Break-even point
The volume or utilisation level at which two options cost the same - typically API vs self-hosting, or renting vs buying a GPU. Below it, one option wins; above it, the other.
What it is
For API vs self-host: self-host $/token = GPU $/hr / (tokens per hour x utilisation). Set it equal to the API price and solve for the utilisation (or token volume) that makes them match.
Why it matters
It turns "should I self-host?" into a number you can check against your real traffic. If you are nowhere near the crossover, the decision is easy; if you are close, the softer costs (engineering, reliability, cold start) decide it.
Example
H100 at $2.50/hr, 70B model at 2M output tok/hr. At 40% utilisation: $3.13 / 1M tokens - worse than a $0.79 hosted 70B. Break-even is around 65-70% utilisation.