than the original. Now,
I might somewhat dispute the premise here that Hollywood sequels
are only made to films that are high quality to
(29:00):
begin with. Um, right, But but I still think this
is onto something because there is a movie that gets
a sequel tends to have something about it something that
people are responding to, whether it's a movie that I
would like or not. Right, I mean, sometimes obviously the
situation is the film just made a lot of money.
I mean, I guess that's the key thing. It didn't
(29:21):
make a lot of money. If so, producers are going
to be more inclined to say, let's do that again,
Let's have that experience again of all that money coming in.
And sometimes this this certainly matches up with a quality film.
You have something that really captures people's imagination and is
of high quality. And uh and you know, so it's
really firing on all cylinders. But you know, and yes,
(29:45):
certainly in some cases it's just the right film at
the right time. Or or maybe it has nothing to
do with the film itself. Maybe it's who's in it,
or I don't know what's going on in the zeitgeist
during that particular era. Well, the way I would think
about this is, and I think that again, this is
onto something. It highlights that when we experience confusion where
we say, like, wow, you know, the Exorcist is such
(30:07):
a great horror movie and the Exorcist too is so bad?
How could that be the case? You know, why is it.
Why is such a bad sequel to such a great movie.
It's because of the comparison of the original to the
sequel that we're experiencing this confusion. Another way you could
just look at it is most horror movies are direc
(30:28):
most movies are bad, and it is only by comparing
the The Exorcist Too to The Exorcist that you notice
this steep drop off where Another way of looking at
it is that The Exorcist Too is bad like most
horror movies are, and the first one was an outlier
at the beginning. It was a first film in a
series that happened to be really good to cut above. Yeah, absolutely, like, yeah,
(30:53):
I think this is the correct way to look at it,
and also keeping in mind it just how amazing it
is that any film gets completed, like even bad film,
Like a lot of people probably work pretty hard to
make that happen, even if the end results don't really
please anyone at all. But but yeah, I think this
is also an interesting inversion of the opening example of
yelling at pilots as well, because most of the time,
(31:15):
if a flawed movie comes out, people are not clamoring
for the sequel. Um sequels are rarely guaranteed, so you're
not often going to hear things like, oh, well that
wasn't great. I hope the next one is an improvement.
I mean some people say that, some people I've said
things like that before, where it will be like, oh,
really flawed film, but maybe there's like a cool idea.
(31:35):
I kind of wish it would they would remake it,
even though there's no like logical reason that there would
be like a there would be money behind that idea. Well,
I guess it's kind of different when you're talking about
a one off creative project versus something. I mean, we
live in a kind of different era now because we
were at the height of this you know, cinematic universe
thing with a huge number of the big budget movies
(31:59):
that come out, the big event movies are not one
off creative products, but they are a product that exists
within some kind of franchise or universe or something. So
you just know automatically that there's gonna be another one,
whether this one is good or not. Yeah, like either
it's an established film universe where like, you know, they
put out another Marvel movie and it's just terrible. Well,
(32:22):
obviously there's enough momentum, they're not going to stop. They're
not gonna be like, oh, well, lesson learned, Well we'll
stop them. No, no, there's gonna be another. Another example
of this might be a successful franchise in another medium,
say a book series, so like the Harry Potter books
for example, or I don't know, Lord of the Rings,
where you know that once they make the Fellowship of
the Rings, there's going to be a follow up, They're
(32:44):
gonna do another one. So in these ways, unless it's
the seventies and it's uh, that Lord of the Rings
movie that that ends with Helm's Deep, well, but they
picked that up eventually, but yeah, okay, but but yeah,
probably the Harry Hotter films are a better example. And
there may be spe specific you know things about how
(33:04):
that wasn't guaranteed either, uh, you know, the economic reality
can always come into play. But for the most part,
like those were when when that started, you knew they
were going to keep making these at least they were
going to make a follow up, so you could have
comments like, well, there that was this was kind of
flawed in some of the some of its execution. I
hope that they fixed that in the next film for
the most part. Yeah, with one offs, this is not
(33:25):
the case. It's like, if if this film fizzles, then
only you know, a few, like rare people are going
to be clamoring for a sequel or dreaming about what
the sequel would be. Yeah. I think this observation but
regression to the mean and movie sequels is actually very
on point, but more so for the films of yester year,
where the more the more common thing was you'd have
(33:46):
a an independent sort of creative product that it's its
own thing, and then if it resonated with somebody, if
it did well, there would be sequels. I think it's
a little it applies a little bit less today when
there's just you know, we're in the world of France,
Chises and extended universes and there's just sort of like
a guaranteed ongoing uh conveyor belt of of new stuff
(34:07):
within the Marvel world or the Star Wars world or whatever. Yeah,
but I think it it is a worthwhile way to
think about creative the creative process, and you know, as
opposed to some of these alternate sort of folk wisdomy
ways of thinking about it. For example, on Weird House, cinema.
