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2-Leg SGP Correlation & Fair Odds Calculator
Enter each leg’s win probability, a correlation coefficient and offered SGP odds. See feasible correlation bounds, joint probability, fair odds and expected edge.
How it works & examplesUnderstand the calculation
How two-leg SGP correlation is calculated
Let p1 and p2 be the marginal win probabilities. Under independence, joint win probability is p1 × p2. With Bernoulli correlation ρ, joint probability becomes p1p2 + ρ√(p1(1−p1)p2(1−p2)).
Correlation changes a fair combined price; the mechanical ticket payout can be checked separately in Parlay Calculator: Combined Odds & Payout.
The joint probability must stay between the Fréchet bounds max(0, p1+p2−1) and min(p1,p2). Those bounds imply the feasible minimum and maximum values of ρ.
Correlation-adjusted fair decimal odds are 1 / joint probability. Expected edge at offered odds is joint probability × offered odds − 1.
Correlation is a scenario input, not something the calculator discovers from the two marginal probabilities. Use a plausible range rather than one precise rho when the dependence is uncertain, then compare how fair odds and edge move across that sensitivity range.
Maths & verification
Adjust a two-leg same-game parlay for Bernoulli correlation and compare independent vs correlated fair odds and EV.
Try the simulator below. Input values stay in your browser; no account or money is involved.
Model assumptions: No. Virtual games use declared teaching models. Verify any actual operator’s payout rules independently.
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How to use the tool
See how correlation changes the fair price of a two-leg same-game parlay.
- Enter your estimated win probability for Leg 1 and Leg 2.
- Enter a Bernoulli correlation coefficient ρ. The calculator checks whether that correlation is mathematically feasible for the two marginal probabilities.
- Add offered SGP decimal odds to compare sportsbook break-even probability with the correlation-adjusted joint probability.
Understanding your result
If both legs have 60% win probability, independence gives 36% joint probability and fair odds 2.7778. With ρ = +0.20, joint probability rises by 0.20 × √(0.6×0.4×0.6×0.4) = 4.8 percentage points to 40.8%, giving fair odds about 2.4510.
Scope and limitations
This is a two-Bernoulli scenario model, not a full sportsbook pricing model. Real SGP pricing can depend on conditional probabilities, game state, market rules, push logic and higher-order dependencies.
Before you rely on the result
- How the calculation works
Formulas, assumptions, rounding and model limits are documented on the methodology page.
- Check the current inputs
Use the odds, RTP, fees, bonus terms or other values currently shown by the operator or market.
SGP correlation calculator: joint probability, fair odds and EV
Same-game parlay pricing is where simple multiplication breaks first. Two legs from the same event can be positively or negatively correlated, so multiplying standalone probabilities can materially misprice the joint event.
This calculator isolates that effect for two binary legs using a transparent Bernoulli-correlation model and mathematically valid Fréchet bounds.
Independence is only the zero-correlation case
If p1 = 60% and p2 = 60%, independence gives 36%. Positive correlation pushes the joint probability higher; negative correlation pushes it lower, within feasible bounds.
Binary correlation has probability-dependent limits
A correlation coefficient that is algebraically between −1 and +1 can still be impossible for the chosen marginals. The calculator therefore derives the feasible ρ interval from the joint-probability bounds.
Offered SGP odds can be compared with adjusted fair odds
Once joint probability is adjusted, fair odds and EV follow directly. This does not prove your probability or correlation assumptions are correct, but it makes the assumptions explicit.
Questions about this calculation
Why can’t correlation always be anywhere from −1 to +1?
For binary events, the marginal probabilities restrict the feasible joint probability. The Fréchet bounds therefore imply a narrower feasible correlation range in many cases.
What does positive correlation do to fair SGP odds?
For two “both must win” legs, positive correlation raises the joint win probability relative to independence and therefore lowers the fair decimal odds.
When is 2-Leg SGP Correlation & Fair Odds Calculator the right tool?
See how correlation changes the fair price of a two-leg same-game parlay.
How should I read the result from 2-Leg SGP Correlation & Fair Odds Calculator?
If both legs have 60% win probability, independence gives 36% joint probability and fair odds 2.7778. With ρ = +0.20, joint probability rises by 0.20 × √(0.6×0.4×0.6×0.4) = 4.8 percentage points to 40.8%, giving fair odds about 2.4510.
What can 2-Leg SGP Correlation & Fair Odds Calculator not tell me?
This is a two-Bernoulli scenario model, not a full sportsbook pricing model. Real SGP pricing can depend on conditional probabilities, game state, market rules, push logic and higher-order dependencies.