Poisson Distribution Calculator

When Poisson fits

The Poisson distribution models count data — goals in soccer, hockey goals, strikeouts, or other relatively independent scoring events. It assumes a known average rate (lambda) and estimates probability of each count.

Poisson works best for low-scoring, discrete events. High-scoring basketball totals often need more complex models because pace and correlation between teams matter more.

Over/under from expected mean

Enter your expected total (lambda) and the market line. The calculator returns over and under probabilities. Half-point lines (2.5) split cleanly; whole-number lines include push probability.

Compare model probability to implied probability from the price to estimate edge. Use the EV Calculator for stake-level expected value once you have a probability estimate.

Limitations

This is an educational model, not a picks service. Real totals depend on pace, weather, injuries, and lineup changes. Poisson ignores correlation between teams and changing game state.

Fantasy Forge does not offer live odds or automated model picks. Use this tool to learn probability math and support your own research.

FAQ

What lambda should I use?

Lambda is your expected count — average goals, points component, or strikeouts based on your model or historical rates. There is no universal default; it depends on matchup and context.

Can I use this for NFL totals?

NFL scoring is less Poisson-like than soccer goals because scoring events are structured differently. Poisson can still be a rough teaching tool for low-count props but may miss nuance on full game totals.