Simulated player error must be sampled per decision, not per tick

Fact

Balance-testing a game with a deliberately bad bot only works if the noise model matches the grain of the decisions. Applying a miss probability inside the simulation loop does not model a bad player: at a 120Hz tick, a 35% chance of skipping the action each tick just delays it by one tick — about 8ms — because the next tick re-evaluates and acts. The survival curve stays flat no matter how high the probability goes.

Measured on an endless runner, a 35% per-tick miss rate left a bot surviving every run to the time cap. Moving the same idea to per-obstacle sampling — one timing offset and one whiff roll drawn once per obstacle — produced a clean gradient of median run lengths: 56s, 19s and 9s for ±30ms/1%, ±60ms/4% and ±100ms/10%.

Why it matters

Both readings look like results and both are wrong in a specific direction. A per-tick model reports that a punishing game is trivial, so the response is to make it harder; a bot with no handicap at all reports that a fair game is brutal, so the response is to make it easier. Either way the tuning moves away from where it should be, and the simulation keeps agreeing with itself.

How to apply

• Sample error once per decision the player actually makes — per obstacle, per shot, per turn — and hold that sample for the whole decision.
• Model timing as a continuous offset (a Gaussian on the trigger point), not as a dropped frame. Reaction error is early-or-late far more often than absent.
• Keep a separate, small whiff probability for decisions missed outright.
• Sanity-check the model before trusting the balance numbers: a perfect bot should never die on a fair game, and survival should fall monotonically as the noise rises. A flat curve means the handicap is not reaching the outcome.
• The rule governs measurement too, and there it under-reports: ticks in which nothing is being decided dilute the denominator. One "fraction of balls that cannot be reached" read 3.5% per tick and 19% per exchange.

Related: [[skill-meter-needs-escalation]].