Sports Betting Math (Winning with Arithmetic)

Sports betting math is necessary if you want to win at sports betting. Bettors who don’t understand sports betting odds and don’t consider sports betting probabilities when wagering are setting themselves up to fail.

The math you need to know as a sports bettor isn’t complicated, especially after you have some exposure to it.

This post explains the basics of the mathematics of sports betting.

The Difference between Odds & Probability

I want to start out with a couple of simple definitions:

  • Probability represents the likelihood that an outcome will happen.
  • Odds represent a ratio of a bettor’s chances of winning to his chances of losing.

Probabilities are listed as numbers between 0 (complete improbability) and 1 (total certainty). Probabilities may be shown as percentages (10%), proportions (1 in 10), decimals (0.1), or fractions (1/10).

Because odds are always a ratio of one thing to another thing, they look and behave differently than probabilities. Like probability figures, odds numbers can be represented in lots of different ways, but they’re always a ratio. I cover the most common odds formats in greater detail below.

Really, probability and odds are the same thing but are expressed in different ways.

The Math Behind How Sportsbooks Use Betting Odds

The number a sportsbook posts doesn’t represent its true belief about that bet’s outcome. The book builds in a buffer, a few points between what they believe will be the real outcome and what they’re willing to pay you for it.

This is not much different from how casinos make money. Few (almost none of them, in fact) casino bets payout equal to their probability. Betting on black in roulette pays out 1:1 as if you have a 50/50 chance of winning. Your true odds of winning with a bet on black are 18/38, or about 47.3%. That 1:1 payout would be 19:9 if it represented your odds of winning.

The difference between the betting odds and the true odds is where betting sites and casinos eat breakfast, lunch, and dinner.

If you buy a team at +400, you’re buying them at a 20% winning probability. The sportsbook doesn’t see it that way. They see it as “We’ll pay you 4/1 if your bet wins.” In all likelihood, they give that bet more like an 18% chance of winning. They’re making money on you in the 2% gap between those two numbers.

Bettors looking for value are looking for situations where a sportsbook sets betting odds close to (or beyond) a bet’s true odds of occurring.

Common Betting Odds Formats

In modern sports betting, you’re only like to come across 3 ways of representing odds.

Decimal Odds

Decimal odds are represented by decimals:

They look like this:

Minnesota Twins              1.909
Cleveland Guardians        1.87

Decimal format is the easiest in terms of calculating your payout. In decimal format, your total return is your bet multiplied by number shown.

For example, if you put $100 on Minnesota and the Twins get the road underdog win, your return is $190.90. If you back the Guardians with $100 and Cleveland gets the home win, your return is $187.

This is not your profit; it’s your entire return, including your original wager. It’s easy enough to work out your pure profit. Just subtract your bet from your return.

Some find it easier to think of decimal formats as percentages.

If we convert the above game line into percentages, it looks like this:

Minnesota Twins              190.9%
Cleveland Guardians        187%

Ignoring the hundreds place in those percentages gives you your profit as a percentage of your bet. In this case, the book will pay you almost 4% more for backing the Twins over the Guardians.

Want to convert your decimal odds to probabilities?

The formula is easy – 100/odds.

Looking at the Twins again from our baseball example, the implied probability is 100/1.909, or 52.38%.

Fractional Odds

Fractional odds are made of fractions.

They look like this – x/y.

In this formula, x is your profit for every y dollars you bet.

Here’s what fractional odds for an NFL game might look like:

Philadelphia Eagles         7/2
Dallas Cowboys                2/1

Here, the sportsbook pays you $2 for every $1 you bet successfully on Dallas at home. They pay you $7 for every $2 you successfully bet on the Eagles pulling off the road upset.

Unlike decimal odds, fractional odds only tell you your profit. To work out your entire return, you add your bet to your profit.

For example, if I bet $100 on the Cowboys and they claim the win, my profit is $200. That’s my bet multiplied by the first number in the fraction. But my total return is that same $200 plus my original $100 bet, or $300.

To convert fractional odds to percentages, first divide the x number in the fraction by the y number. Then multiply that by 100.

In the case of the Eagles in the example from above, that’s 7/2 (3.5) multiplied by 100. That’s a 350% return.

For Cowboys backers, their return is 2/1 (2) multiplied by 100. That’s a 200% return.

