In one sentence
Implied probability is the chance of an outcome that a set of odds is quoting, found by dividing 1 by the decimal odds.
How it works
Every price is a probability in disguise. Decimal odds of 2.00 say "this happens half the time", odds of 4.00 say "one time in four". Converting odds to a percentage lets you compare the market's view with your own on the same scale.
On its own an implied probability is only the market's opinion, not the truth. Bookmaker prices also include a margin, so the implied chances across all outcomes add up to more than 100%. On the Betfair Exchange the back prices usually sum close to 100%, which is why exchange prices are a cleaner read of what the market thinks.
Think of it like a currency conversion. Odds and probability are two ways of writing the same thing, and you need to convert before you can do any sums with them.
The maths
- P implied: the probability the price is quoting, between 0 and 1.
- O: the decimal odds (stake included in the return).
- O effective: the odds you really get once exchange commission is taken from winnings.
- c: the commission rate on net winnings, here 0.02 for 2%.
In plain English: flip the odds upside down to get the chance, and shrink the profit part of the odds by the commission before you do it if you want the price you actually receive.
Worked betting example
Manchester City v Arsenal at a bookmaker: Home 2.10, Draw 3.60, Away 3.80.
- Home: 1 ÷ 2.10 = 0.4762, so 47.62%.
- Draw: 1 ÷ 3.60 = 0.2778, so 27.78%.
- Away: 1 ÷ 3.80 = 0.2632, so 26.32%.
- Total: 0.47619 + 0.27778 + 0.26316 = 1.01713, so 101.71%. The extra 1.71% is the bookmaker's margin (see Overround).
Now suppose you back City on Betfair at 2.10 with 2% commission. Your profit per £1 is 1.10 × 0.98 = £1.078, so your effective odds are 2.078. The break-even chance is 1 ÷ 2.078 = 48.12%, not 47.62%.
You need City to win just over 48% of the time to stand still.
If you lay City at 2.10 for a £10 backer's stake, your liability is £10 × 1.10 = £11. You win £9.80 after 2% commission 52.38% of the time if the price is fair.
Where it's good
- Comparing your model's probabilities with the market on a common scale.
- Spotting when a bookmaker price is wildly out of line with the exchange.
- Reading in-play price moves as changes in win chance, for example a drop from 3.00 to 2.00 is a jump from 33% to 50%.
- Setting break-even targets once commission is included.
- Feeding every other method on this page list: expected value, Kelly staking and closing line value all start here.
Limitations and pitfalls
- A raw implied probability includes the bookmaker's margin, so it overstates the true chance of every outcome. Remove the margin before using it as a fair price.
- The margin is not spread evenly. Longshots usually carry more of it than favourites, so simple conversion misleads most at big prices.
- The best back price and best lay price differ. The midpoint is often a better estimate than either one.
- Forgetting commission makes marginal bets look like value when they are not.
- Implied probability tells you what the market thinks, never what will happen. It is an input, not a signal.
How to build it
- Plain Python or pandas is enough: one column divided into 1. No special library needed.
- Data: best back and lay prices at the time you would bet (Betfair historical data or the Exchange API).
- Practical tip: store both the raw implied probability and a margin-free version, and always log the commission rate alongside so you can rebuild effective odds later.
Related methods
- Overround: what you get when implied probabilities are summed.
- Margin removal: turning biased implied probabilities into fair ones.
- Expected value: combines your probability with the odds to judge a bet.
- Commission-adjusted EV: the exchange version with Betfair commission built in.