### Sports Betting in America Part II

If you haven't already, you should look over Part I. It will be trivial for some of you, but the concepts there are crucial.

How Often do we need to win to break even?

First off, I'll answer the question about why you need to win 51.2% of the time to break even when laying -105 on a bet. To do this, we need to calculate the EV of that bet, assuming the probability we will win is p. Since we win p percent of the time, we will lose (1-p) percent of the time. When we win, we win 100 and when we lose, we lose 105 (or some multiple of those numbers, depending on the size of our bets). Therefore, the EV of the bet can be given by the expression:

100p - 105(1-p)

To figure out the break even point, we set the expression equal to zero and solve for p to get p=105/205 ~= 51.2%

You can do this no matter what the odds are. Suppose you make a bet at +150, your EV is

150p -100(1-p)

So p = 100/250 = 40%

Standard Sportsbook Lines

Last time I mentioned a bet where the lines on both sides where -105. It used to be the case that the standard was -110. It was very rare that you'd find lines better than that, but common to find lines worse.

Today, the standard for most online sportsbooks is still -110, but it is common to find sites that offer better lines. Pinnacle, for instance, offers 4 cent lines (-104) on all of their straight baseball wagers. This is both a good and a bad thing for bettors.

The good (obviously) is that the juice is lower, so you can win a smaller percentage of your bets and still win. Furthermore, winning the same percentage of bets with a 4 cent line will net you more money that it would making the same bets with dime lines.

The bad is that Pinnacle is known for having the sharpest handicappers in the game. It's rare that you'll find a line there that's ever way off. With computer technology it is easier for handicappers to do their work. They can plug in all the variables to a machine and let it go to work. Then, they can adjust the lines by hand as they see fit. Also, with internet betting, they're able to take a lot more bet, and in particular, they're able to take a lot more small bets. When you have to phone in a bet, or walk into a casino, it takes a lot more time and effort for the casinos to take these bets. It is impractical for them to take a bet of $10, because it wastes time they could have spent taking larger wagers.

Finally, it is worth noting that not all sportsbooks offer the same lines on all bets. In general, the bets with lower lines will be on events where they expect to get more action. This is because of two reasons:

a) More action for them means more money coming in, so they can afford to lower the vig and still make a ton of money

b) More action means that they'll spend more time evaluating the lines, so they'll be more accurate.

The second can actually turn out to be quite important because you might be able to find lines that are truly rogue, despite the fact that the books are charging a higher vig.

When To Bet

The question of when to bet has one obvious answer. When the bet is +EV. This means that there will be lots of bets that you just shouldn't take. A compulsive gambler might go through and bet on every single game that's going on during a given day. However, this is a bad method to follow. Let's go back to this example again:

Minnesota -2.5 pts -105

San Antonio +2.5 pts -105

Suppose that you are God and are able to figure out every possible course of action this game would take under similar circumstances. Once you're finished doing this, you find out that Minnesota will beat the Spread 51% of the time. We already know that you need to win 51.2% of the time to break even, so this is a -EV bet. Betting On SA here would be even worse since their end will win only 49% of the time.

This is a game that not even God could beat, unless of course he had a large wager riding on the Wolves and decided to use supernatural powers to adversely affect the outcome, or unless he paid off some of the Spurs.

Why the sportsbooks might offer you a +EV bet

I left with a cliffhanger last time, and now I'm (finally) going to get around to answering it.

Let's take our example again. As I pointed out last time, if the book get the same number of bets on both sides it doesn't matter how often either side wins. Let's assume the Wolves will cover 50% of the time. If they receive the same number of bets (T) on both sides, they will make a total of $5T no matter who wins.

However, it is not reasonable to assume that the books will get the same number of bets on both sides. In this case, the Wolves are playing the defending World Champs, they're playing at San Antonio, and they're still favored. Many people will see this and want to be on San Antonio regardless. They don't bother to do the math and figure out that the Wolves improved team along with the decapitation of Tim Duncan's right arm do make them a 2.5 point favorite in this case.

The books have two main goals which conflict with one another. First, they are concerned with minimizing risk. It's nice for them to be able to turn a profit no matter what. But their second goal is to maximize their profit. Sometimes, this means they are willing to take small risks to do this (but never large ones).

