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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來自 University of Houston System 的課程

Math behind Moneyball

39 個評分

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.

從本節課中

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.

- Professor Wayne WinstonVisiting Professor

Bauer College of Business

Okay, let's apply the Kelly Growth criteria to NFL points [INAUDIBLE] so

let's suppose you're really good against the points.

So you can pick 60% against the point spread,

and a winning bet wins 11,

$10, losing bet loses $11.

Okay, and so what fraction of your bank roll should you bet on each bet?

What fraction of your bankroll

should you bet on each game if this is the case?

So we'll use Kelly Growth here so we can pick the fraction.

Let's start with 10%.

Okay. Now basically, okay,

so if you win what would you end up with?

And if you lose, what would you end up with?

And the probability of winning again we've given you is 0.6.

Losing is 0.4 Okay, so if you win okay,

let's figure what you'd end up with.

And then we can take the log utility over here.

With the log of the return, okay.

And we take the expected log utility.

0.6 times times the log rhythm, the log of the return.

Okay, so if you win basically you would take this fraction,

okay, and basically, you just add that,

suppose you start with a so you'd have let's say, let's suppose you win,

you win a dollar, you lose, you lose a dollar too.

Okay.

So you've bet ten cents out of a dollar, you would win ten cents if you win.

Okay, sorry, it should be D8 plus one.

And if you lose you would have your dollar and you would lose 1.1 times what you bet.

Okay so you would have 89 cents.

Okay, because you lose the 11 cents.

So, the log of where you'd end up would be the log of this.

You can copy that there.

And so, if you would bet 10%.

So, the expected lock return, this is what you want to maximize.

We could do some product, we'll take

0.6 times this log plus one minus,

well plus 0.4 times this log.

We want to maximize this.

So you want to choose the yellow to maximize the right.

Okay, and it's going to turn out about 14%.

You see, if we put this at 14%, I think that number goes up a little bit.

Let's start with the point.

So we go data, solver,

maximize the expected log return.

Change the fraction a bit, and I think it will work without saying it's between zero

and, well, let's just make sure, we'll say the fraction bet's between 0.01 and 0.09.

You don't really need this, but

I worry sometimes I'll get a negative number if I let lots go negative.

Or the changing negative.

So it should be able to get this to.

And the answer is 14.5%.

Bet 14.5% of bankroll on each bet.

And your growth rate per bet is e to this power.

So your capital would grow at about, well subtract one.

Your capital would grow about 1% per bet.

So in other words, after 100 bets on the average, where would you be?

You'd be one plus this to the 100th power.

Okay, you would've tripled after 100 bets if you do this.

You should on the average have tripled your money, okay, which isn't bad.

Of course, you might not triple your money.

And of course, the hard thing is picking against the spread.

Again, break even against the spread.

If you have probability p of winning a bet,

p you win $10, plus one minus p you'd lose 11.

And you'd get p equals 11 over 21.

Right here.

So 52.4% is what you need to pick against the point spread to break even.

Okay, so that concludes our discussion of Kelly Growth.

We'll continue a little bit with our discussion of sports betting.

Well I think we'll take a detour and do regression towards the mean which sort

of ties to sports betting if you look at betting on total wins for an NFL team or

an NBA team or a Major League Baseball team, so we'll see you.