Implied probability is one of the most useful, and frequently misunderstood numbers in sports betting. Implied probability is derived from the odds the sportsbook offers and gives you an understanding of the likelihood for you to win a bet, but more importantly, it can give you insight into the sportsbook’s edge over the bettor, and helps you reduce that edge. Expressed as a percent, it is much more easily understandable than any odds format. Though it will never tell you which team to select, determining the percent implied probability over 100% will point out lines where the book’s advantage is lower.
Calculating implied probability can be a little intimidating to calculate, so if the math below is daunting, head over to the implied probability calculator. That said, it is worth working through the math below to get an understanding of how implied probability.
There are two formulas for calculating implied probability for American odds: one for negative odds, and one for positive. Let’s take the most common odds in sports betting -110 / -110. These are the expected spread betting odds in NFL and NBA. A $100 -110 bet pays $90.91, but we know that the likelihood of one team winning is actually 50%. Let’s look at the implied probability calculation:
Implied Probability = (-1*(Odds)) / (-1(Odds) + 100)
Which looks like:
Implied Probability = (-1*(-110)) / (-1(-110) + 100)
0.524 or 52.4% = 110 / 210
52.4% should be familiar to experienced bettors as the break even winning percentage bettors shoot for in spread betting. Because -110 on one side of a bet usually means -110 on the other side too, we can add all the probabilities (in this case another -110 probability) to determine the sportsbook’s edge.
(Heads Probability + Tails Probability) – 1 = Sportsbook’s Edge
(0.524 + 0.524) – 1 = 0.048 or 4.8%
This means that regardless of side, the sportsbook has a 4.8% advantage over the bettor. Another way to look at it is that the book has the ability to have a 4.8% imbalance in taking in money and remain profitable. The sportsbook edge varies incredibly: sometimes as high as 5% and as low as 0.8%. Ideally you should be looking for bets with the lowest sportsbook edge you can. It is a subtle edge in sports betting, but remember the difference between winning at 52% and 53% is the difference between making money and making a charitable donation.
Let’s work a positive odds example. We’ll use the following moneyline bet where the favorite is -190 and the underdog is +160. First we break down the implied probability on +160 odds :
Implied Probability = 100 / (Odds + 100)
38.5% or 0.385 = 100 / (160 + 100)
This all makes sense: +160 is a pretty big betting dog, and pays out at a high rate, so therefore we would expect this to hit at a much less than 50% rate. To get the other outcome, we calculate the -190 odds:
65.5% or 0.655 = (-1(-190)) / (-1(-190) + 100)
As a heavy favorite, a -190 bet is much more likely than 50% to hit. In the above example we see that the sportsbook’s advantage is:
(0.385 + 0.655) – 1 = 4%
This tells us is that with no other information a bet on the -190/+160 bet is more likely. to be successful over the long term than the -110/-110 example.
Smart sports bettors will take the implied probability numbers and the sportsbook’s edge to determine which games to handicap. There are literally thousands of betting options on an NFL Sunday or an NCAAF Saturday. Make sure you have found the one that gives you the greatest chance of success before wasting time looking at lineups and injuries.