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

Let's continue with our study of Vegas props bets involving the Super Bowl.

So in the 2014 Super Bowl, and

that's the 2013 season, Denver's playing Seattle.

They got destroyed as we know.

Biggest outlier in Superbowl history from the point spread, by the way.

And you could bet on how many touchdown passes Peyton Manning would throw.

I think he actually threw two.

But you get 10 to 1 odds he would throw 0 touchdown passes.

Now what does that mean?

If you bet a dollar on Payton Manning throwing 0 touchdown passes, they would

pay you 10 if you won, It'd be through 0 and you would move 1 if you lost.

You could get 3.5 to 1 odds that he'd throw 1 touchdown pass,

2 to 1 odds that he'd throw 2 touchdown passes, 2.5 to 1 odds he'd throw 3.

10.5 to 1 odds he'd throw 4, and

10 to 1 odds he'd throw at least 5 touchdown passes.

Now, if you've got a bet like If you got x to one odds like ten to one,

what is the probability implied by that, that the event will happen?

Well for it to be an actual, real fair bet,

if we let p be the probability of n happens.

Then for this to be a fair bet, with probability p you'd win x dollars,

and with probability 1 minus p you would lose a dollar.

And if you set that equal to 0,

you get p=1/(x+1).

So example, in a 10 to 1 bet it implies a 1/11th chance that that bet happens if

that's the true odds.

because then you see with probably 1/11th you would win $10.

And with probably 10/11ths

you would lose a dollar.

And that checks out.

And so that would be zero on average, okay?

So we can get an implied probability here from Vegas.

In other words, there is a 1/11th implied probability of 0 touchdown passes.

1/4.5, 22% of 1 touchdown pass, etc.

Now when add these off you don't get 1, and

this'll be true with any time Vegas give you odds on a variety of outcomes.

The probabilities from Vegas won't add to one, they'll add to something

bigger than one because Las Vegas doesn't want to give you a fair bet.

So these add probability implied by the Vegas odds add up to 1.11.

To convert them to true probabilities,

you should divide by the sum of those implied probabilities.

So I would take the implied probability, divide it by the sum and

now these will add to one.

Okay so Vegas is basically implying a 20% chance then.

Gets 1 touch-down pass, 30% chance 2 touchdown passes, etc.

Okay, so now if we were setting the probabilities,

what would be a rational way to do this?

Well, let's assume the regular season would be indicative of the playoffs,

which I really need data to say computer prediction for

how many TD passes a guy would through in a regular season game against an opponent.

And then see in the playoffs how much lower that would be.

Because our probabilities, are going to,

the bookies are assigning a higher probability to lower outcomes than I do.

Probably because playoff games tend to have less touchdown passes than regular

season games, and I just didn't have time to study that.

So I can see why Vegas would have a different answer than I do.

Okay but let's look at that season.

Manning threw the record 55 touchdowns.

The average team scored 25 and a half,

had 25.1 touchdown passes and Seattle gave up 16 touchdown passes.

So if I want to do a multiplicative model, what I could say is,

predict how many touchdown passes for Manning.

TDs in the season.

If he played Seattle every game and divide by 16 games.

So if you understood how we did ratings,

you would start with the average, which is 25.1.

And then if you do a multiplicative model,

Manning threw over twice as many touchdown passes as the average team.

And Seattle gave up way less, about 64% of the average number of touchdown passes.

You'd multiply those ratios times the 25.1.

55.1 / 25 *

16 / 25.1.

Okay, and you get that number, you should divide that by 16 games.

And rounding on, I think I rounded off a little but

there didn't use the exact numbers.

See here about 55.

Yeah that should be a 55, that's my problem.

I don't know how I 55.1.

Okay, well I've got the 0.1 in the wrong place.

So that should be right there.

So when I do this formula, it should be 55 / 25.1.

Okay, that's right.

So we would predict by this method on average,

Peyton Manning would throw 2.19 touchdown passes per game against the Seahawks.

If anything I can use the like in the last video and

figure out the probability of zero.

Here is the mean.

Probability of zero copy it down, probability of one, two three,

four or five.

And you can see, I have got a much more probability of zero one touchdown

passes than Vegas has, probably because they probably adjusted for

using the playoff game results and the distance of the regular season results.

And Manning was not doing as well throwing TD passes in the playoffs as he did in

the regular season.

And Seattle was probably doing better at giving them up.

So they must've had some formula for

adjusting the regular season, giving weight to the regular season prediction

with the post-season prediction to get their mean.

And I'm sure they've got the manpower or people power to do that.

But I'm not surprised that my probabilities are different than

theirs for that very reason.

The playoffs, you can see Manning was not throwing touchdown passes at near

that 55 touchdown raid,

even adjusting for the strength of the defenses he played against.

Now you can also do an additive model, I prefer the multiplicative.

Say Peyton Manning, you start with the mean touch down passes for a season and

basically you would take he threw 55- the league mean.

That's an adjustment for Payton Manning's offense and Seattle's defense, 16- 25.1.

And basically if you do, basically that's going to be 55- 9.

It's going to be about 46 / 16, which is a much higher predicted number of

touchdown passes, which even comes out more different than Vegas.

I prefer that multiplicative model.

Well, let's look at one more here.

You could bet on Peyton Manning's yards passing.

And again, I use the regular season to come up with a forecast.

But again, I should look at how things would go in the playoffs for

a team as opposed to the regular season, and probably adjust this downward.

And Vegas gave you, you could bet Peyton Manning's yards passing in that

Super Bowl would be over or under 290.5 yards.

So their best guess, essentially,

was Peyton Manning would throw around 290 yards passing.

Well, the league average yards passing per game that year was 235.6,

Manning got 340.25 per game.

Seattle gave up 172 yards per game.

So I can start.

The added model comes down closer, but if I do the multiplicative model, okay,

it's interesting.

I would get a lower yards passing than Vegas.

I guess they thought he'd be more conservative well, less conservative and

pass more in the Superbowl.

Okay. It turns out that everything was

a disaster from that first snap with the safety,

which we'll talk about in the next video.

But if you take the league average of 235.6 yards multiplied by

Peyton Manning's yards per game divided by the league average.

And then multiply by Seattle's yards per game given up on defense

divided by the league average.

You get a prediction of 248 yards per game for Peyton Manning when the Vegas had 290.

Now if I do the additive model, I start with the league average.

Take Peyton Manning's average yards per game minus the league average plus Seattle

defense's average yards per game minus the league average.

And I get 277.

So, I'm not sure where the 290.5 came from but, again,

just trying to show you one rational way to try and come up with a prediction for

the yards passing by Peyton Manning in that Super Bowl.

Now in the next video, we'll talk about the Super Bowl prospect when

that is always present, you can bet on what the first score of the game will be.

Will it be a touchdown, a field goal, or a safety?

And you'll see something quite interesting there, okay, when we talk about that.