We recently talked about Toby Hooper. Toby Hooper is one
of those directors who's often you'll often you'll see descriptions.
(34:29):
I think we've even read part of a review where
they they really they talk about, oh, well, you know
he put out Texas Chainsaw Mascre directed that film and
this was great. It was, you know, just a real
lightning bolt um to the cinematic world into horror itself
as a genre. And then the idea that well, he
was never able to capture that magic again, you know,
(34:50):
that is his career was just like one long slide
after that, which I don't think it is a fair assessment,
especially if you employ regression to the mean you the
idea being that, yeah, he did kind of get lightning
in a bottle with that with that first big film,
that that he was able to to really bring something
together that is an outlier, um, but that that that's
(35:13):
just going to happen. That's just the way these things work, right,
So most movies aren't that good. So you know, the
random chance of like how good his ideas and execution
are from one year to the next is going to
set in and you might have a different idea about
his career. If you were to say, like randomly chronologically
reorder all his movies, right, you know, like if you
(35:33):
were to put the worst ones earlier on or something,
people might feel differently about it. Yeah, well then they
would talk about, well, okay, TCM was peak Toby Hooper,
like this was his peak output. Because this is the
kind of the kind of view of an artist's you know,
creative trajectory that we tend to want to um to
follow along, you know, because it's more story shaped, the
(35:55):
idea of ascent and then eventually decent that there's gonna
be h is going to be a period of high
noon in their creative out output, and sometimes that does
match up with the reality. But I don't know even
then we I think we tend to overlook the dogs
in the filmographies of people we love, you know. Oh
yeah uh. But then again, I mean, this is interesting
because in talking about regression to the mean applying to
(36:19):
creative products like movies, we are acknowledging that the creative
process is not purely a product of talent and skill,
that there is a significant amount of chance and luck
involved in something like how good a movie turns out?
To be um, and it's hard to know exactly how
to like how to picture that influence of chance and luck.
(36:39):
You know, like, what what is that in the creative process.
It's obviously true because there are people who can be
incredibly skilled in one instance and then I don't know,
things just don't go right the next time, and to
make something that nobody really likes. But uh, but that's
that's just not often how people like to think about
creative talents and people like to think about the creative
(37:00):
process like it is much more strictly deterministic. Yeah, yeah,
Or or you look at things like the Star Wars
films and you kind of like fall into this idea
of thinking, this is stuff that is mind out of
the mythic earth, and then you know, it just makes
sense that things would accumulate and get better. So um,
but really looking back on it, especially if you actually
(37:20):
like watch documentaries, and there's some great ones about the
production of those films, like it's it's amazing that Star Wars,
the first one in New Hope was as good as
it was, and then it's nothing short of I mean,
it's it's just a pure miracle that the second one
was so much better and like really nailed it. Like
if if the second film had had floundered, I mean,
(37:43):
just imagine how different the cinematical landscape would have been
for decades to come. Yeah, So it's it's amazing if
the first film in a series is good, and it's
super amazing if the second one is good. And and
this is why I think we often find too that
if if part one in part two, if something are
of high quality, then you've got to look out for
(38:04):
that part three because that part three, that part three
may be coming to get you. But likewise, if a
part two is rubbish, um, you know, subjectively, then then
part three might pick it up and uh and get
things back on track. So you certainly see that that
kind of fluctuation as well. I have a question I
actually don't know the answer to, but this would be
interesting in terms of I don't know the high performing output,
(38:29):
whether that is in whether that is a creative endeavor
like you know, writing books or creating movies, or whether
that's something even like athletics, like athletic performance, do you
expect to see more random fluctuation in the performance of
collaborative output versus individual output? So say, um, do you
expect more influence of random chance and fluctuation in the
(38:52):
quality of uh books written by a single author versus
you know, movies that have the input of hundreds of
thousands of people? Uh? Or in in the realm of
say sports, like, do you expect more random variation in
the output of an individual athletes like you know, an
individual gymnast or something, or in team sports? Yeah? I
(39:14):
can see it going both ways, because yeah, if you
think too hard to about even just like the film analogy,
you can easily get into discussions of like, Okay, well
was it the same cast and crew that are producing
the sequel? Uh? You know, what happens when the budget
is different, what happens when there are other constraints, what
happens when suddenly there are a whole bunch of producers
that have their ideas about what things should be. I mean,
there's so many different factors to take into place. Uh.
(39:36):
You know, with this example that you know, perhaps doesn't
bear too close of scrutiny, but but but it's but
it's still I think serves as a nice um illustration
of the overall trend that we're talking about here. Well,
it does bring up the fact that since I mentioned
athletes that, you know, I don't know a lot about sports.
