Fair Price
A combination bet isn't the product of its parts. Here's why that gap exists, how we measure it, and what we have and haven't shown so far.
This is a test, not a tipping service. Nothing here is advice to place a bet. We post combinations so a record exists before kickoff and can be judged later, once enough have settled to mean anything. Nowhere near enough have.
The idea
Ask a bookmaker for two selections on one betslip and the price you're quoted is usually the two prices multiplied together. That arithmetic only works if the two events are independent, meaning the outcome of one tells you nothing about the other.
Football outcomes often aren't independent. They're driven by the same thing: how many goals each side scores. Any two selections that read off that same scoreline are related, and multiplying their prices ignores the relationship.
A worked example
These numbers are illustrative, picked to show the mechanism. They aren't a measured result from this site. Measured results, once there are enough of them, go on the Fair Price combinations page.
Take one match and two selections on it: the draw, and under 2.5 goals.
| Step | Value | Implied fair odds |
|---|---|---|
| Probability of the draw | 0.25 | 4.00 |
| Probability of under 2.5 goals | 0.45 | 2.22 |
| Multiply them, as if independent | 0.25 × 0.45 = 0.1125 | 8.89 |
| Actual probability of both together | 0.155 | 6.45 |
The two aren't independent, and the direction isn't subtle. Draws cluster in the low-scoring results. 0-0 and 1-1 are both draws and unders. Knowing the match finished level makes "under 2.5" a good deal more likely than it was beforehand. So the true joint probability sits well above the product, and the fair price is shorter: 6.45, not 8.89.
A price built by multiplication is therefore too long. That's the gap this engine looks for.
Why this isn't free money
Two things narrow the opportunity a lot, and it would be dishonest to leave them out.
Bookmakers know. Same-match combinations are the obvious case, and most firms either refuse them or price them through a correlation model of their own. Where a book already adjusts for correlation, there's no naive multiplication left to exploit. Any edge lives in the difference between their correlation model and ours, which is a much smaller and much harder claim than "they multiply and we don't".
Across separate matches, independence is roughly right. Two selections in two unrelated fixtures genuinely are close to independent, so multiplying is close to correct and there's little to find. The gap is widest exactly where books are most careful.
What's left is narrow. We'd rather say so than oversell it.
There's also something we simply can't see. No bookmaker's price for a combination is held here. The odds feed supplies the result market, the goals market and both teams to score separately, and nothing at all about same-match combinations. So "the book has this wrong" isn't a claim this site is in a position to make, and won't be made. What can be compared is one pricing method against another on identical inputs, which is what the section below sets out.
What's actually being tested
The claim was written down before any number was computed, and it's deliberately modest:
Given the same market-derived probabilities for each individual selection, a correlation-aware joint model prices the combination more accurately than multiplying those same probabilities as if independent.
Note what that doesn't say. It doesn't say the model beats the market. It takes the market's own single-selection prices as its starting point, so it can't. It doesn't say the combinations posted here will win. It says one method of combining prices is more accurate than another. Both arms of the comparison start from identical inputs, so correlation is the only thing that differs.
How the price is built
- Take the bookmaker's prices for the individual outcomes (the match result, and over or under 2.5 goals) and strip out the margin.
- Find the pair of scoring rates whose implied scoreline distribution best matches those stripped-back prices, using a Dixon-Coles adjustment that corrects the known underestimate of low-scoring results.
- Read the probability of any combination straight off that scoreline distribution instead of multiplying.
- Compare that with the price the same marginals give when multiplied as if independent. Both numbers are recorded for every combination, along with the gap between them.
The correlation parameter is fitted once per competition and then frozen, so it can't be retuned after seeing whether a combination won. The method was locked in writing before the comparison was run.
How the preferred combination is chosen
Each fixture the engine prices produces more than one possible combination. Something has to decide which one gets shown first, and that decision was written down before it was ever applied to a real fixture.
The engine computes two numbers for every combination: the joint fair price, which accounts for correlation between the legs, and the naive price, built by multiplying the single-leg market prices as if the legs were independent. The preferred combination for a fixture is the one where those two disagree most.
The gap is measured in probability, not price and not percentage. A joint probability of 8% against a naive 4% is a bigger and more real gap than 92% against 88%, even though the second pair looks identical as a percentage difference and the first would look enormous as one. Price space compresses at short odds and stretches at long ones. Percentage difference rewards long shots for no better reason than being long.
One combination per fixture, not one per day. A daily headline invites picking whichever fixture had the most dramatic gap, which quietly turns into a performance metric dressed up as a feature. Per-fixture keeps it descriptive: here's where independence would have misled you, on this match, today.
None of this claims the preferred combination is a good bet. It says nothing about whether the joint price is higher or lower than the naive one, only that the two disagree by more than any other combination on the same fixture.
What has been posted
The six-hour pre-match snapshot is wired into the serving job now, so each morning's run prices the fixtures kicking off that day and the site publishes them before those matches start. They are on the Fair Price combinations page.
Every card carries the lead time its price was made with. A price made inside four hours of kickoff is published anyway and says so on the card, rather than being held back. A page that quietly dropped some prices would disagree with the underlying record in a way you had no way of seeing, which is the same problem as posting late, arrived at from the other side.
The sample is small and will be for a good while yet. It is a record being built, not a result.
What would count as evidence
A run of winning combinations wouldn't settle this. Neither would a run of losing ones. At these sample sizes both are consistent with the method being worthless and with it being sound.
What would count is the joint model beating independent multiplication on predictive accuracy across many priced combinations, whether or not those combinations were bet. That test doesn't need us to have staked a penny, and it's the one we'll report against.