Bet builders and correlation: how the price is made

Why you can’t just multiply the odds

Put an accumulator together from separate matches and the maths is simple. Each result is independent, so you multiply the decimal odds. A 1.80 in one game and a 2.00 in another gives 1.80 times 2.00, which is 3.60. Nothing in the first match changes what happens in the second.

A bet builder breaks that assumption. Every leg comes from the same 90 minutes, so the legs aren’t independent. If one leg becomes more likely when the other happens, multiplying the two prices overstates the combined odds, because it double-counts how easy the pair is to land. The bookmaker prices the legs together, accounting for how they move with each other, then adds a margin. The result is almost always shorter than the multiplied singles.

That’s why the same two selections can look like a 3.60 accumulator across two games and a much shorter number as a same game multi on one.

What correlation means here

Correlation is just how two events move together. Two legs are positively correlated when one happening makes the other more likely, negatively correlated when one happening makes the other less likely, and independent when neither affects the other.

Football legs from the same match are rarely independent. A few concrete examples:

• Positively correlated: over 2.5 goals and a striker to score. A game with three or more goals is a game where a forward is more likely to have scored one of them. The two feed each other, so their true combined chance is higher than the two singles imply.
• Positively correlated: a team to win and that team’s winger to have two or more shots on target. A team on top tends to be the team creating chances, so the win and the attacking return tend to show up together.
• Negatively correlated: both teams to score and one team to win to nil. These pull against each other. If the underdog scores, the win-to-nil leg is already dead.
• Mutually exclusive: win to nil and both teams to score. These can’t both be true. A win to nil means the opponent didn’t score; both teams to score means they did. No bet builder will let you combine them, because the combined probability is zero.

The bookmaker’s model estimates the joint probability of the whole build, not each leg on its own. Positive correlation between legs pushes that joint probability up relative to the independent product, which pulls the fair price down.

A worked example

Take two legs, one at 1.80 and one at 2.00. Multiply them and you get 3.60, the price they’d make as a two-fold across separate matches. Now put them in the same game and assume they’re positively correlated, which most attacking bet builder legs are: over 2.5 goals at 1.80 and a named striker to score anytime at 2.00.

Because a high-scoring game and that striker scoring tend to happen together, the true chance of both landing is higher than the independent multiplication assumes. Higher chance means a shorter fair price. So before the bookmaker adds anything, the fair combined price is already below 3.60, somewhere around 3.20 to 3.30 depending on how strongly the model rates the link. Then the bookmaker adds its margin, and a typical offered price on those two legs might come out around 3.10.

The gap from 3.60 down to 3.10 has two parts:

• The correlation adjustment: the drop from 3.60 to roughly 3.20 to 3.30, because the legs aren’t independent and the naive product over-prices them.
• The margin: the further drop from that fair figure down to the 3.10 you’re actually offered, the bookmaker’s built-in edge.

You never see those two parts split out. You see one shorter number. That’s the point of pricing the build as a whole rather than as a chain of singles.

Why some combinations are blocked

Two reasons a bet builder refuses a combination.

The first is that the legs are mutually exclusive: they can’t both be true, so the combined probability is zero and there’s no price to offer. Win to nil plus both teams to score is the clean example.

The second is that the correlation is so strong the bookmaker won’t take the risk of pricing it. If two legs almost always happen together, combining them is close to backing the same thing twice at inflated odds, and the model can’t price the near-certainty of the link cleanly. Books restrict these to protect themselves. The exact blocked list isn’t published and varies between bookmakers, so the only reliable way to find out is to try adding the legs and see whether the builder accepts them.

What happens when a leg is voided

The common case is a player prop where the player doesn’t start. Your bet builder had a striker to score, and he’s named on the bench or not in the squad at all. That leg can’t win or lose, so it’s voided. What happens to the rest of your bet depends on the bookmaker’s own rules, and this is where they genuinely differ.

Which one applies is set out in each bookmaker’s own settlement rules, and it isn’t safe to assume. Some operators publish the recalculation approach plainly: Bovada’s prop builder rules state that a user-built accumulator is settled on the remaining valid legs with the odds recalculated to factor out the voided one, and only voided in full if a single leg is left standing. Others void the whole bet builder if any leg goes.

Why bet builders carry a bigger margin

Even a fairly priced-looking bet builder is worse value than the same legs as singles, because the margin is bigger. Two reasons.

Each leg already carries a margin as a single. Combine several legs and, even after the correlation adjustment, stacking multiple margined prices into one means the total edge the bookmaker holds on the build is larger than on any one leg. It’s the same reason accumulators carry more margin than singles, set out in what is the overround: every extra selection is another price with the book’s cut baked in.

On top of that, bet builders are a discretionary, model-priced product with far less competitive pressure than a headline match-odds market. A 1X2 price gets compared across dozens of books in seconds, so it’s kept tight. A specific five-leg same game multi is priced by one book’s model and almost never compared like for like, so the book can hold a wider margin without losing the business. The overround baked into a bet builder is typically well above the overround on the single markets its legs come from.

If you want to see how much margin sits inside a set of prices, the method is the same as for any market: convert to implied probability and add up, covered in how to devig odds. It’s harder to run on a bet builder, because you don’t get the fair correlated price to compare against, only the single number you’re offered. That opacity is part of why the product holds a wider edge.