How Does the Concept of “Slippage” Relate to Liquidity Pool Depth and Trade Size?

Slippage is the difference between the expected price of a trade and the executed price. It occurs because a trade changes the token ratio in the pool, thus changing the price.

Slippage is inversely related to liquidity pool depth; deeper pools (larger $k$) experience less slippage for the same trade size. Conversely, a large trade size on a shallow pool will cause significant slippage, making the trade more expensive than anticipated.