Sports and Clinical Trials: The 1927 Yankees, 15 Tarzans, and Modern Athletes

In this episode of "In the Interim…", Dr. Scott Berry examines the analytical challenges of comparing performance across eras in both sports and clinical research. Drawing from statistically robust family debates and published research, Scott details how overlapping competitors—such as athletes who played with both Babe Ruth, played with the next generation, who played with …  all the way to playing with Aaron Judge—enable the estimation of temporal effects and allow for objective comparisons between generations. He translates this approach directly into platform clinical trials, demonstrating how overlapping trial arms or shared control groups make it possible to quantify and adjust for time trends. Scott distinguishes between observable, model-based comparisons and subjective judgments, rigorously addressing limitations such as interactions between treatments and era, and emphasizing the foundational importance of empirical overlap over speculative claims.

Key Highlights

• Deconstruction of time-machine thought experiments: analyzing how teams like the 1927 Yankees or athletes such as Johnny Weissmuller and Jesse Owens compare to present-day counterparts using statistical benchmarks.
• Technical explanation of connecting eras empirically through players or trial arms who span multiple time periods, thereby supporting quantitative estimation of temporal shifts.
• Detailed account of linear and hierarchical modeling strategies, with covariate adjustment for player age, period effects, and evolving population composition across baseball, hockey, and golf data.
• Translation of these statistical constructs to adaptive and platform clinical trials, exemplified by I-SPY 2, where overlapping treatment and control arms permit rigorous assessment of evolving treatment effects over a trial’s lifespan.
• Critical discussion of the rare but important possibility of treatment-by-era interactions, and the necessity of data-driven assessment rather than assumption.
• Consideration of how these methods inform not just debates about athletic greatness and Hall of Fame inclusion, but also robust interpretation of treatment effects in longitudinal clinical studies.

For more, visit us at https://www.berryconsultants.com/

Creators and Guests

Host

Scott Berry

President and a Senior Statistical Scientist at Berry Consultants, LLC

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A podcast on statistical science and clinical trials.

Explore the intricacies of Bayesian statistics and adaptive clinical trials. Uncover methods that push beyond conventional paradigms, ushering in data-driven insights that enhance trial outcomes while ensuring safety and efficacy. Join us as we dive into complex medical challenges and regulatory landscapes, offering innovative solutions tailored for pharma pioneers. Featuring expertise from industry leaders, each episode is crafted to provide clarity, foster debate, and challenge mainstream perspectives, ensuring you remain at the forefront of clinical trial excellence.

Judith: Welcome to Berry's In the
Interim podcast, where we explore the

cutting edge of innovative clinical
trial design for the pharmaceutical and

medical industries, and so much more.

Let's dive in.

Well, welcome everybody
back to In the Interim.

I'm your host, Scott Berry.

We dive into all things clinical
trial science, statistics, a wide

range at times here on In the Interim.

Today, I'm gonna do another
episode of bringing the world of

sports, what drug developers could
learn from the world of sports.

This is a topic we've touched on in other
episodes, and I'll come back to that.

I'll, I'll make reference to those.

But I wanna spend more time on the
sports part of this, and then I'm

going to show you an analogous problem
that comes up in clinical trials.

It's a really important problem
in clin- clinical trials, and I

think it's so crystal clear in the
world of sports, and it's very fun.

So we've been having the following
discussion in our family, and yes, uh,

my family has a number of statisticians.

Uh, my, my wife Tammy is a PhD in finance.

I have two PhD kids, very analytical
family, and we love the world of sports.

So when we get together, our
discussions are probably a little

bit different, but we've been
having the following discussion.

My son Cooper, he's 21 years
old, he's a junior at a Division

III college, a baseball team.

He goes to Pitzer College in Claremont,
California, and Pomona College and

Pitzer College, they're, they're two
colleges combined together to play

Division III sports, and he's on their
baseball team, and they're quite good.

They went to the Division III,
uh, College World Series a couple

years ago, so they're a very
good Division III baseball team.

We've been having the
following discussion.

So he-- the Division III baseball team,
how would my son Cooper's Division

III baseball team fare if they could
play the 1927 New York Yankees?

So this is a, a bit of a
global show, so I, I, I, I will

touch on this a little bit.

The 1927 New York Yankees are
a famous team in baseball.

Uh, you-- By the way, you can, you...

I think you'll pick up on what's going on
here, even if baseball is not your sport.

The 1927 New York Yankees
were, were-- They, they even

had the label Murderers Row.

Their top six hitters, in baseball you
have nine players that bat in your batting

order, and you rotate through them.

So you go one through nine and
then back to one through nine.

Typically, they bat, uh,
four or five times in a game.

