Traders often assume that trading twice as much costs twice as much in slippage. The relationship is worse than linear, and the reason sits in the shape of the order book itself.
An order book is a queue at rising prices
Resting sell orders sit at a series of price levels, each with a limited quantity. A market buy consumes the cheapest level first, then the next, then the next.
Every additional unit is therefore filled at a price at least as bad as the previous one. The average fill drifts away from the top of the book as size grows.
Slippage is the gap between that average and the price shown before the order was sent, and it is a property of the book rather than a fee anyone charges.
Depth thins as you move away from the touch
Liquidity is not spread evenly. The tightest prices carry the most size because market makers compete there, and quantities fall off further out.
So an order that exhausts the near levels enters a region where each price step buys less. Progress up the book accelerates.
This is why the second half of a large order typically costs several times what the first half did, and why quoted top-of-book depth flatters what a venue can absorb.
Market makers widen when they detect size
A large order arriving is information. It suggests someone with a view, and possibly more of the same order still to come.
Makers respond by pulling quotes and repricing, so the book that existed when the order started is not the book that fills its remainder.
The reaction is fastest on venues with automated market making, which is most of them, and it means impact partly reflects response rather than pure consumption.
Automated market makers follow a curve
On a constant-product pool the price moves along a mathematical curve, and impact rises steeply as the trade size approaches a meaningful fraction of the pool.
The formula makes this explicit rather than emergent, so impact is calculable in advance instead of being discovered on execution.
Concentrated liquidity designs pack depth into a narrow band, which reduces impact for ordinary trades and makes the cliff sharper once the band is exhausted.
Splitting orders trades impact for exposure
Breaking a large order into pieces spread over time lets the book replenish between them, which reduces total impact.
The cost is that the price can move during execution for reasons unrelated to the order, so slippage is exchanged for timing risk.
Execution algorithms exist to balance those two costs, and the right split depends on how quickly a particular market restores its depth after being hit.