Implied Probability and What Odds Really Say
Learn how to convert any football price into an implied probability, remove the built-in margin to estimate a fair chance, and avoid the common misreadings of what odds really say.
A football team is listed at -200. Someone says, "The market gives them a two-in-three chance." Someone else answers, "No, it gives them a bit less than that, because of the vig." A third person adds, "Odds are not predictions at all. They are prices."
All three are partly right, and sorting them out is the point of this article. Odds contain a probability, but it is a probability wrapped in a margin and shaped by the money coming in. Learning to extract the probability, strip out the margin and keep a realistic idea of what a percentage means will help you understand a price board, whether you ever place a wager or just want to read the numbers on our odds page with more insight.
This is an explanation of arithmetic and ideas, not advice to wager. Every example is hypothetical.
From a price to a probability
If you are new to the formats themselves, our guide to how odds work covers American, decimal and fractional prices. The conversions to probability are short.
American odds
- Negative price: divide the number (without its minus sign) by that number plus 100.
- For -200: 200 / (200 + 100) = 0.667, or 66.7 percent.
- For -110: 110 / (110 + 100) = 0.524, or 52.4 percent.
- Positive price: divide 100 by the price plus 100.
- For +150: 100 / (150 + 100) = 0.40, or 40 percent.
- For +300: 100 / (300 + 100) = 0.25, or 25 percent.
Decimal odds
Divide 1 by the decimal price. A price of 2.50 gives 1 / 2.50 = 0.40, or 40 percent. A price of 1.25 gives 0.80, or 80 percent.
Fractional odds
Divide the bottom number by the sum of the two numbers. For 3/1: 1 / (1 + 3) = 0.25, or 25 percent. For 1/4: 4 / (4 + 1) = 0.80, or 80 percent.
The three methods give the same answers for the same price, as they should. A +300 price, a 4.00 price and a 3/1 price all imply 25 percent.
The break-even idea
The easiest way to understand an implied probability is to see it as a break-even point. At a given price, it is the share of the time an outcome must happen for the wager to neither gain nor lose money over many repetitions.
Take a price of -200. The implied probability is 66.7 percent. Imagine placing the same wager three times, staking 200 to win 100 each time. If you win two of the three, you gain 100 + 100 = 200 and lose 200, which is break-even. You need to win exactly two in three, or 66.7 percent, to come out even. Win less often and you lose money. Win more often and you gain.
Now take +150. The implied probability is 40 percent. Stake 100 to win 150, five times. If you win two of the five, you gain 300 and lose 300, so you break even. Two in five is 40 percent.
| Price | Break-even share |
|---|---|
| +300 | 25.0% |
| +150 | 40.0% |
| +100 | 50.0% |
| -110 | 52.4% |
| -150 | 60.0% |
| -200 | 66.7% |
| -400 | 80.0% |
This table shows something many people overlook: -110, the standard price on spread and total markets, does not imply 50 percent. It implies about 52.4 percent, so even a coin-flip bet needs to win more than half the time just to break even. That gap is the margin at work.
Why the two sides add up to more than 100 percent
In a market with two outcomes, the true chances must total 100 percent. Convert the two prices and you will find they total more.
Consider a hypothetical game with Team A at -200 and Team B at +170.
- Team A: 200 / 300 = 66.67 percent.
- Team B: 100 / 270 = 37.04 percent.
- Total: 103.70 percent.
The extra 3.70 points is the margin, often called the overround. It is how the company offering the market is paid. Our article on understanding the vig explains where it comes from and how it varies between markets.
In a spread market with both sides at -110, each side implies 52.38 percent, for a total of 104.76 percent. The margin in that case is 4.76 points.
Removing the margin to estimate a fair chance
If you want to guess what the market is saying about the real chance, you can strip the margin out. The usual method is simple: divide each implied probability by the total. This is called normalizing, or finding the no-vig probability.
For the Team A and Team B example:
- Team A: 66.67 / 103.70 = 64.29 percent.
- Team B: 37.04 / 103.70 = 35.71 percent.
These now total 100 percent. The result suggests that a margin-free market would price Team A at about 64 percent and Team B at about 36 percent.
Another example with a smaller gap: Team C at -150 and Team D at +130.
- Team C: 150 / 250 = 60.00 percent.
- Team D: 100 / 230 = 43.48 percent.
- Total: 103.48 percent.
- Normalized: Team C 57.98 percent, Team D 42.02 percent.
For a spread priced -110 on both sides, each side normalizes to exactly 50 percent. That is a useful way of saying that a spread is built to make the two sides about even.
Be aware that this method assumes the margin is spread evenly over both outcomes. Real markets can load more margin onto one side, particularly on a lopsided game, so the normalized figure is an estimate, not a precise measurement. The result is a useful rule of thumb, nothing more.
Going the other way: from a probability to a price
You can also convert a probability into odds, which is a good way to test your understanding.
- If a probability is above 50 percent, the American price is negative: -100 × p / (1 - p). For 80 percent: 100 × 0.80 / 0.20 = -400.
- If a probability is below 50 percent, the American price is positive: 100 × (1 - p) / p. For 25 percent: 100 × 0.75 / 0.25 = +300.
- For decimal, take 1 divided by the probability. For 25 percent: 4.00.
When someone describes a team as having a "one in four chance," you can now picture the price: about +300, or 4.00, or 3/1, before any margin.
Odds are not predictions
A common mistake is to treat an implied probability as the market's forecast of what will happen. A better description is that it is the price at which the market clears.