Their top six hitters were famous,
uh, baseball players, two of them Hall

of Famers in Lou Gehrig, and you may
have heard of Lou Gehrig as ALS is

referred to as Lou Gehrig's disease.

Was incredible baseball player.

He's in the, the Hall of Fame, and Babe
Ruth, who might be the famous, most famous

baseball player of all time for, for, for
multiple reasons and, and well-earned,

incredible, uh, baseball player and really
brought on the, the advent of hitting

home runs in baseball wasn't something
that was really done before Babe Ruth.

He hit more home runs than
some teams did in the 1920s.

So that team played in 1927, uh,
just we'll, we'll call it a hundred

years, essentially a hundred years
ago, and they're one of the most

famous teams in professional baseball.

Now, what does it mean?

Uh, the, the-- this question is you
have to spend a lot of time talking

about what do you mean by this?

And what, what our discussion goes
to is not if Babe Ruth grew up

and was born in 2004 when my son
was born and, and, and lived now.

It's if you could fly a time machine
back to 1927, you could put them on the,

the, the time machine and bring them
forward today to play a game against

my son's Division III baseball team.

Who would win?

Now, it, it, it, it's-- that, that's
what I'm gonna refer to as this time

machine aspect of this, is I'm not, I'm
not interested in alternative scenarios

where my son is born in 19- uh, 1904
or, or 1920-- 1906 and he's twenty-one

in 1927 and had to grow up in that era.

Alternatively, what would happen if
you could take a time machine and

move the Pomona-Pitzer Division III
baseball team to 1927 and they play in

Yankee Stadium with the 1927 equipment?

And of course, if the Yankees move
forward to today, they get to use

the aluminum bats that my son's team
use, the baseballs, the catcher's

equipment, the gloves, all of that.

They, they, they get
to use that equipment.

So the two teams play
with the same equipment.

They don't have to use that equipment.

So it's, it's a fair game.

Now, we'll come back to that question.

We'll come back to that.

But that's the sort of
question being posed.

Now- Many baseball fans would
say, oh my God, they'd get

destroyed by the 1927 Yankees.

But we know something about this era.

So one of, and I wrote a chance column
years ago where I presented this,

and I'm fascinated by how different
athletes would have done at different

times and why and what that all means.

So Johnny Weissmuller was an an
Olympic swimmer, and he won the

1924 and 1928 Olympics in swimming.

He won the 100-meter freestyle
gold gold medal in 1924 and 1928.

He's an interesting guy
because he became a movie star.

He played Tarzan in the movies and
became a a very famous guy and was,

at the time, this good-looking guy,

muscular, strong, was was idolized at
the time and was this incredible athlete.

So he was sort of the epitome of this
incredible athlete in 1924 and 1928.

In the 100 meters in 1924, his
his gold medal time in the 100

meters was 59 seconds flat.

If you took that time and you allowed
Tarzan, and I'll apologize for this,

but I'll call Johnny Weissmuller Tarzan.

If you took Tarzan and allowed Tarzan
to swim 15 separate Tarzans, so they're

all completely rested up and they and
they swim 15 consecutive 100 meters.

So 59, 59, 59 consecutively for 15
100-meter swims, he would swim 1445.

59 seconds, 15 consecutive times.

At the time, by the way, a Swedish swimmer
had the Olympic record in the 100 meters.

It was 2115.

So 15 Tarzans would have done 1445 and
the Olympic record at the time was 2115, a

50% increase over 15 consecutive Tarzans.

So this incredible athlete is
allowed to swim 15 consecutively,

perfectly rested, would swim 1445.

The current Olympic record is 1430.

Bobby Fink, and I may be saying his
name wrong, I'm not a big swimming

person, a United States swimmer, has
the current Olympic record of 1430.

By the way, the current
women's Olympic record is 1520.

They, of course, would destroy the
swimmers who had to swim 15 lengths.

They, they, they absolutely destroy them.

Essentially, they would finish,
uh, you know, at 1430, and the

record, it was 2115 at the time.

Uh, but you could even take Johnny
Weissmuller, Tarzan, and allow him to

swim 15 in a row, and the current swimmers
would beat them, would beat that time.

If-- The-- I, I imagine if you
said something to somebody at the

time, it would be unimaginable
that a human could accomplish that.

But that's a nine...

That's mid-1920s swimmers compared
to swimmers nowadays would

destroy swimmers at the time.

We know this is true.

A-and by the way, I'm using that as
an example because it's completely

cl- comparable in terms of, uh,
timing somebody in a pool at the time.

It, it's, it's translatable.

It's apples to apples.

Another case is just thinking
about the hundred-meter run.

And Jesse Owens is, is famous.

