NOVA

The future unfolds before our eyes...

but is it always beyond our grasp?

What was once the province of the gods

has now come more clearly into view

through mathematics and data.

Out of some early observations about gambling

arose tools that guide

our scientific understanding of the world

and more...

through the power of prediction.

From our decisions about the weather...

The strongest hurricane ever on record...

To finding someone lost at sea...

Commencing search pattern.

Keep a good look out!

Every day mathematics and data combine

to help us envision what might be...

It's the best crystal ball that humankind can have.

Take a trip on the wings of probability

into the future.

We're thinking about luck

or misfortune,

but they just basically are a question of math, right?

"Prediction by the Numbers"...

Right now, on "NOVA."

Major funding for "NOVA is provided by the following:"

The Orange County Fair, held in Southern California.

In theory, these crowds hold a predictive power

that can have startling accuracy,

but it doesn't belong to any individual, only the group.

And even then, it has to be viewed

through the lens of mathematics.

The theory is known as the "wisdom of crowds,"

a phenomenon first documented about a hundred years ago.

Statistician Talithia Williams is here

to see if the theory checks out, and to spend some time

with the fair's most beloved animal,

Patches, a 14-year-old ox.

It was a fair kind of like this one

where, in 1906,

Sir Francis Galton came across a contest

where you had to guess the weight of an ox,

like Patches you see here behind me.

After the ox weight-guessing contest was over,

Galton took all the entries home and analyzed them statistically.

To his surprise,

while none of the individual guesses were correct,

the average of all the guesses

was off by less than one percent.

That's the wisdom of crowds.

But is it still true?

So, here's how I think we can test that today.

What if we ask a random sample of people here at the fair

if they can guess how many jelly beans they think are in the jar.

And then, we take those numbers and average them

and see if that's actually close

to the true number of jelly beans.

Guess how many jelly beans are in here.

Come on, guys, everybody's got to have their guess.

I see your mind churning.

1,227.

846.

Probably like 925?

I think a thousand.

So just write your number down.

Uh huh, there you go.

Can I have a jelly bean?

The 135 guesses gathered from the crowd vary wildly.

The range of our guesses was,

from the smallest was 183, the largest was 12,000.

So you can tell, folks were really guessing.

But when we take the average of our guesses, we get 1,522.

So the question is,

how close is our average to the actual number of jelly beans?

Well, now's the moment of truth.

All right, so the real number of jelly beans was 1,676.

The average of our guesses was off by less than ten percent.

So there actually was some wisdom in our crowd.

Though off by about ten percent,

the average of the crowd's estimates

was still more accurate

than the vast majority of the individual guesses.

Even so, the wisdom of crowds does have limits.

It can be easily undermined by outside influences

and tends to work best on questions with clear answers,

like a number.

The steps Talithia took

reflect a process going on all around us these days

in the work of statisticians.

Thanks, everybody.

So we collected this data,

right, we analyzed it mathematically,

and we got an estimate that was pretty close

to the actual true value.

That's math and statistics at work.

We didn't always use math and statistics to make predictions.

The Romans studied the flights and cries of birds.

The Chinese cracked "oracle" bones with a hot metal rod

and read the results

19th-century Russians used chickens.

Throughout history, we've sought the future

in moles on people's faces,

clouds in the sky,

or a pearl cast into an iron pot.

And that list of things used for predicting goes on and on.

But more recently... that is the last couple hundred years...

To see into the future, we've turned to science

and made some remarkable predictions

from the existence of Neptune,

or radio waves,

or black holes,

to the future location of a comet with such precision

we could land a space probe on it.

But if you pop the hood of science,

inside you'll find a field of applied mathematics

that's made many of those predictions possible:

statistics.

Statistics is kind of unique.

It's not an empirical science itself, but it's not pure math,

but it's not philosophy either.

It's the framework, the language,

the rules by which we do science.

From that, we can make decisions,

we can make conclusions, we can make predictions.

That's what... that's what statisticians try to do.

Why I love statistics is that

it predicts the likelihood of future occurrences,

which really means it's the best crystal ball

that humankind can have.

Ultimately, all the predictive power of statistics

rests on a revolutionary insight from about 500 years ago...

That chance itself can be tamed

through the mathematics of probability.

Viva Las Vegas!

Here's a city full of palaces

built on understanding probability

and fueled by gambling,

which may seem a funny place

to find mathematician Keith Devlin.

But mathematics and gambling

have been tied together for centuries.

Today in a casino, you'll find roulette,

slot machines,

blackjack.

Playing craps is also known as "rolling the bones,"

which is more accurate than you might think.

Humans have been gambling

since the beginnings of modern civilization.

The ancient Greeks, the ancient Egyptians,

would use the ankle bones of sheep as a form of early dice.

Surprisingly, while the Greeks laid the foundation

for our mathematics, they didn't spend any effort

trying to analyze games of chance.

It seems to have never occurred to them,

or indeed to anybody way up until the 15th, 16th century,

that you could apply mathematics

to calculate the way these games would come out.

16th-century Italian mathematician Gerolamo Cardano

made a key early observation:

that the more times a game of chance is played,

the better mathematical probability

predicts the outcome,

later proven as the law of large numbers.

Examples of the law of large numbers at work surround us.

When I flip this coin,

we have no way of knowing

whether it's going to come up heads or tails.

That time it was heads.

On the other hand, if I were to toss a coin 100 times,

roughly 50% of the time it would come up heads,

and 50% of the time it would come up tails.

We can't predict a single toss.

We can predict the aggregate behavior over a 100 tosses.

That's the law of large numbers.

In fact, casinos are a testament

to the iron hand of the law of large numbers.

The games are designed

to give the casinos a slight edge over the gambler.

Take American roulette:

on the wheel are the numbers one through 36,

half red and half black.

Betting a dollar on one color or the other

seems like a 50-50 proposition.

But the wheel also has two green slots with zeros.

If the ball lands in those,

the casino wins all the bets on either red or black.

And that's the kind of edge

that makes the casino money over the long run.

Customers are gambling.

The casino is absolutely not gambling.

Because they may lose money,

they may lose a lot of money to one or two players,

but if you have thousands and thousands of players,

by the law of large numbers,

you are guaranteed to make money.

The law of large numbers

comes into play outside of gambling too.

In basketball, a field goal or shooting percentage

is the number of baskets made

divided by the number of shots taken.