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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来自 University of Houston System 的课程

Math behind Moneyball

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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.

从本节课中

Module 9

You will learn how to rate NASCAR drivers and get an introduction to sports betting concepts such as the Money line, Props Bets, and evaluation of gambling betting systems.

- Professor Wayne WinstonVisiting Professor

Bauer College of Business

In this video we'll talk about how the point spread on a game and the so

called money line help you figure out the chance of a team winning the game.

Okay, so a good site to find the information any day on betting

lines scoresandodds.com.

Okay, I'm taping this video on June 4, 2015,

game one of the NBA finals.

It's going to be tonight, exciting.

And Golden State is definitely favored to win this series.

I'm picking the Cavs, not on math, but I think LeBron will guard Curry,

and shut him down.

So, when you hear this video, you'll know if I was right, or if I was wrong.

I'm not betting on it.

Okay, now I've found the scores and odds only gives the odds the day of the game.

And I was writing this file up the day before the game.

So I guess there's a site called Odd Shark that I got this for.

Okay so the betting line is game one was at the Golden State Warriors,

there a home edge in the NBA about three points.

Cavaliers were +5.5, Warriors -5.5.

So, if the Warriors won by six or more and you bet on the Warriors,

you'd win on the point spread bet.

If they won by five or less, you'd win a bet on the Cavaliers or

lose a bet on the Warriors.

Then there's this thing called the money line, so let's talk about that.

So for game one the Cavaliers are +195, and the Warriors are -235.

Now what that means is, If

you bet $235 on the Warriors to win, the minus is the favor.

You win $100 if they win.

If you bet $100 on Cleveland,

the team with the plus,

the underdog, you get $195.

Okay, so let's try and

figure out the chance of the Warriors winning the game according to Las Vegas.

Well, there is two ways to do this.

We can assume, okay,

the outcome of the game from the Warrior standpoint is normal, or

received to be normal in pro sports certainly for basketball,

with a mean of 5.5 and the standard deviation is about 12.

Okay, so we can figure out the chance the Warriors win the game which would mean

chance the Warriors win.

So the Warriors can win if we sort of want to be precise.

If they win by at least half a point,

because we're assuming fractional values are possible.

Or they win by between -0.5 and

plus 0.5 because that would be overtime, a tie game.

And then win the overtime.

And we'll figure this out using that norm disk function we talked about.

And we'll get about 68% and

we'll see that's exactly consistent with what they have on the money line.

Okay, so how could they win in regulation.

They have to win by more than one and a half points.

And that's just one minus the area to the left by more than half a point.

That's 1- the probability the win by less than half a point.

Okay, so NORM.DIST you have to say 0.5 and

there we'll get the area of the left of 0.5.

The mean is 12, sigma minus 5.5.

The sigma is 12 and we put the word true.

Okay, so the chance the Warriors will win in regulation is 66%.

Now, what's the chance they win in overtime?

The chance they win by between minus 0.5 and

plus 0.5 is the area to the left of 0.5 minus the area to the left of minus 0.5.

And then we have to multiply that by a half.

So we take a half times norm.

Dist, 0.5, mean is 5.5, sigma 12.

That's the chance they'll win by less than 0.5.

Subtract off the chance they'll win by, Less than -0.5.

And I'm multiplying that whole thing by 0.5.

Okay, 0.014, so you add those two together.

And you get that the point spread implies a 68% chance of winning the game.

Now what does the money line imply?

Well let p be the chance the Warriors win the game.

Let's figure out at what values of p, make a bet on the Warriors profitable.

What values of p make a bet on the Cavaliers profitable, and

if you average those, you certainly get an estimate of the chance

of the Warriors winning the game according to the book makers.

And you get basically, exactly the same answer.

And again, why do the bookies make money, if half the money's bet on each side?

Let's suppose that everybody bets ten dollars.

For each $10t, okay remember the way it works is,

a $10, you win $10 if you win.

But you lose 11 if you lose.

And so half the bets go on either side,

the bookies will pocket $11 and pay out 10.

Okay, so now what this p,

the chance of the Warrior having to win the game be to make the game profitable.

So remember, bet on the Warriors you win 100 if they win and lose 235 if they lose.

So what's your expected payout?

With probability p you win 100.

With probability 1 minus p you lose 235.

So as long as this is greater than zero right here,

you would have a profitable bet.

So you solve for p, you get to break even.

It's 235 over 335 or use goal seek if you want and that's 70%,

so the Warriors need at least a 70% chance to win the game for

a bet on the Warriors to be profitable.

Okay, but we know that with the bookies think there's a 68% chance so

will not be a profitable bet in terms of expected value.

Now what about the bet on the Cav?

See these numbers are different than 195 and 235.

Okay, in other words When you bet the Warriors you've gotta bet way,

you have to bet more to win 100.

Then basically you win if the Cavs win.

And that gives the head bookies an edge.

So what is the expected profit on a Cavs bet?

Well if the Warriors lose that's probably 1-p you'll win 195 and

if the Warrior Warriors win you'll lose $100 on that bet.

So you get minus a hundred probably p as long as this is greater than zero

an expected value to bet on the Cavaliers is probable.

And that will happen as long as p is less than 195 over 295 and that's 66%.

So if the chance of winning the game is less than 66%,

a bet on the Cavs is profitable.

Chance is greater than 70%, a bet on the Warriors is profitable.

And if you average those you get 68% which

is basically just what we got when we used the point spread estimate.

So the money line and the points spread are usually consistent.

Now if there's truly a 68% chance that the Warriors win this game,

notice neither money line bet is profitable on average,

because 68% is not greater than 70%, and then 68% is not less than 66%.

So the bookies are very clever, and

must have pretty good mathematical consultants, or the oddsmakers in Vegas.

And I think there are consulting firms in Vegas that helped set the point spread.

Well that's a brief explanation about how the money line and

point spread fit together.

In the next video, I think we'll return to the NFL point spread analysis we did in

the last video, and try and see if betting on home underdogs, who are big underdogs,

eight points or more, Is profitable at a statistically significant level.