He's famous for his, uh, Olympics
in Berlin with Adolf Hitler

there, and Adolf Hitler's...

I, I, I don't have to go through
this, but Jesse Owens, incredibly

famous for in the face of Adolf
Hitler, he won four gold medals.

Uh, this incredible feat.

And in, in the 1936 Olympics, he ran
ten point three in the hundred meters.

Now, if you compare that to the,
the, the, the Olympic record now is

nine point six three, uh, Usain Bolt.

The-- Essentially, if Usain Bolt
at that time would've raced Jesse

Owens, Jesse Owens would be about
seven meters behind when Usain Bolt

finishes, uh, essentially destroying
Jesse Owens, the, this phenomenal

athlete who accomplished a great deal.

The NCAA record, by the way, now
is nine point eight two seconds,

also destroying Jesse Owens.

If you could take Jesse Owens and move him
in a time machine from 1936 Berlin to now,

he wouldn't even make these NCAA teams.

Now, the important part of this,
a- and I'm gonna, I'm gonna say

this as we go through this, I'm not
interested in what they accomplished.

Jesse Owens accomplished an incredible
amount, and he was the best runner of his

time, and he should be rewarded for that.

If you're gonna do something like a
hall of fame, Jesse Owens is in it.

He's in every hall of fame you
should ever think about for track

and field, for every reason.

The fact that he would now not make the,
the better NCAA teams, I, I, I'm not even

sure where that fits in with high school,
uh, doesn't take away from his accomplish.

But if you could take him in a time
machine, that's the truth of it, and

we know this from many other sports.

The shot put is something that
hasn't changed, and in the 1920s

they threw it about 50 meters for
records, and now they throw it...

Uh, sorry, um, over 50 feet, and
now they throw it over 75 feet.

Again, a, a 50% increase in the time.

So the 1920s and now are
very, very different.

Uh, and we know this looking
at objective measures.

It's much harder in a team sport.

It's much harder thinking
about baseball because we don't

have those objective measures.

Looking at a home run in 1927 and a
home run for, uh, uh, an NCAA team

now are very, very different things.

Now, what...

By the way, why?

Why are athletes better now?

I think the number one reason, and
by the way, I wrote a s- uh, a chance

column on this, uh, 15 Tarzans compared
to one modern man, is population.

There are just many, many more
people now than there were then,

and if you take the, the most elite
of them compared to the most elite

when there's a smaller population,
they're largely gonna be better.

Now, you get into extreme value
theory and the, the, the chance of

getting this outlier in it, and it can
happen in, in parts of different era.

Now, there's no question the world
has changed in terms of better health.

Humans are healthier now than then.

It also changes the,
the access of somebody.

How many people in 1927 had access
to professional baseball that

they would have ha- led a life
that gave them access to that?

In 1927, Blacks couldn't have
played for the, the, the Yankees

at that time, and, uh, that...

But many people lived in scenarios
where even if they had been this

elite athlete- They would have
not ended up on the 1927 Yankees.

Now, there's much more access to that
from a much wider population base.

If my son would have end up being
this elite extreme value, he might

be in the major leagues at this time.

Now, there- so there's better health,
there's better access, they're stronger,

they're taller, they're bigger.

The training is absolutely
better, strength training

is better, diet is better.

I'll bet my son, Cooper, has played
more baseball than those 27 Yankees by

the time they got to, to the Yankees.

Now, they played a ton of baseball,
154 games a year at that time and

all that, but at 21 years old,
he's played a lot of baseball.

Played competitive baseball in the youth,
and there are many, many people like that.

Video training and all
of this, uh, at the time.

So there are many things different.

I, I don't so much care about that.

I care about the time machine part of it.

A direct comparison of the teams
or the players across these

eras is, is, is my interest.

Now,

can we address this question of
comparing players of different eras?

So I'm interested, what would Babe Ruth
do if you could take a time machine, go

back to 1927, you could pull him forward
and let him play in 2026 for the Yankees,

uh, batting in front of Aaron Judge.

What would Babe Ruth do?

I'm fascinated by that question.

Fascinated by the question, what
would happen if you took Aaron

Judge and you could send him back
to 1927 and put him on the Yankees?

Aaron Judge is, like, six foot seven,
a, a phenomenal athlete, phenomenal

baseball player, uh, uh, of any era.

What would happen?

So th- th- this is my question.

Now, generally, this, yes, this becomes
pub fodder and lots of people discuss,

and generally they say, "You can't
compare players of different eras."

But of course we can.

And we can do these models,
we can do these estimates,

we can do these comparisons.

So I am, I'm gonna touch on a paper that,
uh, I wrote with Shane Reese and Pat

Larkey, and it came out in the American
Statistical Association in JASA in 1999.