Suppose now that they assume that they can get the same number of bets on both sides if they change the line to the following:

Minnesota -2.5 pts pk

San Antonio +2.5 pts -110

Also, let's assume that 60% of the money comes in on the Spurs. What happens to their EV? There were 2T bets in the previous example, so with a 60/40 split, .8T are on MN and 1.2T are on SA. If Minnesota covers (half the time), their EV is -.8T*100 + 1.2T*110 = 52T. If they don't cover, the books will make -.8T*(-100) - 1.2T*100 = -40T. Since each of these happens half of the time, they make a total of $6T on average. So the books make more money by taking this extra risk.

At the same time that this was happening, the books offered you a bet that was neutral EV. However, you can see how the line might move to actually give you one that is +EV. I just kept it basic here to keep the math simple.

So if the sportsbook is knowingly offering you a bet that's -EV for them, why do they do it? There are a couple of reasons. First, they're providing a service. People will stop coming to them if they won't allow you to bet on your favorite team half the time. They also can't just change half of the line, because people will become frustrated when they see the books taking a larger than normal vig very often. Finally, there's the matter of risk aversion. With the amount of money that comes in on one side, they might have trouble covering all the bets if they don't take any on the other side. Even if they do, a short run of bad luck might do them in.

What normally happens in sports betting is that you try to bet against the public. This is referred to as fading. Because too many people bet on the Spurs, we were able to find a bet that was +EV on the wolves. When you see lines moving, this is the reason. For teams that the public will tend to favor, the books will often build this bias into their initial lines. However, if the books don't get the action they expected on one side, they might start moving the line back towards the center, so don't get carried away when you see a line moving!

An example of this type of bet, which I plan to use early and often this season will be to bet against Miami. Miami is obviously going to be a strong team and they made a huge trade during the off season to acquire Antoine Walker as well as some other players. Walker has always been an overrated player. Sure, he gets tons of points, but he gets those points by taking a ridiculously large number of shots. His career FG% and 3PT% have never been stellar.

Now, they're taking him and putting him on a team with Dwyane Wade and Shaq, and Shaq has started to complain about not getting the ball enough. I just don't see how he's going to be able to help the team at all. In addition, it usually takes a while for teams to learn how to work together, so they will likely underperform for a while. In basketball, as much as in any other sport, a team is more than the sum of its parts. This doesn't mean the Heat won't win, I just don't expect them to win as much, or cover the spread as much. Since the public figures to bet heavily on them, the lines might tend to be skewed, paving the way for plenty of +EV bets!

How Often do we need to win to break even?

First off, I'll answer the question about why you need to win 51.2% of the time to break even when laying -105 on a bet. To do this, we need to calculate the EV of that bet, assuming the probability we will win is p. Since we win p percent of the time, we will lose (1-p) percent of the time. When we win, we win 100 and when we lose, we lose 105 (or some multiple of those numbers, depending on the size of our bets). Therefore, the EV of the bet can be given by the expression:

100p - 105(1-p)

To figure out the break even point, we set the expression equal to zero and solve for p to get p=105/205 ~= 51.2%

You can do this no matter what the odds are. Suppose you make a bet at +150, your EV is

150p -100(1-p)

So p = 100/250 = 40%

Standard Sportsbook Lines

Last time I mentioned a bet where the lines on both sides where -105. It used to be the case that the standard was -110. It was very rare that you'd find lines better than that, but common to find lines worse.

Today, the standard for most online sportsbooks is still -110, but it is common to find sites that offer better lines. Pinnacle, for instance, offers 4 cent lines (-104) on all of their straight baseball wagers. This is both a good and a bad thing for bettors.

The good (obviously) is that the juice is lower, so you can win a smaller percentage of your bets and still win. Furthermore, winning the same percentage of bets with a 4 cent line will net you more money that it would making the same bets with dime lines.

The bad is that Pinnacle is known for having the sharpest handicappers in the game. It's rare that you'll find a line there that's ever way off. With computer technology it is easier for handicappers to do their work. They can plug in all the variables to a machine and let it go to work. Then, they can adjust the lines by hand as they see fit. Also, with internet betting, they're able to take a lot more bet, and in particular, they're able to take a lot more small bets. When you have to phone in a bet, or walk into a casino, it takes a lot more time and effort for the casinos to take these bets. It is impractical for them to take a bet of $10, because it wastes time they could have spent taking larger wagers.

Finally, it is worth noting that not all sportsbooks offer the same lines on all bets. In general, the bets with lower lines will be on events where they expect to get more action. This is because of two reasons:

a) More action for them means more money coming in, so they can afford to lower the vig and still make a ton of money

b) More action means that they'll spend more time evaluating the lines, so they'll be more accurate.

