Bet Builders: How Correlated Legs Are Priced, and Why the Margin Is Bigger Than It Looks

Pick a team to win, add over 2.5 goals, add a player to score, and a bet builder hands you one price for the lot. The price looks short next to what the same selections would pay as an ordinary accumulator, and many players conclude the sportsbook is shortchanging them. Sometimes it is. But multiplied singles are the wrong yardstick, and once you use the right one the margin on a bet builder usually turns out bigger, not smaller, than it first seemed.

Why legs from one match cannot simply be multiplied

An accumulator multiplies its legs because results in different matches are, for pricing purposes, independent. Legs from the same match are not. A team that wins is more likely to have played in a high-scoring game than a team that loses; a striker who scores makes his team's win more likely; a game with plenty of goals tends to produce more shots and corners. The legs are correlated, and the probability that they all land is not the product of their separate probabilities.

Positive correlation means the combination lands more often than independence suggests, so its fair price is shorter than the product. Negative correlation works the other way: "home win and under 1.5 goals" needs exactly a 1–0, so it lands less often than the product implies and its fair price is longer.

A worked example

Take a match where the home team's fair chance of winning is 50% and the fair chance of over 2.5 goals is also 50%.

• If the legs were independent, both would land 50% × 50% = 25% of the time. Fair price: 4.00.
• Allowing for correlation, suppose the true chance of a home win with three or more goals is 30%. Fair price: 1 ÷ 0.30 = 3.33.
• As multiplied singles at a sportsbook pricing each leg at 1.90, the accumulator would pay 1.90 × 1.90 = 3.61.
• As a bet builder, suppose the same sportsbook offers 3.00.

Against 3.61, the builder looks 17% short. That comparison is wrong, because 3.61 is the price of two independent events and these two are not. Compare 3.00 with the fair 3.33 instead: the builder implies a 33.3% chance against a true 30%, a markup of 33.3 ÷ 30 = 1.111. The margin on this two-leg builder is about 11%, more than double the 5.3% markup on each single priced at 1.90 against a fair 50%.

The numbers in the example are illustrative: nobody outside a sportsbook knows its correlation model. The structure, though, is general. A builder price has to be judged against the correlated fair probability, which cannot be read off the singles, and the sportsbook sets both the correlation estimate and the margin on top of it.

How the margin compounds as you add legs

Each leg carries its own markup, and the markups multiply. If each leg's probability is marked up by 5% and nothing else is added:

• two legs: 1.05² = 1.103, a 10.3% markup;
• three legs: 1.05³ = 1.158, a 15.8% markup;
• four legs: 1.05⁴ = 1.216, a 21.6% markup.

A 15.8% markup means the price pays about 86% of fair odds, since 1 ÷ 1.158 = 0.864. Player markets such as shots, cards and corners often carry wider margins than the match result, so a builder full of player legs compounds from a higher starting point. A two-way player market priced at 1.80 and 1.90, for instance, adds up to 1/1.80 + 1/1.90 = 108.2%: an 8.2% margin on a single leg before anything is combined. Any two-way market can be checked the same way with the margin calculator.

Uncertainty is priced in as well

The correlation between, say, a player's shots on target and his team's corners is hard to estimate. When a sportsbook is unsure, the safe direction for it is to assume the legs land together more often than they may, which shortens the price. That caution is a cost you pay on top of the leg margins, and it grows with every unusual leg you add.

What a builder refund offer is worth

Bet builders are a favourite subject for promotions, and the right terms can turn a negative-value bet into a positive one. Nomini, for example, advertises a Bet Builder offer that refunds 50% of a losing €50 slip. The value depends entirely on the form the refund takes. Take a €50 builder at 6.00 whose true chance of landing is 15%; the price implies 16.7%, an 11% markup.

• Without the offer: 50 × (0.15 × 6.00 − 1) = −€5.00 expected.
• With a €25 cash refund on a loss: the slip loses 85% of the time, so the refund adds 0.85 × €25 = €21.25. Expected value: +€16.25.
• With a €25 free bet whose stake is not returned, used at odds of 3.00 on a selection with a true 30% chance: the free bet is worth 25 × 0.30 × 2.00 = €15.00, so the refund adds 0.85 × €15 = €12.75. Expected value: +€7.75.

If the refund arrives as bonus money with its own turnover requirement, deduct the expected cost of that turnover as well. Check, too, whether builder bets count towards any welcome-offer requirement you are working through: Granawin's terms exclude bet builder bets from its sports promotions. The current welcome and free-bet offers are collected on the free bet page.

How to use bet builders without overpaying

• Never judge a builder price against multiplied singles. That comparison flatters or condemns it for the wrong reason.
• Keep the legs few. Every extra leg multiplies the markup.
• Prefer legs from deep markets such as the result, totals and handicaps over player specials, which start from a wider margin.
• Treat a combination that looks mispriced with suspicion. The obvious correlations are the ones every model handles.
• Compare the same builder at more than one sportsbook. Correlation models differ, so the same combination can be priced differently from one book to the next. The country hubs, such as the Irish betting hub, list the sportsbooks that accept players from each country.
• Value a refund at what it is paid in, not at its face value.

For legs in different matches, where the product rule does apply, the accumulator calculator multiplies the prices and the stake for you.

FAQ

Are bet builders always worse value than singles?

On margin alone, usually yes: the markups on each leg compound, and the sportsbook adds caution for correlations it cannot estimate well. A builder can still be the right bet when it expresses a view the singles cannot, or when a promotion pays enough to cover the margin.

Why is my bet builder shorter than the same legs in an accumulator?

Because the legs are positively correlated: if one lands, the others become more likely. The sportsbook prices the combination at its correlated probability, which is higher than the product of the separate legs.

Can I place the same legs as an ordinary accumulator instead?

Sportsbooks generally block selections from the same match in an ordinary accumulator for exactly this reason and route them to the builder. A multiplied price would ignore the correlation, which is why it is rarely available.

Do bet builders count towards a sportsbook bonus requirement?

It depends on the terms. Some offers exclude them outright, and others count them only above a minimum price. Read the qualifying-bet rules before you rely on a builder to clear a requirement.