It was selected as the Applications and
Case Studies paper award, so it was-- it

had its own presentation at JSM in, must
have been 2000, uh, when that came out.

Uh, when, when that discussion
came out where we did exactly that.

Now, how can we compare?

Now, I wanna go back, and I'm gonna
give you results from that paper.

Now, that was conducted in 1997, so we
did the analyses and the data in 1997.

It would be so much more fun 30
years later to update a lot of

these, and we have plans to do
this, but, uh, ha- haven't done...

Some have, and I'll
make reference to those.

Uh, Shane Reese has done
some updates of that.

In 1997...

Now, now, th- how can we
compare those players?

So I'm gonna make reference to Mark
McGwire, and Mark McGwire had set a home

run record at that time that crushed
Babe Ruth, and he hit 70 home runs,

where Babe Ruth had the re- had, uh,
once had the record at 60 home runs.

And people, that's not comparable.

Babe Ruth hitting 60 home runs, I think
it was 1924, to Mark McGwire in 1996

hitting 70, you can't compare them.

But Babe Ruth played with players
like Jimmie Foxx, and they

overlapped at different times.

Jimmie Foxx was a home run hitter,
and Jimmie Foxx played with, I

think he actually even managed Ted
Williams, who had a long career.

And so Babe Ruth and Ted Williams never
played at the same time, but Jimmie Foxx

played with both of them, and so he's a
bridge from Babe Ruth to Ted Williams.

Now, Ted Williams had somewhat of
a long career, played, um, uh...

It was incredibly good when he was older.

He overlapped with Hank Aaron, and Hank
Aaron had an incredibly long career,

so they played at the same time.

And again, Hank Aaron never
played with Babe Ruth.

Uh, Hank Aaron was Black, and Babe
Ruth played at a time when Blacks

were not in the Major Leagues.

But there was an overlap of Jimmie Foxx to
Ted Williams to Hank Aaron, and then Hank

Aaron overlapped with Reggie Jackson, Mr.

October, who did overlap
with Mark McGwire.

There is a bridge of players from
Babe Ruth to Mark McGwire, and it's

not just that bridge of four players.

There were thousands of players
that overlapped from Babe Ruth all

the way through to Mark McGwire.

This is not a broken, uh,
a broken s- uh, graph here.

There's complete overlap or
bridging from player to player.

So we fit a model, and you can think
of all of these are linear models.

Now, we did three sports, and those
sports were baseball, where we modeled

home runs, home run percentage.

That's a, a good outcome in baseball
where you hit the ball over the fence,

and you have a certain number of, of
attempts and successes, binary data.

Also, a common thing in baseball is how
many successful hits you get, not just

home runs, and that's batting average.

And again, that's, uh, a binary
outcome of, of success and

failure, so your proportion of
those is your batting average.

We did batting average, home run average.

We did NHL scoring, so-- and
that's a Poisson distribution

within a game of points.

And we have the data, and
I'll say a little bit more

about the data in a minute.

And so when we set up this
linear model, it's just a, a log

linear model in the Poisson rate.

And it's a, uh, logistic regression model
for baseball and in the, the log odds.

And we did golf.

And golf is...

I'm gonna come back to golf.

Golf is the most pure of these.

Golf, we can do this incredibly
well, and I'll come back to some of

the issues in baseball and hockey.

Uh, partly it's that the score--
the, the things we're looking at are

not the full measure of a player,
which, which i-is a bit different.

Uh, but golf, there's only one goal in
golf, and that's to shoot a low score.

And we have the scores of golfers
over time from the nineteen

twenties through now, and we have an
incredible amount of overlap in those.

So think of a linear model
that's modeling the player.

It's modeling the year.

And that year, embedded in the year is
the equipment and the rules and the,

the dynamic of the game at that time.

But we're estimating what that is.

That's an important part, is we
estimate the effect of time, and we

can do it because of this overlap.

So the player and the time, and you
have this giant linear model across it.

Now, the, the-- And you're sitting
there saying, "Aha," but the, the,

the issue you have is players' age
And in that we have to model age.

So it's player, it's year, it's age, and
in each sport it's a little bit different.

For example, in golf, we model every
round in golf because weather, course

difficulty, all of that, we can
estimate that incredibly well, and

that's kind of embedded within time.

So each one of these has a, a, some
different factors to them that are

relatively straightforward covariates.

But age is critical in this whole
aspect of modeling different

players over time in sport.

We modeled that there was a region
in the middle of your career where

that's what we're trying to estimate.

And for example, in, in home run hitting,
by the way, the optimal year for home

run hitting is twenty-nine years old.

For batting average, it's twenty-seven.

