The average tells you almost nothing about the far end of the range. Alternate player props ask for 100 or more receiving yards when the main line sits at 64.5, or four or more threes when it sits at 2.5. A projection mean cannot price those outcomes. You will build the full distribution from opportunities first, such as minutes, routes and attempts, then events per opportunity. A binomial three-point example shows a player expected to make 2.1 threes still has a modest chance of reaching four. You will also see how skew, overdispersion and mixed playing-time scenarios fatten the tail, and how to convert a probability into a break-even price.
Learning objectives
- Explain and apply the named analytical technique.
- Reproduce the example and critique its assumptions.
- Distinguish a model estimate from an executable market opportunity.
