# Middles Sample Problems

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Sample Problems

Problem 1

There are a number of two- and three-game middles available on major-league baseball season wins. How much are they worth? Assume that all bets are offered at -110.

Problem 2

What are the middles for other sports that are about equally attractive as a three-game middle at baseball?

Solutions to Sample Problems

Problem 1

There are a number of two- and three-game middles available on major-league baseball season wins. How much are they worth? Assume that all bets are offered at -110.

The major-league baseball season is 162 games. The probability of middles hitting is 6.3 percent for one game, 12.4 percent for two games, and 18.4 percent for three games.

Constructing a middle involves making two bets at \$110 each, for a total investment of \$220. If the middle won, the amount won would be \$200. Other bet sizes could be used, providing the ratio of wins to investment is 200/220. A \$220 middle containing one game would win \$200 6.3 percent of the time and would lose \$10 the other 93.7 percent of the time. That’s an average win of \$3.23 on a \$220 investment, a return of 1.6 percent.

A \$220 middle containing two games would win \$200 12.4 percent of the time and would lose \$10 the other 87.6 percent of the time. That’s an average win of \$16.04 on a \$220 investment, a return of 7.3 percent.

A \$220 middle containing three games would win \$200 18.4 percent of the time and would lose \$10 the other 81.6 percent of the time. That’s an average win of \$28.64 on a \$220 investment, a return of 13.0 percent.

The method used to get those numbers is approximate, and thus the answers should be rounded off. I suggest using 2 percent, 7 percent, and 13 percent as the values of baseball middles of one, two, and three games if all bets are made at -110.

The problem is you have to tie up your money until the end of the season. You have to decide for yourself if you are willing to do that, for an investment of this risk. Earning 13 percent in six months is fine if it is risk-free, but a three-game middle gives you roughly 18.4 percent chance of winning both bets and a 81.6 percent chance of winning one bet and losing the other.

For me personally, I’d say buying a three-game middle would be worthwhile as long as I am confident that all the sportsbooks involved are going to survive to buy back any winning tickets. I would not invest in baseball season-total middles of less than three games; the expected return is too small to warrant investing my money for six months. What your minimum requirements are is up to you.

Problem 2

What are the middles for other sports that are about equally attractive as a three-game middle at baseball?

## NFL

The NFL season is 16 games, and lasts for four months. A one-game middle on NFL games wins about 19.6 percent of the time. That makes a one-game NFL middle slightly more profitable than a three-game baseball middle.

A half-game NFL middle is about as attractive as a two-game baseball middle.

## NBA

The NBA plays 82 games in a six-month season. A two-game NBA middle is almost as attractive as a three-game baseball middle. The two-game middle will hit 17.4 percent of the time. The math shows that to be a 12 percent return on a six-month investment.

## NHL

The NHL plays the same length season as the NBA: 82 games in six months. Thus the middle requirements for a worthwhile NHL middle are the same as for the NBA: a two-game middle will return about 12 percent on a six-month investment.

This is part of an occasional series of articles.

Excerpted with permission from Sharp Sports Betting by Stanford Wong, edited for this format.