Pass attempts and receiving yards in the same game tend to rise together, so why price them as if they did not? Same-game parlay correlation changes the real chance that every leg wins. This lesson starts with simple arithmetic: two 60 percent events give 36 percent if independent, but could land at 45 or 30 depending on how they depend on each other. You learn the bounds that limit any joint probability, and why a model owes you an explanation for where it falls inside them. Then you see how simulating shared game states like pace and blowouts beats running players separately. A small shift in the joint number can flip a payout from positive to negative, so the details decide whether you bet or pass.
Learning objectives
- Explain the method and key assumptions in your own words.
- Reproduce the quantitative example and check settlement equivalence.
- Identify a concrete failure mode and explain a defensible pass decision.