So there's an, a, a region around
that, and then we model age.

How do players age in a, a
specific young and a specific

old parameter for each player?

So we model even that some
players age differently in that.

Tiger Woods in golf has aged differently
than, say, a Ben Hogan or a Jack

Nicklaus in that, and he's aged poorly
actually for, for well-known reasons.

He- mostly health reasons.

So we can model the age of those players,
and when I talk about estimating their

skill, I'm gonna talk about during
that time of, of optimal performance.

Now, there are a few players
that are a little weird.

Barry Bonds, for example, hit
a large number of home runs

when he was a little bit older.

What it essentially sa- uh, estimates
is that he aged incredibly well from,

fro- over this time period, uh, in it.

Now, we also model, important part 'cause
I'm gonna come back to the populations.

How good were players in the
'20s, '30s, '40s, is we have a

random effects model for players
from the era in which they come.

We actually did ten-year chunks in that.

I would do it differently now,
thirty years later, hopefully.

Uh, hopefully as a statistician, I've aged
better, and I would model this better now.

Uh, within it, I would model it
really as this sort of, uh, uh, moving

normal dynamic linear model where
there we did ten-year chunks in it.

So a player comes from the
era in which they were born.

Now, I do wanna say one more
thing about the data availability.

When we were doing this in the late '90s,
nowhere near the data availability now.

And, um, my, my wife, my, my wife
Tammy will remember, we bought a

book called Total Hockey And we
sat in a room where she read me

the stats of NHL players over time.

We drew a line and said you had
to play a certain number of games.

So she went page by page, she read me
the stats and their birth date, and I

typed them in, and we must have spent
a month, multiple hours doing this.

Pat Larkey was able to get
it-- the, the data on golf.

We ended up using only majors for golf
because we just didn't have the data.

Now you can go online, and I think
you could, you could ask one of

these large language models to get
you this data and the birth date,

and you have it in a, a minute.

You'd have phenomenal data.

In baseball as well, there's
incredible resources for base-baseball.

Uh, I...

There were good data for baseball
at the time, uh, wi-with ages.

Hockey and golf was much more challenging.

So the data availability, we,
we didn't necessarily have it.

We didn't actually...

We couldn't find every golfer and,
uh, in that, but much better data now.

Okay.

So just some results.

And interestingly, at the...

Remember we did this in the late
nineties, and the best home run

hitter, if you could pull everybody
out at their elite, was Mark McGwire.

It said Mark McGwire is the best home
run hitter of all time, at that time.

Tony Gwynn was the best batting
average of all time, at that time.

The best NHL scorer, rather
surprisingly, was Mario Lemieux.

It was not Wayne Gretzky,
and I was shocked by that.

And now I won't go in...

I, I don't wanna spend too much
detail on that, but largely, Wayne

Gretzky played in an era where there
was significantly more scoring.

Now, he contributed to that.

Uh, and Mario Lemieux, they did overlap in
time within that, and Mario Lemieux, much

of his career was a time where scoring
was, was significantly lower, and yet

he still posted, uh, crazy good numbers.

And the best golfer of all
time was Jack Nicklaus.

Interestingly, that was nineteen
ninety-seven, and in the dataset

was this youngster, Tiger Woods.

He was in the dataset, and he
had won the nineteen ninety-seven

Masters, famously going away, and
he was very young at the time.

I don't know, twenty,
twenty-one years old maybe.

And, um, and so that was really
the only data in there, and the

random effects model shrunk him,
and he was number twenty on there.

Shane Reese says, "Rerun this,"
and says Tiger Woods comes

out as the best of all time.

And, uh, I believe that And it, it's
a similar thing to the Jesse Owens

thing, the Johnny Weissmuller thing,
for, for all of these, and I'll come

back to the population part of it.

Now, you can go in and look at the
paper a- and look at these estimates.

It also gives estimates of their
career profile, and there's some

certainly some interesting career
profiles where some players, uh, aged

much better, some aged worse, but
this is a- at, at their peak time.

And but I'm really interested in
how performance changed over time.

So I mentioned hockey and baseball are
a little bit challenging, so when we

look at how the population performs
for home runs over time, it's a bit

odd because there are some players in
baseball who don't want to hit home runs.

Ozzie Smith famously was an
incredible defensive player,

and he's in the Hall of Fame.

He didn't hit home runs.

You know, he might hit one
or two a year accidentally.

And so if you look at populations,
how they behave over time, it's a bit

misleading 'cause he's in there, and
he's a quite poor home run hitter.

So you don't wanna compare him
to somebody at the other time.

So hockey also, there are players in
there who are not trying to score goals.

Their, their job is not to score goals.

They, they're, they...

