Attacking the shape of a game's outcome distribution — specifically its standard deviation (volatility) — rather than just the median line. Most bettors only bet the median (spread, moneyline). A model that produces a full probability distribution reveals whether the market has the right SPREAD of outcomes, not just the right center. Mismatches in implied vs. modeled volatility create distinct bet types: middles, alternate lines, and totals driven by distribution-width expectations.
Your model produces a full probability distribution for game outcomes, not just a point estimate. You compare your model's standard deviation to the market's implied standard deviation (derivable from alternate line pricing). When your model says the distribution should be wider than the market implies, you attack by taking alternate lines at both extremes (creating a middle) or backing high totals. When your model says the distribution should be narrower, you fade the extremes and target tighter outcomes. You understand that different games have different distribution shapes — not every NFL game in a week has the same volatility.
The main spread in major sports receives the most analytical attention from bookmakers and sharp bettors. Alternate lines (and their implied distribution shape) often receive much less. This creates a second-order inefficiency: the median is correct, but the variance structure is mispriced. A model that produces full distributions can find value in the alternate market even when the main spread has no edge.
When a key playmaker (QB, center, point guard) is injured, the distribution of outcomes widens — the game becomes more random because the remaining players have higher uncertainty. The market adjusts the median line for the expected average impact, but often fails to widen the distribution appropriately. The alternate lines and totals remain priced as if the game were "normal variance."