An order book discovers price by matching what buyers and sellers say they will accept. A liquidity pool never asks anyone, and derives a price entirely from the balances it holds.
The formula sets the price mechanically
A pool holds reserves of two assets and quotes an exchange rate determined by their ratio, following a rule the contract enforces on every trade.
Under the common constant-product rule, the product of the two reserves must not fall, so removing more of one asset requires adding progressively more of the other.
Price emerges from arithmetic rather than from opinion, which means a quote is always available regardless of whether anyone is watching.
Nobody has to be online
An order book empties when market makers withdraw, and quotes disappear exactly when volatility makes them most needed.
A pool cannot withdraw. The reserves sit there and the contract keeps quoting, which is why long-tail assets with no professional makers still trade.
The trade-off is that the pool also cannot decline a trade it should refuse, and it has no way to widen its quote when it is about to be picked off.
Arbitrage is the price discovery mechanism
Because the pool does not observe outside markets, its price only tracks them when someone profits from correcting the difference.
Arbitrageurs trade against the pool until its rate matches elsewhere, and their profit comes from the pool's liquidity providers.
The alignment is therefore purchased continuously, and its cost rises with volatility because larger and more frequent corrections are required.
Providers hold a shifting basket
A provider's share of the reserves changes composition as trades occur, accumulating whichever asset is being sold and shedding the one being bought.
The position ends up holding more of the underperforming asset, which is why the value of a share can lag simply holding both assets separately.
Fee income offsets that drift, and whether it offsets it fully depends on volume relative to how far prices moved during the period.
Concentration changed the economics
Later designs let providers allocate liquidity to a chosen price range rather than spreading it across every conceivable price.
Capital efficiency improves sharply, since depth is placed where trades actually occur, and fee income per unit of capital rises with it.
The cost is that providers must manage their ranges as prices move, which turns a passive position into an active one and reintroduces the work the original design removed.