It's to or, or to assist on goals.

It is to, uh, play defense.

And so hockey is a little
bit awkward as well.

Now, the same pattern holds in both
those sports despite this, is that

we can look at the estimate of every
player in this data set if they

were to all play in the same season.

That's the beauty of this time machine,
is you can subtract time effects, and

you can subtract age effects and say,
you take at their peak, and they play

at the same time, who's the best?

That was the question I
always was after here in that.

So I wanna focus especially on
golf because measuring golf is...

There's only one goal in
golf, to shoot a low number.

So there is not this players, you
know, are really good putters,

but they shoot high numbers, but
they're trying to be good putters.

Uh, if you, if you did a scramble
or something, it might be there,

but golf is a pure thing at this.

You see this incredible change when
you look at the year they were born

and their estimate of if they played
all at the same time, you see this

incredible downward Uh, to good scores.

Downward progression of players over
time in, in, in two ways you see,

and we plot the median, the 90th
percentile, and the 10th percentile.

They all come down sharply
from 1920 through...

At this time it was sort of 19,
yeah, you know, 65 through 1970

were the years they were born by
the time we did this analysis.

There's a sharp decline.

The ni- the 90th percentile,
which is on the bad end of

golf, decreases dramatically.

So somebody born in 1930, they're...

The, the 90th percentile was about 76
on this fictional, uh, same golf course.

That 90th percentile for those
born in the mid-1960s comes

down to about 73 and a half.

Two shots difference,
which is enormous in golf.

The median comes down, and that's
about a shot plus different,

which is also enormous.

The 10th percentile goes down
with a slightly less slope.

So you see this huge shrinking of players
down to the better ones reflective of

there are many, many more players that
could be on the PGA Tour and could play

in these majors that weren't there in
the 1930s, and it's reflective of this

population all getting down to this.

Now, some of the elite players at
those times, as we talked about this

extreme value theory, were there.

And the Ben Hogans and the Sam
Sneads, they were great players.

Now, the median player at the time
isn't nearly as good as the median

player later within that, and this
analysis is reflective of that.

It says exactly that w- in
this, in this time machine that

we're able to look at this.

An interesting thing about golf
is my brother's in this data set.

So, uh, my brother was born 1961, I think.

Um, and he, um, he played
in, uh, six majors, I think.

He played in the 1991 US Open
and he played in several PGAs.

He's a professional golfer, and
he was never on the PGA Tour.

He went to Q-school, was a very,
very good player at the time, but

wasn't good enough to be on the PGA
Tour, but was good enough to qualify

for majors and played in majors.

Interestingly, if you'd have taken
him and moved him back 30 or 40

years, he would have been better than
the median player at those times.

So it's, I, you know, it's, it's this time
machine aspect, and we can measure this

incredibly well in golf And by the way,
golf is a sport that if we updated this,

I think you'd even see drastically in the
last, from the time we did this, in the

last 30 years, because so many players
now have access to play golf and to be

in this data set and to be in the elite.

And golf has exploded.

Part of it is money.

The money availability, the
training, and all of that.

Yeah, I know that, uh, uh...

You know, I hit the ball farther now
than I did when I was younger because

of the equipment, but this is taking
the equipment out of it because the,

the round and the time pulls that out.

Okay.

So the population part of
that, uh, comes out of that.

Interestingly, when these results
came out, it got quite a bit of

press and people interested in that,
and I, I wanna reflect on this.

The LPGA Tour actually contacted
me, and they were interested.

I didn't run women's golf, and I
felt bad all of a sudden when they

contacted me, but they, they've
always tried to figure out automatic

qualifications for the Hall of Fame.

And they were interested in whether
a model like that could do that

for the Hall of Fame, and it comes
back to what I mentioned on this.

This is not about Hall of Fame.

It could say, for example, that all the
women that played in the 1960s couldn't

even play on the LB- PGA Tour right now.

Doesn't mean they shouldn't
be in the Hall of Fame.

The Hall of Fame should measure relative
to your peers, how did you perform?

What did you accomplish in golf?

Otherwise, we have to throw
everybody out of the Hall of Fame,

and it's only recent players.

If it's purely objectively, how
would that player have done?

Now, the best of the best are
much more comparable within that.

By the way, Babe Ruth came out as the
third-best home run hitter at that time.

I think if you move that forward now,
he probably drops into the teens or

the 20s, that the world of, of home
runs has changed dramatically in that.

Uh, but Jack Nicklaus is comparable.

You could take Jack Nicklaus of 1965
and move him now and playing, and

he would be one of the best players.

Canada, of course, cared about hockey
and actually did a, a, a call-in show,

uh, from a show in Winnipeg, and the...

A call in...

They, they did.

