Odds, probability and commission: how to tell if a price is worth it
Odds are not a prize: they are a price. They tell you how likely the market thinks an event is and how much it pays if it happens. Working out whether a price is worth it means comparing two numbers: the probability inside the odds and the probability you estimate. In between there is a third number many people forget: the commission.
From odds to probability
The probability contained in odds is called implied probability and it is simply the inverse of the odds:
Odds of 2.50 correspond to 40%, odds of 2.00 to 50%, odds of 1.25 to 80%. On the exchange, in a liquid market, the implied probabilities of the best back odds add up to just over 100%: in a 1X2 market with back odds of 2.18, 3.45 and 3.75 the total is about 101.5%. With a traditional bookmaker the same total often reaches 105% or more: that difference is its margin.
Fair odds
If you think an event has a certain probability, the odds that would pay it "fairly", with no edge for anyone, are the inverse of your estimate:
If you estimate 55%, the fair odds are 1.82. Higher odds pay more than fair, lower odds pay less. But be careful: once you add commission, fair odds are no longer enough.
Expected value, commission included
On the exchange, commission is charged only on net winnings. For every euro backed, the average expected result is:
where p is your probability and c the commission. An example with 4.5% commission: you estimate 55% and find odds of 2.00.
From this you get the minimum odds worth backing, the odds at which the expected value is zero:
With 55% and 4.5% commission it comes to 1.86: higher than the fair odds (1.82). Commission raises the bar: below 1.86, even with a correct estimate, you lose on average.
And when laying?
When you lay, you collect the other person's stake if the event does not happen and pay the liability if it does. For every euro laid:
If you give the event a 30% probability and the odds are 3.00: 0.70 × 0.955 − 0.30 × 2 = +0.0685 per euro laid, against 2 euros of liability. The maximum odds worth laying are:
With 30% it comes to 3.23: above those odds, laying costs more than it returns on average.
Expected ROI
Expected value in euros means little until you compare it with what you risk. That's why we use expected ROI: expected value divided by risk. When backing, the risk is the stake, so in the 55% example the expected ROI is about +7.5%. When laying, the risk is the liability: +0.0685 on 2 euros, about +3.4%.
A positive expected ROI means that, if the estimate is right, the trade pays on average at that price. A negative one means you are paying too much, even if the event is likely.
Why a few trades prove nothing
Even with a correct estimate, results swing. Always backing at odds of 2.00, the uncertainty on the measured ROI is roughly this:
| Trades | Typical ROI swing (±1 error) | Margin to allow (±2 errors) |
|---|---|---|
| 50 | ± 14% | ± 28% |
| 100 | ± 10% | ± 20% |
| 400 | ± 5% | ± 10% |
| 1,000 | ± 3% | ± 6% |
In other words: +15% over 50 trades is compatible with a method that actually loses. Before judging an idea you need hundreds of trades, ideally split into two periods that show the same sign. Everything else is noise.
How OraGol PRO shows it
The OraGol PRO trade calculator does this maths for you: choose the market, back or lay, the stake and the odds you find, and you get the success rate according to the OraGol estimate, the fair odds, the odds from which the trade pays off (when backing) or up to which it pays off (when laying), and the expected ROI: green if the price is worth it, red if you are paying too much, commission already included. The probability is our estimate and does not change with the odds you type: the odds only tell you whether the price is good.
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