Bettors often seek out new tools to help refine the process of assigning accurate probabilities to the chances of uncertain events happening. This article discusses how Bayesian Analysis – the theory of an 18th Century English Presbyterian Minister named Thomas Bayes – can help sports bettors gauge the outcome of an event.

The birth of Bayesian analysis

Thomas Bayes was born around 1701 in England, and divided his life between studying matters theological and mathematical. It wasn’t until after his death in 1761 that one of his studies “An Essay towards solving a Problem in the Doctrine of Chances” was submitted to the England’s Royal Society and posthumously acknowledged the significance of his work.

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It took, however, until the advent of desktop computers – 200 years later – for Bayes’ work to really be appreciated and gain widespread acceptance. Since then Bayesian analysis has been interpreted and applied in many different spheres such as artificial intelligence. In its simple form the Bayesian approach is arguably the most sensible way to use probability and reasoning to make decisions in the face of uncertainty, and that includes gambling.

It applies an iterative process of assessing what you know about the probability of a future event, and then testing the impact of new evidence as it becomes available.

The Bayesian analysis Formula

Bayesian analysis can go by many names, ‘Bayesian Inference’, ‘Inverse Probability’, ‘Bayesian Updating’… but at the end of the day it is about a fairly simple formula:

Probability of A Given B equals Probability of A times Probability of B Given A divided by Probability of B

If you want to know the probability of A when you know that B is also present (given), you can get the answer by multiplying your prior estimation of A (Probability of A) by how much more likely B is when A is present (i.e. P(B A)/P(B)).

Using Bayesian analysis to predict the weather

So, suppose you estimate that there is a 30% chance it will rain tomorrow.

And you know that on an average day there is a 50% chance of clouds in the sky.

You also know that the likelihood of clouds is 100% given that rain is 100% (there will always be clouds if there is rain).

You have the following information:

• P(A)= Probability of rain= 30%
• P(B)= Probability of clouds= 50%
• P(B A)= Probability of clouds given rain= 100%

You wake up in the morning and are blessed with a new piece of information: there are clouds in the sky. You should now perform a Bayesian update on the probability of it raining, Given that there are clouds in the sky.

So, as we recall, P(A B)=P(A)*P(B A)/P(B)= chance of rain * chance of clouds given rain/chance of clouds=30%*100%/50%=60%

You can now update your belief about it raining to 60%.

Bayesian analysis and sports betting

Now, let’s transpose this to a sports betting example. Suppose you are interested in a Bayern Munich match, where you believe they have a 50% chance to win outright. You also know that when they win, it rains 11% of the time, compared to the usual likelihood of rain in a Bayern Munich Match of 10%.

Calculation:

• P(A)= Probability Bayern Munich wins= 50%
• P(B)= Probability of rain in a Bayern Munich match= 10%
• P(B A)= Probability of rain in a football game when Bayern Munich wins= 11%.

Now, if you receive information about the weather, there is no need to scramble to consider how it will affect the odds. You can, as do many professionals in many fields (including sports betting), perform a Bayesian Update.

If there is rain, you know that P(A B)=P(A)*P(B A)/P(B)= 50%*11%/10%= 55%.

Notice that P(B A)/P(B) is the same as asking “how much More likely is B happening, given A?”- In this case, 11/10 (11%/10%).

Once you know that B is a given, your new estimation of A can change accordingly by simply multiplying them- i.e. P(A)*P(B A)/P(B).

Summary

A bettor’s biggest enemy is often himself, with dogmatic adherence to a particular outcome in the face of changing circumstances, a common mistake. Bayesian analysis breaks this habit by allowing and encouraging the constant testing of new evidence against your position, in essence a positive feedback loop of refining your estimates of likelihood of an event.

It isn’t however a mathematical crystal ball, as with any formulas, the GIGO law applies – garbage in, garbage out – but if you have confidence in your assessment of whatever it is your are testing, then the Bayesian approach can unearth sports betting value. And you’ve got an 18th century priest to thank for it.

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Learning how sports betting odds work can be intimidating at first, but our guide will teach you how to read odds in no time! This primer is designed for beginners who are curious about common wagering practices and terms.

Learn to Bet on Sports & Gamble Online & Offline

For starters, you will need somewhere to place bets. If you are in Vegas, great! You can bet at one of the sportsbooks in their casinos. As more and more states pass laws to legalize sports betting, you will also be able to place wagers at local casinos in your area. You could also find a local bookie to bet through, but we recommend betting online.

How Online Betting Works

We have an excellent list of the top places to bet online (that take U.S. customers). If you are looking to maximize your first deposit, we also have a great comparison of the best sportsbooks signup bonuses for you. Once you’ve read the primer below on reading the odds, you will have no problem navigating these sites.

Las Vegas Sports Betting at the Ticket Window

Betting sports in Vegas is likely going to be the option with the biggest learning curve. You will understand the odds after reading this article, but there are a few other rules and common practices you want to be familiar with that are specific to Vegas.