They, they, they allowed listeners
to call in and ask questions of me.

And, and interestingly, they weren't all
that worried about the Lemieux-Gretzky

thing because they're both Canadian, and
had one of them been a, a US, I think

that, that they would've been upset
about that, but they were both Canadian.

But the, the caller said, "What
does a Texan know about hockey?"

And I said, "By the way,
I grew up in Minneapolis."

I actually grew up playing
hockey, um, in, in that.

I grew up in Minneapolis
and immediately, "Oh, okay.

That's okay then."

It was so-- So it was sort of
didn't matter my statistical chops.

It's where do I know
something about hockey?

And, and then another caller came
in and said, "Yeah, but your model

can't measure heart, the heart of
these players that played back then."

Um, of course, my comment was,
"Well, they should have scored more.

They should have used heart to
score more, uh, within that."

But hockey again is, is much more
complicated to model because,

uh, of the differing goals.

The UK cared about the golf and the US
cared about home runs, mostly home runs.

They didn't care so much
about batting average.

All right.

So this has now been some 30 plus minutes.

I haven't said a thing about clinical
trials, and I did this work before

I ever worked on a clinical trial.

This was-- I was on faculty at
Texas A&M, and I did this work

and, um, I was fascinated by this.

I was fascinated by the dynamics
of populations in sports.

Still am fascinated by this.

And then I went into
designing clinical trials.

In 2000, we started Berry Consultants
and started working on this, and soon

after, uh, the following issue came up.

We were involved, and Don Berry was
the, the co-PI of the I-SPY 2 trial.

It was a trial in, in neoadjuvant
breast cancer where multiple arms would

go into the trial at the same time.

There's a control arm in the trial,
and then arms A, B, and C come in, and

it's a phase II trial, so they had as
many as 120 patients, and they could

adaptively stop this before that.

And then that arm leaves the
trial, but new arms come in.

But there was a constant control over
time, and then there are multiple arms.

And it ended up, I believe,
27 or 28 different arms came

in this trial over time.

And at one point, they
had to change the control

because there was-- there were
new treatments for that subgroup,

that subtype of breast cancer.

They're stratified by H- HER2 status
and hormone receptor status, so it

had a basket aspect to the trial.

But within one of these baskets,
there was a new control arm.

The beauty of that was that control
was actually in the trial as an

e-experimental arm before that, and
we w- we're gonna use that as a new

control, but we're also interested in
the new arms compared to the old control.

So now we've got arm 21 in the trial and
we're trying to compare it to an arm that

was earlier, and they never overlapped.

They didn't play in the
trial in the same era.

And the question was, how do we do
these analyses for this new arm because

we want to make that comparison, and
we want to make a comparison to the

new control, which by the way, was in
earlier and then came in later, and

it had a gap in time between that.

This is exactly the same problem.

So platform trials have exactly the
same thing, where we're trying to

make comparisons, direct comparisons.

We don't wanna look at the raw data of
what an arm did early in this trial to

an-- what an arm did late in the trial.

It's the Babe Ruth, Mark McGwire problem.

It's different eras, but you
don't just throw your arms up

and say, "We can't do that."

We can do that incredibly well.

So we instituted the same model that
was in that bridging eras of different

sports into the I-SPY 2 trial.

We institute this model in many,
many platform trials because it's

exactly this scenario in a-- this
new thing called a platform trial

as it is in that sports application.

And we can pull two arms out, and
we can make that direct comparison

between those two arms by bridging.

Now, what you want is
to have this overlap.

So arm three and arm fifteen weren't
in at the same time, but arm three

overlapped with four, um, overlapped
with eight, overlapped with eleven,

that overlapped with fifteen, and
the other arms in there overlap.

We can estimate time and what time
does in the trial, the same thing

we-- as we can estimate in sports.

Now, we, we, we have a, a paper
that talks about the Bayesian time

machine, and it does e-exactly this.

Saville, Berry, Berry, Veli and Berry.

So you can look that up if
that's of interest in there.

But this exact same modeling.

Now, let's go back for a second
and think about what this means.

Let's go back to the sports.

Where does this model maybe break down?

So if things are these additive effects
of players, the model's perfect.

So in sports, if there's an
interaction, that's when it breaks down.

Now, what is an
interaction in sports mean?

So if we're comparing Jack Nicklaus
and his rounds in the 1960's to Scottie

Scheffler's rounds in the twenty, uh, 2026

the equipment's very, very
different, no question about it.

Golf balls are very, very different.

But we're not, we're not saying
Jack has to bring his equipment.

He could play with today's equipment
when he was nine-- in 1965.

But suppose the new sand wedges
and the new balls they have,

that Jack just can't utilize them
the way Scottie Scheffler can.

