An affine per-unit reward barely separates skill levels; a compounding one does
Fact
A reward shaped base * (k + m*quality) is affine in quality, so the ratio between a flawless unit and a merely good one is bounded and usually small. At 0.35 + 0.85q, quality 1.0 pays 1.20 and quality 0.85 pays 1.07 — a 12% edge for the difference between perfect and good.
When the failure condition is a fixed cost growing against a capped throughput, that 12% buys almost no extra survival: expert and competent play die at nearly the same point, and the run length stops reporting skill.
A multiplier that compounds across consecutive successes fixes the top end without touching the bottom, because only sustained quality reaches it. Measured on one game with everything else held constant, adding a streak multiplier on the tip (×1 to ×2 over ten clean units, reset by any lapse) moved median days survived from 17 to 24 for a flawless bot and 15 to 20 for a good one — the gap between them doubled.
Why it matters
The flat top end is easy to misread as "the game is too hard" or "the ramp is too steep", and both readings lead to changing the difficulty curve, which moves every skill level together and leaves them just as indistinguishable.
It also shows up late: the levels separate fine early, when the cost is well below the income ceiling, and converge only in the endgame where the score is actually decided.
How to apply
- Check the payout ratio between a perfect and a merely good unit before tuning anything else. If it is under about 1.2x, no amount of curve adjustment will separate them.
- Add the compounding term to the discretionary part of the reward (tips, bonus, combo), not the base, so a struggling player is not further punished.
- Reset it on any lapse and cap it, or it becomes the only thing that matters.
- Verify by isolation: toggle the multiplier alone, with cost and throughput fixed, and compare the gap between bots rather than either bot's absolute number.
Related: [[skill-meter-needs-escalation]], [[simulated-error-is-per-decision]].