Welcome to the third installment of our series on profitable sports betting. In this post, we're diving deeper into the mechanics of betting odds and how they translate into implied probabilities. This understanding is vital for anyone looking to make informed and strategic betting decisions.
We've already laid the groundwork by exploring the basics of sports betting and the crucial concept of expected value (EV). In Parts 1 and 2, we demystified some foundational principles and discussed how bookmakers set odds, which allowed us to begin thinking critically about where and how to find value in betting markets.
Before we proceed, let's briefly recap what we've covered in this series:
Part 1: Introduction to Sports Betting and Expected Value
Part 2: How Bookmakers Set the Odds
Now, let's expand on these ideas by focusing on the implied probability in sports betting.
Implied probability is a concept that transforms betting odds into a more understandable measure of likelihood. Simply put, it is the probability implied by the bookmakers' odds of a particular outcome occurring. This transformation from odds to probability helps bettors assess the value and potential profitability of a bet.
American odds, presented as either positive (+) or negative (-) numbers, indicate the potential return on a bet relative to the risk involved.
Below is a screen shot from Optimal’s mobile platform that show the current line on an NBA game posted at DraftKings:
In this image, you can see the teams listed (Pacers and Knicks), the current point spread (-4.5) with odds (-110), the moneyline odds (-185 / +154) and the total with odds (o/u 220 / -110). It’s time to dive into how odds translate into Implied Probability.
To convert these odds into implied probabilities, we use specific formulas for favorites (negative odds) and underdogs (positive odds):
The formula to calculate the implied probability for a favorite is:
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The formula to calculate the implied probability for an underdog is:
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Based on these formulas, we can calculate the following implied probabilities that DraftKings has priced into any of these lines. Let’s use the moneyline odds:
For the favorite to win this game, the Knicks (the favorite at -185):
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DraftKings is telling us that they calculate the Knicks win will this game 64.91% of the time.
Now, let’s do the same calculation for the underdogs, the Pacers (at +154)
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Draftkings is telling us that they calculate the Pacers to win this game 39.37% of the time.
But wait - if you add those two probabilities together, you get 104.3%. How is it possible that the totals add up to more than 100%?
That’s because that extra probability seemingly baked in there (called the “overround”) represents the vigorish, or juice, that the sportsbook has placed on this bet. More on that in Part 5; for now, focus on understanding how odds convert into probabilities.
But lines aren’t static, as we learned in Part 2. Bookmakers open the line, take action, and move the line in response. As the line moves, the implied probability of the other possible point spreads necessarily adjust.
Let’s take a look at how that works in practice.
Using Optimal, we can take a look at the odds provided for every line offered on this Knicks-Pacers matchup, giving us a full picture of the prices offered for each. As the point spread increases, the odds on the favorite to win by that higher point total get longer (less likely to happen), and the odds on the underdog to cover that spread get shorter (more likely to happen).
In this image, you see that DraftKings has different odds for different point spreads. -4.5 is listed at -110, while -5 is listed at -105 and -6 at +110. It’s easier to cover a 4.5 point spread than a 6 point spread, and the odds at each number reflect that. You can also see how other sportsbooks have priced the same point spreads.
Let's use the ongoing example from Part 2 of this series, where the Chicago Bears faced the Green Bay Packers. We'll calculate the implied probabilities at different point spreads as the line moves based on betting action, and we’ll ignore the vigorish at this point to keep things simple.
Opening line: Bears -3:
As discussed in the example in Part 2, Pinnacle opens the line with the Chicago Bears as a 3 point favorite to beat the Green Bay Packers. This odds line is expressed as Bears -3 (-110).
Pinnacle is communicating via its opening line that the probability of the Bears winning this game by 4 or more points is 52.38%.
Line movement to Bears -4:
By Monday morning, sharp action betting heavy on -3 has communicated to Pinnacle that this point spread at -3 is too few points. In response, they move the line to -4, which is now the “main line” for this game. The odds on the previous line, Bears -3, are adjusted to reflect the fact that Pinnacle now believes there’s a higher probability of the Bears covering -3.
The new Bears line of -4 has been set at -110 odds, which means that this spread now has a 52.38% implied probability.
Pinnacle is now communicating via its updated line that the probability of the Bears winning this game by 5 or more points is 52.38%.
What about that original -3 spread? After moving the main line point spread to Bears -4, the Bears -3 line odds are adjusted to -130.
Using our formula to convert odds to implied probability:
We see now that Pinnacle is communicating that the implied probability of the Bears covering a spread of -3 has increased to 56.52%. A bettor wanting to take the Bears at -3 will now have to wager $130 to win $100, whereas betting the opening line at -110 odds required a bet of $110 to win $100.
Closing Line settles at Bears -5.5:
After several days of taking action and raising limits, the line on this game has settled at Bears -5.5 at -110 odds.
The implied probability of the Bears covering -5.5 points is 52.38%, whereas the opening line assigned the same probability to the Bears covering 3 points. Sharp action coming in has given Pinnacle information over the course of the week that -5.5 is the correct spread, not the lower numbers of -3 or -4. The spread -5.5 has been assigned the same probability as -3 had been assigned early in the week.
What happened to the odds on Bears -3 and -4? The following table shows the full closing line odds on the Bears at -3, -4 and -5.5, along with the implied probabilities calculated for you:
These examples show how the implied probability of the wager winning changes as the line moves. In this case, the move from Bears -3 to bears -5.5 over the course of the week reflects a higher confidence by the bookmaker (based on the sharp action taken) that the correct margin of victory by the Bears is 5.5 points.
If, when the line opened, you placed a wager on the Bears at -3 / -110, you were buying that bet at a price that implied a 52.38% of winning. By game time, you would have to pay a price of -165 for Bears -3, a price implying a 62.26% of covering that number.
You paid for a 52.38% chance of winning that bet, but the actual chance of that bet winning turned out to be 62.26%. Over the long run, betting into opportunities like this one, you’re going to profit.
To reinforce a critical concept, odds are simply probabilities converted into prices. The concept of "implied probability" is key here, which is the likelihood of an event happening as inferred from the given odds.
The posted odds for a wager give you an implied probability of that event happening.
Understanding how to convert betting odds into implied probabilities is crucial for assessing the value offered by different bets. It allows bettors to make more informed decisions by comparing the implied probability to their assessment of the actual probability of an event occurring.
This knowledge serves as a foundation for our next discussion in this series, where we will delve into different betting markets such as moneyline, point spreads, totals, props, and futures. Each market has unique characteristics, and understanding how expected value can vary across these markets will help you identify the best opportunities based on your knowledge and interests.