Prices reflect several things at once.
- Beliefs about the teams. Injuries, matchups and form shape opinion.
- The flow of money. If more money arrives on one side, the company may move the price to balance its exposure, even without any new football information. Terms such as public money and sharp money describe this flow.
- The company's margin. As above, the total exceeds 100 percent.
- Popular preferences. Bettors in aggregate sometimes favor well-known teams, and companies may shade prices to reflect it.
Because of these factors, a price is a mix of probability and market behavior. Treat it as information about what the market expects, and not as the truth.
Markets with more than two outcomes
Not every market is a two-way choice. A futures market, such as which team will win a division, has several outcomes, and the same logic applies with more terms to add up.
Take a hypothetical division with four teams priced at +100, +250, +400 and +600.
| Team | Price | Implied probability | After removing the margin |
|---|---|---|---|
| Team 1 | +100 | 50.00% | 44.30% |
| Team 2 | +250 | 28.57% | 25.31% |
| Team 3 | +400 | 20.00% | 17.72% |
| Team 4 | +600 | 14.29% | 12.66% |
| Total | 112.86% | 100% |
The raw total is almost 113 percent, so the margin in this imaginary market is much larger than in a single game. Futures and other markets with many outcomes tend to carry bigger margins than a point spread, which is one reason they are worth understanding before reading too much into a long-shot price. In some betting markets, studies over the years have suggested that long shots are priced as a bit more likely than they turn out to be, though how much, and in which markets, varies. Treat that as a reason for caution rather than a rule.
Practice problems
Try these before reading the answers. Each one uses the formulas above.
- A team is priced at +250. What does that imply?
- A team is priced at -125. What does that imply?
- A team is priced at 1.80 in decimal. What does that imply?
- A team is priced at 7/2 in fractional. What does that imply?
- A market has two sides, -120 and +100. What is the combined implied probability?
The answers: (1) 100 / 350 = 28.57 percent. (2) 125 / 225 = 55.56 percent. (3) 1 / 1.80 = 55.56 percent, which is the same as -125, so the two prices are equivalent. (4) 2 / 9 = 22.22 percent. (5) -120 implies 120 / 220 = 54.55 percent and +100 implies 50 percent, so the total is 104.55 percent.
If you got all five, you can read most price boards. If a calculation tripped you up, return to the formula for that format and try it again with a different number. The arithmetic is the same every time.
Reading an odds board with probabilities in mind
Our odds page lists football prices, and it is a good place to practice. Pick a game and convert the moneylines on both sides. Check whether they add up to roughly 104 or 105 percent, as is common. Then look at the spread and the total, and note that both sides are priced near -110, which implies roughly even chances on each side. Finally, compare a game with a heavy favorite against one with an even matchup and see how the percentages differ.
You will begin to notice that a lopsided game has a more extreme moneyline but the spread still sits near an even price. That is not a contradiction. A spread is designed to turn an uneven matchup into an even question, and the moneyline asks the original question about who wins outright. The two markets measure different things.
Another good habit is to check how a price changes over the week. Compare it with the earlier number and ask what changed: an injury, new information or simply the money coming in. The injuries page will often explain the answer, and reading the two together makes both clearer.
What a percentage really means
Even when a probability is accurate, people misread it. A 70 percent chance is not a promise. It means that in many repeated situations, the outcome would occur about seven times in ten and fail about three times in ten. Football is a game of small samples. Each team plays a short season, and results can swing on a bounce of the ball, a penalty or an injury.
Here are some ways to keep the idea in perspective.
- A favorite at 75 percent loses one time in four. If you watched four such games, you would not be surprised to see one upset.
- A single result tells you little. If a 70 percent favorite loses, the price was not necessarily wrong. The 30 percent happened.
- Streaks are not evidence. A run of correct or incorrect outcomes can arise by chance. Our guide to why betting systems fail examines this.
- Rare things happen. A price of +5000 implies about 2 percent, and 2 percent events occur regularly across a whole league and season.
When people say "the odds were against it," they often mean that the outcome was less likely, not impossible.
Where implied probability is used
Understanding the idea has uses beyond the betting world.
- Reading a preview. When an article says a team is "a 3-point favorite," you can think about the rough chance that implies, though a spread is not the same as a moneyline.
- Comparing opinions. If you believe a team has a different chance than the price implies, the difference is the starting point for the concept of expected value. Our article on expected value explains how to think about it. Having an opinion does not make it correct, and most opinions are no better than the market's.
- Evaluating claims. If someone says a pick is "a lock," you can look at the price. A lock would have an implied probability near 100 percent, and no football game does.
- Understanding fantasy and pool decisions. Players in survivor pools and pick'em contests use probabilities to plan, as the pool guides in our fantasy section describe.
A caution
Sports betting is legal only in some places and only for adults of legal age. Understanding probability does not guarantee anything about outcomes, and wagering carries a real risk of loss. The National Problem Gambling Helpline, 1-800-GAMBLER, is available to anyone who is worried about their own habits or someone else's.
The short version
- Implied probability is a price converted to a percentage, and it is the break-even win rate at that price.
- A standard -110 price implies about 52.4 percent, not 50 percent.
- The implied probabilities of all outcomes add up to more than 100 percent because of the margin.
- Divide each probability by the total to remove the margin and estimate a fair chance.
- A price is not a prediction: it blends opinion, money flow and margin.
- A 70 percent chance fails 30 percent of the time, and a single result proves little.