_**Note:** This article was originally published all the way back in 2018 when Action Backers was just a blog. That said, the principles are still sound today._

The only way to make money betting on sports, in the long run, is by placing bets that have a positive Expected Value (+EV). You will also need to understand Implied Probabilities and betting Margins.  
  
Unfortunately, even if you make all the right decisions over an entire season of betting, that doesn't ensure you'll come out ahead.  
  
You can make great picks and still lose because sports betting is heavily influenced by luck (we’re talking about humans here), but mostly in the short term.  
  
If you understand and deploy the concept of expected value (EV), though, you'll see you can control your profits in the long run.

### So, what is EV? What is value betting?

Every decision you make when placing a bet can be classified as either Plus (+) EV or Negative (-) EV.

Simply put:

**+EV is a good choice**: one that will make you money in the long term.

**(-)EV is a bad choice:** one that will lose you money in the long run.

> _"In probability theory the expected value of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by the outcome value (or payoff).  
> "Thus, it represents the average amount one 'expects' as the outcome of the random trial when identical odds are repeated many times."_
> 
> [Expected Value](https://en.wikipedia.org/wiki/Expected_value) as explained by Wikipedia

In plain English: **_Expected value is the amount of money you would win or lose, on average, on your bet._**

#### The math of expected value

If you and a friend were to bet on the outcome of a coin flip, and agree that you would be paid $5 for every time it came heads and you would pay them $5 every time it came tails, you would win half the time and they would win the other half of the time.

That would make the bet a neutral EV bet.

Let's say, though, that your opponent decided:

-   They would pay you $10 for every heads
-   You would still only pay them $5 for every tails

The wager now becomes a **+EV bet**.

You'll still win 50% of all of the flips over the long term. But when you win you'll be paid double what you pay them when you lose.

Your expected value on every flip is now **$2.50**.

##### _What the math says:_

One outcome of the flip is it lands tails (-$5), the other outcome is heads (+$10).

So 50% of the time you'll win $10 and the other 50% of the time you'll lose $5.

To calculate EV, use the following formula:

  
**(Amount won per bet * probability of winning) – (Amount lost per bet * probability of losing)**

The above example looks like this:

(Amount won: $10 * Probability: 50%) - (Amount lost: $5 * Probability: 50%)

($10*0.5) - ($5*0.5)  
($5) - ($2.50)  
**EV = + $2.50**

#### What this means

In sports betting, this means you **only want to make bets that show a positive expectation** and avoid ones with a negative expectation. This is where your money comes from - making bets that only show a positive expectation.

Okay great, this all makes sense… but you’re probably wondering how do I apply this to sports betting when the odds aren’t 50/50?  
  
Unlike a coin toss, betting odds are subjective, and therefore if you accurately predict an outcome compared to the bookmaker, you’re likely to make a profit.  
  
If you calculate your own probability for an outcome that differs from the implied probability of the odds, you can identify a positive EV.

### What is implied probability?

As per [smarkets.com](https://smarkets.com):  
“_Implied probability is a conversion of betting odds into a percentage. It takes into account the bookmaker margin to express the expected probability of an outcome occurring.”_  
  
This is a fundamental part of finding value in your bets and is imperative to winning in the long run.

**To calculate Implied probabilities**, use the following formulas (or just use our betting tools in-app): There are two instances of American odds (positive and negative) which require separate calculations.

**Converting negative American odds**

The equation to convert negative American odds is:

negative American odds / (negative American odds + 100) * 100 = implied probability

**Converting positive American odds**

The equation to convert positive American odds is:

100 / (positive American odds + 100) * 100 = implied probability

#### Practical application

Now you understand how to calculate the implied probability behind the odds, you can identify potential value in a betting market. If the bookmaker's implied probability is less than your own assessed probability, that outcome represents a value betting opportunity.  
  
Let’s look at a real-life example from 2018 when this post was first published. For simplicity's sake, we will use an NHL Moneyline Bet, using [MoneyPuck.com](http://moneypuck.com/) as the basis of our model (***_this is for example purposes, we always recommend building your own model!_**)  
  
The New York Islanders are on the road against the Vegas Golden Knights. On the face, you might think that Vegas is a “lock” to win this game. But we want to be betting numbers, not teams. So let’s dig into some numbers.  
  
Pinnacle has the following line available:  
  
Islanders ML (+171)  
Vegas ML (-190)  
  
Vegas is an overwhelming favourite and our Implied Probabilities tell us the following:  
  
Islanders Chance of winning: 36.9%  
Vegas Chance of winning: 65.52%  
  
(**_wait_ _a second, doesn’t that add up to 102.42%? Yes, it does. Congrats! You just learned how to calculate the sportsbooks margin; in this case 2.42%. This is their “take” no matter which side wins or loses the game_**)  
  
But here’s where we find our value. Let's say that we think the Islanders (using our model, or in this case MoneyPuck) **_actually_** have a **43.5%** chance of winning and that Vegas only has a **56.5%** chance of winning.  
  
This means that we have an implied edge of **6.6%**! We should bet on the Islanders in this spot. In fact, the Expected Value of making this bet based on a $100 wager is + **$17.89**!

![NHL betting example](https://res.cloudinary.com/actionbackers/image/upload/v1667399535/Screen-Shot-2018-12-20-at-12.33.19-PM_rp2iih.png "NHL betting example")
_Betting Vegas in this spot would have an Expected Value of - $26.15_

#### Sportsbet like poker a poker player.

It’s important to note that this particular bet might not win, but your strategy should be for betting for the long run. Think of it like poker. If you know you are making the correct play, in the long run you will win money. Short term variance is a fact of gambling, but you can expect to win long term when making only +EV bets.

### Tips & tricks for value betting

It’s important to understand that your edge will always be perceived so take it with a grain of salt and always practice good bankroll management. We take the approach that we want to have _at least_ a perceived edge of 4% or greater. Treat this as your noise floor. Anything less than 4% and you’re still basically flipping a coin.  
  
Not sure how to build a model (_**update: we can help! Join Action Backers today and learn how to build your first model.**_)? That’s okay! Not everybody has the time or knowledge to build a model of their own. You can still apply value betting in an easy, and beatable way. The concept is simple:

#### Use sharp books to beat square books.

"Sharp" books, such as Pinnacle offer the highest limits and lowest margins for a reason- their lines are sharp and they are rarely exposed. If you take the line that Pinnacle is offering and shop it around at some square books (books who favour public bettors- typically those who predominantly bet favourites and overs) you can often apply a value strategy and beat the book. The old adage: “if you can’t beat ‘em, join ‘em” rings true here, where you’re essentially joining the sharp book to beat the square book. 

It’s worth noting that you **_must_** practice good bankroll management if you want to succeed long-term. Especially if you are playing a lot of underdogs, you need to be able to withstand the short-term variance. Depending on your bankroll, as a general starting point, we recommend playing _no more_ than 3.5% of your roll on any one game, and this should be closer to 1-2% as your bankroll increases.

Have questions? Let us know on [Twitter](https://twitter.com/actionbackers) or become a member and join our discord community!

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Value betting is about the fundamentals. Finding postive expectations and attacking edge for consistent profits.

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