I'm not a big sports fan. But but clearly, but
regression to the mean is something that has widely been
(39:57):
applied to the world of sports. Uh for example, in
the observation that often after having a really stellar season,
either an individual athlete or a sports team will be
perceived to underperform the next season. And again that very
well could have something to do with regression to the mean. Like,
you know, the fact that they're observed having an amazing
(40:19):
season is actually an outlier. You're starting your expectations then
and saying like, Okay, now they're going to be the
best forever. Just by random fluctuation over time, you would
expect their next season to probably be not as good
as the first. I wonder to what an extent this
can be applied to, say, the world of the culinary arts,
or even just like various food crops, like say the
(40:41):
selecting a cantalope at the grocery store, that sort of thing.
I mean, I guess it would apply to pretty much
anything where you're sampling in a series over time. There's
plenty of random fluctuation in what you're sampling and the
first thing you sample is an outlier in some way
really good or really bad. If those things true, then
you can probably expect you're going to see some regression
(41:04):
one way or the other. Yeah. Yeah. By the way,
I was looking around for like really stellar examples of
a sequel film that is widely believed to be uh rubbish,
and I think The Exorcist Too is the primary example.
Like you get into some of the other examples that
pop up, I feel like there's room for disagreement. Um.
For instance, Texas Chainsaw Masker two is one which I
(41:26):
saw popping up on some of these lists for disappointing sequels.
But I think that's entirely based on who you ask.
I think if you ask us, we will agree that
that that t c M two is is actually a
great film. It's different from the first one perhaps if
you go into if you go into part two with
the expectations you had for part one, you may see
it as a dip in quality. But depending on what
(41:48):
else you're bringing to the table, you might see it
as an increase in in quality or at least or
something that maybe is different but on par with the original.
I mean it's certainly not for everybody. I mean, it
is a it is a gross, disgusting film in in
a way like the first one, probably even grosser, but
also a sort of satirical masterpiece. Um. But I just
had another thought when you said that The Exorcist Too
(42:09):
is regarded as like one of the best examples of
a sequel. That's really rubbish. I mean, it makes me
also wonder about the pretty high estimation critics generally have
of The Exorcist three. Makes me wonder if the effect
of the Exorcist to being so bad actually makes people
sort of over you know, they're like they're ready to
be impressed by the Exorcist three. Yeah. Yeah, I wonder
(42:31):
if that's the case too with it with especially when
you have a situation with a part three coming back
and restoring uh some I don't know, some level of
quality to a franchise. I mean there's also like the
Star Trek h example, right, I mean that was long
the Long held up as an example of like, okay,
you have you even Star Treks and your odd Star Treks, right. Uh.
And I think you've made a similar case for the
(42:55):
Faster and Furious movies, right, I mean once you get
to a certain point in the series, I think it's
pretty much all uh, you know, a nitrous boosted brain.
It's it gets you know, it's all like we're driving
cars in space now and flying and all that. But um,
but for the earlier ones, yeah, i'd say the odd
ones are better, Like, uh, three is the first one
(43:15):
where it really starts getting ludicrously weird. Four is kind
of a uh, and then five starts. Five is when
the rock shows up, and then but by seven year
Golden All right, well, we're gonna go ahead and close
this one out here. But we'd obviously love to hear
from everyone about this about regression towards the mean, just
(43:36):
in our daily lives, in various scientific studies. Perhaps you
have thoughts about how this applies to something we've discussed
on the show in the past, because I know we've
we've mentioned regression to the mean in passing before, but
certainly we've never taken the opportunity to really dive into
it and explain it like we did today. Yeah, I
know it's come up in passing, just in us making
(43:58):
comments here and there about like the import of of
randomized trials and control groups and all that. In the meantime,
if you would like to listen to other episodes of
Stuff to Blow Your Mind, you will find them wherever
you get your podcast. Just look for the Stuff to
Blow your Mind podcast feed. We have our core episodes
on Tuesdays and Thursday's, Artifact episodes on Wednesday, listener mail
(44:18):
on Monday's. On Fridays, we do a little bit of
a weird house cinema. That's our times. We just talk
about some sort of a strange film. Uh, and you know,
teas apart what makes it strange? Uh, let's see what else. So, yeah,
you go to Stuff to Blow your Mind dot com
that will send you to the I heart listing for
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(44:40):
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(45:03):
These are just for fun. This is just purely extra clothing. Okay,
this should not be your core clothing. Huge thanks as
always to our excellent audio producer Seth Nicholas Johnson. If
you would like to get in touch with us with
feedback on this episode or any other, to suggest a
topic for the future, just to say hello, you can
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(45:33):
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