The floor and the ceiling
Take two legs from one game: a team wins the game (55¢) and wins the first half (52¢). Multiplied, they come to 0.55 × 0.52 = 28.6¢. But the true chance of both happening can be anywhere in a range:
- Ceiling: 52¢. Both can't happen more often than the less likely leg alone.
- Floor: 7¢. 55 + 52 − 100 = 7. Even if the legs worked against each other, they would have to overlap at least that much.
floor = max(0, P₁ + P₂ − 100) · ceiling = the smaller of P₁ and P₂
Why the multiplication misleads here
Winning the first half and winning the game are strongly related. A team that leads at halftime wins far more often than a team that trails. So the true chance of both is well above 28.6%, and a quote that looks overpriced on the simple check may be fair.
| Your estimate that both happen | Real markup on a 36¢ quote |
|---|---|
| 28.6% (no relationship) | +26% |
| 30% | +20% |
| 35% | +3% |
| 40% | −10% (below fair) |
| 45% | −20% (below fair) |
Which way do common pairs lean?
- Usually together: a team wins and its lead running back goes over his rushing yards; a quarterback's passing yards and his top receiver's yards; a lopsided win and the game going over the total.
- Usually against each other: a team wins and the opposing quarterback goes over his passing yards; an underdog wins and the favorite's running back goes over.
These are tendencies, not rules, and the market prices them in. For legs that move together, the real markup is smaller than the simple check shows. For legs that work against each other, it is larger.
A three-step check for same-game combos
- Find the floor, the legs multiplied, and the ceiling.
- Estimate where the true chance sits, given how the legs relate.
- Compare the quote with your estimate, not with the product.
