The wave difficulty curve

Every map with waves meets the same question: how fast should the enemy get stronger? The usual answer is a single exponential percentage, and there is a reason that one number does not work.

A team's power is S-shaped, not exponential: early on income turns straight into units and it climbs fast, then the upgrades come in, and then it flattens because there is nothing left to buy. A wave written as one exponential climbs at the same rate forever.

The fix is two phases: a fast rate early so a fresh team meets a wall, and a much slower one from some round on so a grown team can keep going.

A model that counts only units will be wrong. The upgrade ladders are nearly all of the late-game power: damage, cooldown and range each multiply, so a few hundred levels is a few thousand times. Unit counts have a ceiling and ladders usually do not. Count only the units and you understate late defence by orders of magnitude.

And if the ladders are team-wide while the money comes from individual wallets, modelling one player inverts the answer: each head pays the lobby surcharge while the other six wallets that justify it are missing from the model. Seven wallets against a 2.8x price is 2.5x the buying power.

The yardstick changes too: the round of the first leak is not the wall.

The wave steps every N rounds while income arrives every round, so the margin sags before each step and recovers after it. The first leak is a dip, not the end. What to aim at is a margin that stays near 1.0, not the round where one leak happened.

Change one price and the whole balance table needs revisiting. Double a unit's price and its value per coin halves, while every other line priced against it stays where it was and is silently twice as strong. When price and value are defined against each other, you cannot change one of them alone.

Finally, a word about how a limit is enforced. In any map with a ceiling - so many turrets per player, so many units - when you enforce it matters.

A limiter that counts once a second and removes one unit per pass is not a limit. Hold or mash the key and one is created per logical pass, so about nine a second outrun the clawback and keep accumulating. And trigger-created units ignore placement rules, so they stack in the creator's own tile.

The failure that produces is distinctive. A few hundred weapon-carrying units in one tile each re-acquire a target against the wave every frame - quadratic work inside one tile, so a frame stops finishing and the game freezes rather than crashing. A freeze and a crash have disjoint cause lists, so establish which one happened before you start looking.

There is one fix: check the ceiling at the moment of creation, and increment the counter there too. A count that is a second old still lets a spammer place a full extra allowance between scans.