Many books now offer their own betting apps that make this process a little bit easier, however, the drawbacks are that you must make a deposit upfront for how much you want to bet with, plus you don’t get free drink tickets when you place bets on the app. We’ll step through how you would place a bet in person at the ticket window.

Step-by-Step Guide to Placing Sports Wagers in Vegas

“I’ll take number 403, Cowboys -8, for $110 straight up.”

1. Use the rotation number/numbers and the name of the team/teams you want to bet on. The rotation number appears to the left of each team (see image above) and is used as a unique identifier so that there is no confusion about what you want.
2. State the amount you would like to bet. This is how much you are wagering, not how much you want to win. Most books use -110 odds (more on this later), so if you want to win $100, you’d state $110 as your wager amount.
3. Indicate the type of bet you are placing. For individual bets, just say “straight” or “straight up”, otherwise you will need to explain that you are taking a parlay or some other bet type.
4. Repeat as necessary.

How to Read Sports Betting Lines

There are nearly infinite ways to bet sports. If you can think of something to bet on, there is a good chance you can find somewhere to bet on it. What we are going to focus on is the most common types of wagers: point spreads, over/unders (totals), and money lines.

What Does the Plus (+) and Minus (-) Mean in Sports Betting?

One of the first and most important aspects of sports betting every new player must learn is what the different symbols mean. A plus or a minus can mean different things in different situations. They are used for both point spread and money line betting, as well as for the price/juice of each bet.

This is explained in more detail below, but the most important thing to be aware of is that negative numbers represent favorites, while positive numbers represent underdogs. The same is true whether you are looking at a spread or a moneyline, but how these numbers are used is very different. You also need to know that prices on spreads/totals do not impact who/what is favored, it is used to determine how much the bet pays out. Read on for the complete explanation of each of these concepts.

Point Spreads Explained

The point spread is the projected number of points that separate two teams. A game with a spread will have a favorite (the team expected to win) and an underdog (the team expected to lose). A favorite “gives” points and is identified with a minus sign next to their point spread. The underdog “gets” points and is identified with a plus sign next to their point spread.

In the example above, the point spread is 7 points. Patriots are favored by 7 points against the Jets.

If you bet on the Jets +7, they must either win the game outright or lose by 6 points or less. If they lose by exactly 7 points, the bet is considered a push and is canceled.

If you bet on the Patriots -7, they must win the game outright by more than 7 points. If they win by exactly 7 points, it’s a push.

Bet Prices: What Does -110 Mean? If I Bet $100, What do I Win?

The 3-digit numbers to the far right are the listed prices for these bets. This is also called the odds, vig, or juice. An easy way to think of it is the amount you must risk to win $100 on this wager. In our example, -110 means you must risk $110 if you want to win $100. -110 is pretty standard, but you will find different options. We will cover those in more depth when we talk about money lines. The price of the bet has no impact on which team is favored. Only the plus or minus on the point spread matters. This is handled differently when you bet strictly on the moneyline.

What is the Money Line? (How Moneyline Betting Works)

A moneyline bet is on a team to win the game outright (without a point spread) at an adjusted cost. Just like with point spread betting, the favorite will have negative odds, while the underdog will have positive odds. The difference here is in the price or payout depending on which team you take.

A favorite (e.g. Patriots -280) on the money line works just like our bet price example above. In our new example, the Patriots are listed at -280, meaning you would need to risk $280 for a return of $100 on them. It follows that a winning bet on the Pats pays $100 (plus your initial investment of $280 back). This added risk is why betting the spread is usually more popular, especially on favorites.

Underdogs (e.g. Jets +240) work a bit differently. Instead showing how much you need to risk to win $100, this line tells you how much you stand to win on a $100 wager. That means if you bet $100 on the Jets, and they win, you would win $240. If the Jets lose, you are only out your original $100 wager.

Totals: What Over/Under Means in Sports Betting

The terms “total” and “over/under” are synonymous when placing wagers. This type of bet is on the sum of the points scored by both teams in a game. The bookie sets the number for the total, then you predict whether they will score more or less points than the set number.

The over/under in this example has been set at 42.5. If you project the Jets and Patriots to combine to score more than 42.5 points, you would place a wager on the over. If you think they will score less than 42.5 points, you would bet the under. Let’s say the final score of this game is Patriots 27, Jets 24. Which bet would lose and which bet would win? The sum of all points scored is 27 + 24 = 51, so an over bet wins and an under bet loses.

You may also note the bet price is not -110 like we have seen before. It is common practice by sportsbooks to adjust prices on or around key numbers for spreads and totals, especially in football.

Understanding Sports Betting

We hope this short beginner’s guide to understanding and interpreting odds will give you the confidence to get out there and start making winning bets. Our experts are here to help you on this journey, so do not hesitate to contact us with any questions you have about sports betting! We have only scratched the surface on reading betting lines, but this is an excellent place to start.

Sports Betting Explained Nfl

One sport that has a few extra quirks is golf. I wrote up a guide to golf betting that explains these unique features so you can feel comfortable wagering on PGA events too.