10.2 Kelly Growth Part II

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Math behind Moneyball

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University of Houston System

Math behind Moneyball

41 classificações

Learn how probability, math, and statistics can be used to help baseball, football and basketball teams improve, player and lineup selection as well as in game strategy.

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Module 10

You will learn how Kelly Growth can optimize your sports betting, how regression to the mean explains the SI cover jinx and how to optimize a daily fantasy sports lineup. We close with a discussion of golf analytics.

10.2 Kelly Growth Part II5:10

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Professor Wayne Winston
Visiting Professor
Bauer College of Business

A lot of you probably know that phrase, Show Me I'm from Missouri.

Harry Truman, one of my favorite presidents of the 20th century,

was a haberdasher from Missouri.

Should all read Truman by David McCullough,

the great author who wrote the John Adams book and many other books.

But I truly think Truman was a great biography.

Okay, so if you believe in Show Me, I'm From Missouri,

let's show you Kelly Growth really works with simulation.

Okay, so let's have a two way data table.

Okay, going across the row is the percentage or money allocated in Stock 1,

using the example that we just discussed.

So here we'll use .5.

Okay, and then we figure out basically, a random number for Stock 1.

If it's less than .5, Stock 1 doubles.

Otherwise it gets cut in half.

And the same for Stock 2.

So we begin with a dollar.

What happens to our Stock 1 money?

If Stock 1 goes down, okay.

Then basically we would double our money in Stock 1.

Sorry.

At random numbers less than .5, Stock 1 goes up.

We double our money.

Otherwise, we cut it in half.

The same for Stock 2.

So our final cash position would be the fraction in Stock 1, times the initial

capital, because that's what's in Stock 1, times the growth rate for Stock 1.

Plus one minus the fraction in Stock 1, because that's in Stock 2 times basically

the initial capital, that's the amount in Stock 2 times the growth rate for Stock 2.

And that's the final position.

We begin the next year with what we ended the last year with and we'd run this.

I ran it I guess 50 years growth rate,

since you started with a dollar is the 50th root.

Okay.

Okay.

Of your final cash position divided by your initial cash position.

Your initial cash position was one.

I guess I can put that in there.

Then you subtract one.

So here we grew three percent a year, okay.

We ended up with five dollars.

We can also grow negative amount.

It's going to be slow here.

We grew 16%.

So I did a two way data table.

I got 5,000 rows.

These are the iterations.

And then I have the fraction in Stock 1 going across, and

then I make the output cell is that growth rate.

So per period.

So we can average that growth rate for each fraction in Stock 1.

Zero through 90% because 100% in Stock 1 means nothing in Stock 2,

which is equivalent to having nothing in stock.

This is nothing in Stock 1 means everything in Stock 2.

100% in Stock 1 means nothing in Stock 2, okay.

So they're fairly equivalent, so I would do,

we could do this data table again from scratch, so what we could do is,

okay, so the output sale is going to be the growth rate.

And we do control shift, right arrow, control shift, down arrow.

We do data, what if analysis,

data table, a column input cell is any blank cell like it is in all simulations.

The row input cell is the fraction in Stock 1.

That's right there.

We may have to hit F9 to make these change, I guess I gotta hit F9, okay.

So you can see data, it's running there.

So you can see if you have half your money,

you get 12% annual return in stock if you have half your money in Stock 1.

If you put nothing in Stock 1, you basically break even,

I could run this 10,000, 5,000 more times.

And you'll see the same thing, you put all of your money in Stock 1, nothing in

Stock 1, all in Stock 2, you hardly grow at all, but you grow around 12% here.

Let's do it one more time.

So that should convince you there is something to Kelly growth,

here we grew 11.9%, here we grew 0.36%.

So basically we can see by putting half our money Stock 1 and

half our money in Stock 2, we sort of hedge our risk.

We rebalance our portfolio each year, and sort of lets us buy low and

sell high in a sense.

And that's much better than putting all our money in one stock or the other.

And so, this will lead us in the next video to basically applying the Kelly

growth criteria to figure out, if you know your probability of winning a bet,

basically, what fraction of you money should you place on each bet.

And basically, when we talk about family fantasy sports,

if you think you know the chance of your lineup winning, you could apply Kelly

growth to family fantasy sports games like Skill zone, Draft Kings or Phantom.

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