Same-Game Combo Correlation: Why the Legs Aren't Independent
Multiplying leg probabilities only works when outcomes are unrelated. Inside a single game, they rarely are.
Published 2026-10-28 · Market & data intelligence · Educational, not advice.
A same-game combo pays only if every leg resolves YES. The intuitive way to price it is to multiply the legs' implied probabilities, but that only works when outcomes are independent. Inside one game they almost never are. Shared game script pushes legs together or apart, so the true joint probability is often above or below the simple product. On an exchange, buyers and sellers typically set the price of that correlation rather than a house.
A same-game combo puts several outcomes from one event into a single contract. It pays only if every leg resolves YES. For example: a team wins, total points go over a line, and a particular player clears a stat threshold. All three happen, or the contract pays nothing.
The tempting way to think about that price is to multiply. If each leg has an implied probability, the combo should be their product. That shortcut is clean and quick, and inside a single game it is usually wrong. The reason is correlation.
The multiplication rule and its fine print
Multiplying probabilities works under one condition: the events are independent, which means knowing one outcome tells you nothing about the other. A coin flip in Ohio and a coin flip in Oregon are independent. The product of their probabilities is exactly the chance that both land heads.
Outcomes inside the same game almost never meet that condition. They share the same clock, the same scoreboard, the same weather and the same game script. If one team builds a big lead early, that single fact changes how the rest of the game unfolds, for both teams and for every player on the field.
So the joint probability of two legs is not P(A) times P(B). It is P(A) times P(B given A). If B becomes more likely once A happens, the true joint probability is higher than the simple product. If B becomes less likely, it is lower.
A worked example with made-up numbers
These figures are hypothetical and only show the arithmetic. Say a contract on Team A winning trades at an implied probability of 60 percent. A contract on Team A's quarterback throwing for more than a set yardage line trades at 50 percent.
Multiply them and you get 30 percent. That would be the combo's price if the two outcomes had nothing to do with each other.
But they plausibly do. In this hypothetical, suppose that in games Team A wins, the quarterback clears the yardage line 58 percent of the time. The joint probability is then 60 percent times 58 percent, or about 35 percent. That gap between 30 and 35 is what correlation looks like in practice. The five points come entirely from the relationship between the legs.
Reverse the relationship and the number moves the other way. If the team tends to win by running the ball and protecting a lead, the yardage leg could become less likely given a win. The true joint probability would then sit below the simple product.
Positive, negative, and the direction problem
Positive correlation means the legs tend to happen together. A favorite winning comfortably and the game total going over can be linked if the favorite's offense is driving both. A player's scoring line and their team's points line share obvious mechanics, because the player's points are part of the team's total.
Negative correlation means one leg makes the other harder. Two receivers on the same team who compete for the same targets can work against one another.
The hard part is that the direction is not always obvious, and it can change with context. Whether a win goes with more passing or less depends on how a particular team tends to win. That is why pricing a combo depends less on formulas and more on modeling how a specific game might unfold.
Why this matters on an exchange
On a typical prediction market exchange, contracts trade between buyers and sellers rather than against a house. A combo contract's price, like any contract's, is set by trades between participants and can move until the outcome is known. How a given venue handles fees and market-making varies, so check each venue's rules.
In that setup, correlation is left largely to the participants. The seller of a combo is the counterparty if every leg hits, so the seller has to think about how the legs relate. The buyer is doing the same reasoning from the other side. The resulting price tends to reflect their combined view of the joint probability, rather than a formula an operator applied.
A sportsbook typically works differently. It sets its own price on a same-game combo and usually takes the other side of wagers, so the correlation adjustment is generally a number the book chooses. On an exchange, it is largely negotiated by the market.
Reading a combo price with correlation in mind
A few habits make combo prices easier to interpret:
- Compute the naive product. Multiply the individual leg prices to get a baseline. It shows what the price would be if the legs were unrelated.
- Compare it to the combo price. The difference reflects the market's implied view of correlation, along with fees and spread. A combo priced above the product suggests participants see the legs moving together. A combo priced below it suggests they see the legs pulling apart.
- Ask what single fact links the legs. Usually it is game script: who leads, by how much, and how early. If you can name the shared driver, you understand the correlation.
- Account for the spread. Combo contracts may trade less often than single legs, in which case the gap between what buyers will pay and what sellers will accept can be wider. Not all of the difference from the naive product is correlation.
None of this says whether a price is right. It explains why the number is what it is.
What comes next
Correlation is why a same-game combo cannot be priced with a calculator alone. The legs share one game, so they share one story, and the price has to account for how that story connects them. Delta Arc's Prediction Markets page covers how we approach these markets.
Next in The Line: how fees and spreads build up across multi-leg contracts, and why a combo's cost can end up more than the sum of its parts.
Sources
This explainer quotes no live prices. These are the regulator and platform pages that define how event contracts work.
References for this topic
- CFTC: Prediction markets (Learn and Protect)cftc.gov
- Kalshi Help Centerhelp.kalshi.com
- Polymarket documentation: Polymarket 101docs.polymarket.com
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