The second can actually turn out to be quite important because you might be able to find lines that are truly rogue, despite the fact that the books are charging a higher vig.

When To Bet

The question of when to bet has one obvious answer. When the bet is +EV. This means that there will be lots of bets that you just shouldn't take. A compulsive gambler might go through and bet on every single game that's going on during a given day. However, this is a bad method to follow. Let's go back to this example again:

Minnesota -2.5 pts -105

San Antonio +2.5 pts -105

Suppose that you are God and are able to figure out every possible course of action this game would take under similar circumstances. Once you're finished doing this, you find out that Minnesota will beat the Spread 51% of the time. We already know that you need to win 51.2% of the time to break even, so this is a -EV bet. Betting On SA here would be even worse since their end will win only 49% of the time.

This is a game that not even God could beat, unless of course he had a large wager riding on the Wolves and decided to use supernatural powers to adversely affect the outcome, or unless he paid off some of the Spurs.

Why the sportsbooks might offer you a +EV bet

I left with a cliffhanger last time, and now I'm (finally) going to get around to answering it.

Let's take our example again. As I pointed out last time, if the book get the same number of bets on both sides it doesn't matter how often either side wins. Let's assume the Wolves will cover 50% of the time. If they receive the same number of bets (T) on both sides, they will make a total of $5T no matter who wins.

However, it is not reasonable to assume that the books will get the same number of bets on both sides. In this case, the Wolves are playing the defending World Champs, they're playing at San Antonio, and they're still favored. Many people will see this and want to be on San Antonio regardless. They don't bother to do the math and figure out that the Wolves improved team along with the decapitation of Tim Duncan's right arm do make them a 2.5 point favorite in this case.

The books have two main goals which conflict with one another. First, they are concerned with minimizing risk. It's nice for them to be able to turn a profit no matter what. But their second goal is to maximize their profit. Sometimes, this means they are willing to take small risks to do this (but never large ones).

Suppose now that they assume that they can get the same number of bets on both sides if they change the line to the following:

Minnesota -2.5 pts pk

San Antonio +2.5 pts -110

Also, let's assume that 60% of the money comes in on the Spurs. What happens to their EV? There were 2T bets in the previous example, so with a 60/40 split, .8T are on MN and 1.2T are on SA. If Minnesota covers (half the time), their EV is -.8T*100 + 1.2T*110 = 52T. If they don't cover, the books will make -.8T*(-100) - 1.2T*100 = -40T. Since each of these happens half of the time, they make a total of $6T on average. So the books make more money by taking this extra risk.

At the same time that this was happening, the books offered you a bet that was neutral EV. However, you can see how the line might move to actually give you one that is +EV. I just kept it basic here to keep the math simple.

So if the sportsbook is knowingly offering you a bet that's -EV for them, why do they do it? There are a couple of reasons. First, they're providing a service. People will stop coming to them if they won't allow you to bet on your favorite team half the time. They also can't just change half of the line, because people will become frustrated when they see the books taking a larger than normal vig very often. Finally, there's the matter of risk aversion. With the amount of money that comes in on one side, they might have trouble covering all the bets if they don't take any on the other side. Even if they do, a short run of bad luck might do them in.

What normally happens in sports betting is that you try to bet against the public. This is referred to as fading. Because too many people bet on the Spurs, we were able to find a bet that was +EV on the wolves. When you see lines moving, this is the reason. For teams that the public will tend to favor, the books will often build this bias into their initial lines. However, if the books don't get the action they expected on one side, they might start moving the line back towards the center, so don't get carried away when you see a line moving!

An example of this type of bet, which I plan to use early and often this season will be to bet against Miami. Miami is obviously going to be a strong team and they made a huge trade during the off season to acquire Antoine Walker as well as some other players. Walker has always been an overrated player. Sure, he gets tons of points, but he gets those points by taking a ridiculously large number of shots. His career FG% and 3PT% have never been stellar.

Now, they're taking him and putting him on a team with Dwyane Wade and Shaq, and Shaq has started to complain about not getting the ball enough. I just don't see how he's going to be able to help the team at all. In addition, it usually takes a while for teams to learn how to work together, so they will likely underperform for a while. In basketball, as much as in any other sport, a team is more than the sum of its parts. This doesn't mean the Heat won't win, I just don't expect them to win as much, or cover the spread as much. Since the public figures to bet heavily on them, the lines might tend to be skewed, paving the way for plenty of +EV bets!