Parlay legs from one game move together — and naive multiplication ignores it. What correlation does to a slip's real probability.
The independent-legs shortcut
Multiply three 50% legs and you get 12.5% — fair odds of 8.0. Every parlay calculator on the internet does exactly this. It is correct only when the legs have nothing to do with each other, and inside one NFL game that is almost never true.
Football legs pull on each other
We measured three seasons of our own game logs: a QB's passing yards and his top target's receiving yards correlate at +0.55. Passing volume tracks the game total at +0.43. A lead running back's yardage follows his team's winning margin at +0.31. Stack a QB over with his receiver's over and the game total over, and you have one bet expressed three ways — far more likely than the naive product admits.
Correlation cuts both ways
Legs can also fight: a passing-yards over next to the game-total under is asking the quarterback to rack up yards in a game with few points. The combined probability drops below the independent estimate, and a price that looks generous is anything but.
What the books do about it
Bookmakers know all of this — their same-game-parlay engines price correlation in and shade the payout accordingly. The practical takeaway: never judge an SGP price against the naive product. Judge it against a correlation-aware fair price.