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

So, one more example of a props bet from the 2014 Super Bowl.

You could bet on what the first type of score would be.

A touchdown, field goal, or a safety, and

basically you could bet on it, based on the team.

So, Seattle, you could get 5 to 1 odds that the first score would be a Seattle

rushing touchdown.

5 to 1, a Seattle passing touchdown, etc.

Okay, Seattle, and I guess it didn't pay off if there was a pick six, or

something like that.

Seattle field goal 7 to 2, Denver field goal 7 to 2, and safety by Seattle or

Denver 40 to 1.

And you probably remember the first score was a Denver, or

I guess it was a Seattle safety because Seattle scored the safety.

It doesn't really matter for our purposes here, okay.

So, the probability of winning based on these odds would be one-sixth,

one-sixth, one-eighth, one-quarter, etc.

These add up to 120%.

So, if you want to normalize them to get an adjusted probability,

you basically take each one of these and divide by the sum.

So instead of the bookie's implied probability, it's a rushing touchdown and

Seattle was the first score, you would say it, it was 16%, you say it's 14%.

Okay.

Now let's look at the NFL and see what fraction of scorers were touch downs,

field goals, and

safeties because the first score shouldn't be any different than the other score.

And courtesy of profootballreference.com, again a great site we've used many

times in the course, we found out during the season, the 2013 regular season,

There were 1,338 touchdowns,

I guess I'm counting all the touchdowns including the ones on the pick sixes.

Eight returned touchdowns.

863 field goals and 20 safeties.

Okay.

So what percent of the scores were touchdowns?

60%, 39%, and 1% for safeties.

Now, from the odds, what implied adjusted odds?

What's the chance of a touchdown?

Well you add up these four here, you get about 59%.

And it being a little bit more makes sense,

because they were some non-rushing passing touchdowns.

Now field goals you get 37% here.

Okay.

And the actual percentage of scores that were field goals were 39%.

Very, very close.

But now look at safeties and we'll explain why the difference here.

The odds that they give you would imply a probability of 4% of the scores

being safeties, but only 1% are safeties.

So, Vegas is giving you really crummy odds on a safety.

Okay? They're giving you 40 to 1,

which implies really there should be a 4% chance that the first score is a safety to

make that fair.

There's only a 1% chance that the first score's a safety.

So why do they do that?

because when you give somebody 40 to 1 they love to take that bet.

I mean people based on their utility towards money,

which we'll talk about a little bit when we talk about Kelly growth.

Basically people like to buy lottery tickets or

take this is essentially a lottery ticket, and it turned out it paid off because

the first score was a Seattle safety in that game.

So actuarially they should give you much higher than 40 to 1 there,

maybe 60 to 1, 70 to 1, 60 to 1.

Okay, the chance would be roughly the right odds to give you on a safety,

because then the chance would be 1 over 61.

Oh, more than that.

Okay. It should be like 200 to 1,

because then the chance is 1 divided by 201.

And if you double that.

You would get about the probability in safety.

So they should give you like at least 150 or 200 to 1,

to make that safety a fair bet, but they only have to give you 40 to 1 for

people to take it, because people love to bet on long shots.

Okay, in the next video we'll talk about something that's really important in

finance as well as sports, Kelly growth criteria.

Which basically, if you are a really good sports better,

we'll tell you how to manage your money.

You should never bet 100% of your bankroll on a bet, because if you do,

even if it's a 90% change of winning the bet, if you lose you're bankrupt.

So Kelly growth is used by a lot of successful hedge funds and we'll learn how

you can apply that to sports betting in the next video or maybe two videos.