American Odds

Leave it up to us Americans to create the goofiest odds representation format.

To explain the American betting odds format, I need to start with an example:

Seattle Sounders              -120
CF Montreal                       +320

The +/- symbol and the numbers tell you two vital pieces of information. They tell it in two different ways.

In American odds, the team with a minus symbol (-) is the favorite. The minus symbol combined with the number means you have to bet $120 on Seattle to win a $100 payout.

The team with the plus symbol (+) is the underdog. The plus symbol combined with the number means you will win $320 for every $100 you bet successfully on CF Montreal.

If you want to know your total return, rather than just your profits, add your bet to the payout number.

Converting underdog odds to percentages is easy. The number listed is the percentage. In the example above, your percentage return would be 320% on a successful Montreal bet.

Converting favorite odds requires a little math. Divide 10,000 by the number listed. Your percentage return on a successful bet on the Sounders would be about 83.3%.

Calculating Sports Betting Break-Even Percentages

Imagine this scenario:

You’re at a sportsbook. You have $1,000 to bet. You decide to place 100 $10 bets. For the sake of simplicity, all 100 bets were at -110 odds.

(-110 American odds converts to 10/11 fractional odds and 1.91 decimal odds.)

What percent of those bets have to win in order for you to break even?

First, let’s work out how much you’re winning on each winning bets.

When you divide 100 by our odds (100/110) you get about 91%. Each winning bet will return about 91% of your bet to your bankroll, plus your initial bet. Since each bet is $10, we know that every time you win, your profit is $9.10. That means $19.10 (profit plus bet) goes back into your bankroll.

If we divide our sample size of 100 bets by our average return of 1.91 on wins, we get 52.35%. That tells you what percent of your 100 bets have to win for you to avoid posting a loss.

Since we can’t lose .35% of a bet, let’s round it up to 53%.

If 53 of your bets win and the other 47 lose, you make a profit of $12.30.

If you can push that win rate up to 60%, things start to get interesting. Winning 60 bets and losing 40 returns a profit of $146.

The Sports Betting Math Behind Unit Bets

In sports betting jargon, a “unit” is just another way of talking about money.

Smart bettors create what’s known as a unit bet. That means they wager the same amount on every contest. It’s also sometimes called flat betting because it doesn’t fluctuate up or down.

Why would a unit bet or flat betting help sports bettors?

For starters, it makes sports betting math less complicated. It’s easier to consider things like expected value and probability when you know exactly how much you’re going to bet. A flat $100 bet on all NFL games makes it much easier to do the math in your head when you look at sportsbook odds.

Unit bets also help with bankroll management and planning. Let’s say I have $1,000 I can afford to lose betting on the NFL. Breaking that up among the 18-game season, I know I can afford to lose $55 a week and my budget won’t be blown.

You can also break your bankroll up into bets by percentage. Conservative bettors may bet 1-2% of their total bankroll on each game. You probably shouldn’t be betting more than 5% of your bankroll on any one game. This will conserve your money for the long haul of a sports season.

That same $1,000 bankroll broken up into units of 3% would mean $30 per week on NFL games. It would also be enough money to bet $30 on one or two MLB games per week.

Some Great Resources about Sports Betting Arithmetic

I can’t cover sports betting math comprehensively in one page, but I have multiple other new pages in the works on the subject. I also have a few other recommended resources related to the subject:

  • The first recommendation I have is to read Sharp Sports Betting by Stanford Wong. It’s the best book I’ve read on the subject of sports betting, and the math sections are fantastic.
  • The second recommendation I have is to read The Logic of Sports Betting by Ed Miller and Matthew Davidow. It’s as good as the Wong book, but it’s more modern and not quite as dry.
  • You can find some details about the legality of sports betting in the United States here. Michael’s website is one of my favorite resources on the internet for information about gambling in Las Vegas.
  • Finally, get some insight into how online sports betting promo codes can help you win more money using math. Unlike the some of the other resources on this list, this isn’t a book — just a web page, but it’s well worth your time. Free money from the sportsbooks can change the math in your favor, at least when you’re starting out.

Conclusion: Sports Betting Math Can Help You Win

Sports betting math can help you plan and execute your bets smarter.

You don’t need to be a math whiz to break even or even make a little money on your sports bets. But you should understand the basics of probability and odds before you bet.