Implied Probability: Simple Example
Let’s take a look at several examples of implied probability in action. We’ll start with a simple example.
Let’s imagine you and a friend are flipping a fair coin. You both get paid even money (+100) on a chosen side, heads or tails. You are betting $100 per flip.
For each time the coin lands on heads, you win $100. For each time the coin lands on tails, your friend wins $100. The implied probability of each side is $100/$200, or 50%. You must take the original amount risked and add it to the amount won to get the total payout of $200 in this case.
This means that for each $100 you risk, you expect to get back 50% of $200, or $100, which makes the bet exactly 50/50.
What happens if we change the payouts?
Now let’s assume your friend gets paid +200 , or $200 for every tails, while you still only get paid $100 for heads.
Your implied probability remains the same, 50%. However, now the implied probability of tails coming up is only $100/$300, or 33.33%. Adding the two probabilities, we get 83.33%. Clearly there is a 100% probability that either heads or tails will come up, and if we assume a fair coin, your friend has a 16.66% edge over you in this bet (100% minus the 83.33% implied probability).
Implied Probability in Sports Betting
In sports betting, the house edge, or vigorish, means that the implied probability of a set of events will always add up to over 100%. The amount over 100% is the bookie’s over round. This is their expected profit.
Let’s see an example of this in action.
On an NFL game, a sports book lists a game as
Denver -3.5 (
Oakland +3.5 ( -110 )
What is the implied probability of each outcome?
If we bet $110 on Denver -3.5, we have a possible payout of $0 for a loss or $210 for a win.
If we bet $110 on Oakland +3.5, we have a possible payout of $0 for a loss or $210 for a win.
We only have these two possible outcomes. We take the amount we risk and divide it by the total payout to get the implied probability for each outcome:
Denver covers: $110/$210=.524 or 52.4%
Oakland covers: $110/$210=.524 or 52.4%
If we add these two outcomes, we get 104.8%. This means that if we bet both teams, we would need to risk $104.8 to get back $100. The bookies clearly have the edge here, in this case a 4.8% house edge for each dollar wagered.
How do the odds and implied probabilities change for odds other than -110?
The same NFL game has a moneyline of
What is the implied probability of each outcome, ignoring pushes?
If we bet $190 on Denver, we have a possible payout of $0 for a loss or $290 for a win.
If we bet $100 on Oakland, we have a possible payout of $0 for a loss or $260 for a win.
If we ignore pushes, we only have these two possible outcomes. Again we take the amount we risk and divide it by the total payout to get the implied probability for each outcome:
Denver wins: $190/$290=.655 or 65.5%
Oakland wins: $100/$260=.385 or 38.5%
If we add these two outcomes, we get 104%. Again, if we bet both teams, we automatically lose, this time $4 for every $100 wagered in the long run. This extra juice is the bookie’s edge.
Implied Probability in the Sports Betting Futures Market
Finally, let us check the implied probability for the sports betting futures market, where there are more than 2 possible outcomes.
For the World Cup soccer tournament, there might be a futures market listed as follows:
What is the implied probability of each team winning? Again, remember that we must divide our amount risked by the total payout to get the implied probability %.
Brazil: 100/500=.2 or 20%
Germany: 100/900=.111 or 11.11%
Argentina: 100/1000=.1 or 10%
Italy: 100/1150=.087 or 8.7%
USA: 100/3600=.028 or 2.8%
Field: 100/200=.5 or 50%
Adding all these percentages, we come up with 102.61%. The house edge in this market is actually pretty low, only 2.61%. You can see that the field has a very high probability of winning in this case. Taking the field just means that, in this market, any team other than Brazil/Germany/Argentina/Italy/USA will win the World Cup. Based on these odds, that’s about a 50/50 chance.
Implied probability is useful in many aspects of markets, especially sports betting. If you have the listed odds, you can figure out the implied probability of an event happening. If you find a team that has a low implied probability, but you think is primed for the upset, you may have a solid bet on your hands. However, the bookies usually don’t mind taking bets on underdogs or long shot teams, because their house edge is built in to each side, and your winnings will be paid out mostly from other bettors who laid the extra juice to play the favorite. Tread carefully but have fun!
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To convert betting odds to probability, you must use the selection’s chance of winning as the numerator and divide by the total number of chances (both winning and losing). For instance, if the odds are 5.00, the probability equals 1 / 1 + 4) = 1/5 or 20%.
Implied probability suggests the likelihood of an outcome happening. It is calculated by dividing one by the decimal odds. Therefore, if Manchester United are given odds of 2.50 to win a match, their implied probability of winning is 0.4 (40%). This is how successful bettors find value bets.
Many people wrongfully assume odds and probabilities are the same thing. Odds are ratios between outcomes happening, while a probability is the ratio between an outcome and all possible outcomes.