And-- But yet you didn't have sand
wedges of the same, uh, incredible...

That's one thing that's actually
changed over time with a golf ball.

That there's this interaction
between them, and, um, moving Scottie

Scheffler back would have not just
an additive effect, but would have

an interaction because he couldn't
play with the wedges of the time.

Now, I think these are strikingly
rare i-in, in in sports that these

interactions-- There may be a little bit
to a dynamic sport like hockey, where a

player in the 1940s was much smaller, and
it may be harder to kind of do the same

things they did where players are larger.

But mostly, you gotta work
really, really hard to figure

out interactions in those sports.

And I know you can come up with them,
but, uh, I, I want you to think really

hard about whether it, it, it's reality.

Now, in clinical trials,
it's the exact same thing.

That's the potential challenge here.

Is when we do this adjustment,
are there interactions?

I would say that they're actually
less likely in clinical trials

than they were in sports.

By the way, interestingly, the, the
beautiful thing about clinical trials

is we don't have the age effect.

You don't have to model how
players age in this bridging

part of it in clinical trials.

Drugs don't age within that.

Now, what might an interaction be?

And the, the prime candidate for where
there might be interactions are probably

infectious disease, where an old trial
had a result relative to placebo,

and now the disease is different.

So the current trial, maybe that
treatment wouldn't be as good Even

those I think are, are unlikely.

COVID was the one prime example
because the disease morphed so

quickly and changed so much.

Now, most of the hospitalized trials we
did in COVID, it's about the host, and

the host is sick, and it's not really
about the, the, the viral-- virus anymore.

But even in that case, it's not
clear that there are interactions.

And by the way, if we think there are
interactions where treatment was in a

trial before an overlap placebo, and
now we have this overlap of arms, and

we think that the relative differences
of the arms could switch, we can't

do non-inferiority trials anymore.

And actually, when a trial's over, I'm--
I don't even know if we can think does the

drug work because right now it might have
switched with placebo, uh, within that,

and do we know if the treatment works?

So if you're looking at...

And, and what's really interesting, we can
test this because of an arm's length of

its career in a trial and the different
arms, we can look to see whether it

looks like it varies relative to control.

In I-SPY 2, if you took the same
treatment in there at different

times, it was incredibly stable.

Neoadjuvant breast cancer, whether
this is ALS, whether this is, um, a

cardiovascular disease, weight loss,
this is, um, uh, many other diseases,

it's really hard to think about
interactions within those trials.

But that would be the same way in
which in a platform trial you would

be concerned about using this model to
compare treatments that are in the trial

at different times and different eras.

Okay.

Well,

uh, by the way, if you're, if you're
interested in this, you can jump

to episodes twenty and twenty-one,
talk about I-SPY 2 with, with Don.

Um, a incredible story in and
of itself, but part of that

talks about the time machine.

And then episode twenty-two talks
about the time machine much more

from a statistical standpoint
with, uh, co-host Kurt Vile.

So those may be of interest to you.

So coming back to the original
lead-in to this, uh, Cooper's

team against the 1927 Yankees.

By the way, we don't have the
data to make that bridging because

we don't have Division III teams
playing pro teams and even Division

I teams playing pro teams in that.

Uh, though, though my son's team
did scrimmage, uh, this year a, um,

a rookie league professional team.

Um, in college hockey I think
it's clear a college hockey team

now would beat a 1920s NHL team.

E- And yes, they would use the same
equipment, so the, that NHL team could

get a little bit of time to practice
and use the equipment and all of that.

So it, it, you know, seamlessly that,
I, I think a college hockey team now

would beat a team back then for sure.

I think an NCAA Division I baseball
team now beats the 1927 Yankees.

I think it, it's just the world has moved
on, the, the speed of these pitchers.

I don't know if any 1927
Yankees threw 90 miles an hour.

I don't think they did.

I think a D1 team would, would
beat up the 1927 Yankees.

And in golf, it's absolutely clear.

NCAA golfers now are better
than the, the, the 1920s.

I, I know there's Bobby Jones
and other players like that, but

they would, I think they would,
quote-unquote, "beat up" on 1927 golfers.

So where does that leave Division III
baseball team now against the '27 Yankees?

I don't know the answer to that.

I think it would actually
be a really good game.

And maybe Babe Ruth calls his
shot and hits the winning home

run, uh, in a game like that.

But I actually think it would
be a reasonable competition.

All right.

Well, um, this is coming to you
through a time machine, by the way.

It's recorded, and through time
you got to hear this through a time

machine about The Time Machine.

And next time, the next episode may be
better because of, of, uh, era effects.

But until the next time,
we'll be here in the interim