# Weighted liquidity pools: why every AMM is not fifty-fifty

A weighted pool generalizes the constant-product AMM by assigning normalized weights to its assets. Balancer’s weighted math derives prices from balances divided by their weights. An 80/20 pool is therefore not priced by the raw token-count ratio used for a simple equal-weight pair.

Evidence: [Weighted Math](https://docs.balancer.fi/concepts/explore-available-balancer-pools/weighted-pool/weighted-math.html)

Canonical: https://degreesofsatoshi.com/encyclopedia/weighted-liquidity-pools/
Published: 2026-10-02
Substantively modified: 2026-10-02
Independently verified by an automated reviewer: 2026-10-02T19:18:00.092Z
Data current through: 2026-10-02

AI-assisted research and drafting with a separate automated source-verification pass; no external expert or named human review is implied.

## Key facts

- **Weights:** Normalized asset weights sum to one. ([Weighted Math](https://docs.balancer.fi/concepts/explore-available-balancer-pools/weighted-pool/weighted-math.html))
- **Invariant:** The weighted invariant multiplies balances raised to their respective weights. ([Weighted Math](https://docs.balancer.fi/concepts/explore-available-balancer-pools/weighted-pool/weighted-math.html))
- **Spot price:** Pair prices depend on both balances and weights. ([Weighted Math](https://docs.balancer.fi/concepts/explore-available-balancer-pools/weighted-pool/weighted-math.html))

## Normalize balances before comparing

Suppose a hypothetical pool contains 80 A and 20 B with weights 80% and 20%. The normalized balances are 80 ÷ 0.8 = 100 and 20 ÷ 0.2 = 100. Their ratio gives a fee-free marginal price of one A per B under this convention.

The raw balance ratio is four, which would be the wrong shortcut. This is a marginal price, not the average price of a large swap; execution changes balances.

Evidence: [Weighted Math](https://docs.balancer.fi/concepts/explore-available-balancer-pools/weighted-pool/weighted-math.html)

## Weights change how inventory responds

For two assets, the invariant is A raised to weight A multiplied by B raised to weight B. Equal weights reduce to a transformation of the familiar constant-product relationship. Unequal weights alter how much of each asset is held at a given relative market price.

The weights describe the pool’s mathematical arrangement, not a promise that depositors avoid losses or can sell any amount at the quoted marginal price.

Evidence: [Weighted Math](https://docs.balancer.fi/concepts/explore-available-balancer-pools/weighted-pool/weighted-math.html)

## Read the pool and join method

A proportional deposit and a deposit containing only one asset have different effects on balances. Non-proportional actions can include swap-like costs. Identify the actual pool implementation, weights and add/remove-liquidity method before comparing a displayed pool-token value with a wallet’s starting assets.

Evidence: [Add/Remove Liquidity Types](https://docs.balancer.fi/concepts/vault/add-remove-liquidity-types.html); [Weighted Math](https://docs.balancer.fi/concepts/explore-available-balancer-pools/weighted-pool/weighted-math.html)

## Questions

### Does an 80/20 pool mean I must hold exactly four times as many A tokens?

No. Weights interact with relative prices. Token counts alone do not specify the value proportions when the assets have different prices.

Evidence: [Weighted Math](https://docs.balancer.fi/concepts/explore-available-balancer-pools/weighted-pool/weighted-math.html)

## Claims and scope

### weighted-liquidity-pools-quick-answer

A weighted pool generalizes the constant-product AMM by assigning normalized weights to its assets. Balancer’s weighted math derives prices from balances divided by their weights. An 80/20 pool is therefore not priced by the raw token-count ratio used for a simple equal-weight pair.

Scope: {"collection":"defi","dataAsOf":"2026-10-02","blockHeight":null}

### weighted-liquidity-pools-fact-weights

Weights: Normalized asset weights sum to one.

Scope: {"collection":"defi","dataAsOf":"2026-10-02","blockHeight":null}

### weighted-liquidity-pools-fact-invariant

Invariant: The weighted invariant multiplies balances raised to their respective weights.

Scope: {"collection":"defi","dataAsOf":"2026-10-02","blockHeight":null}

### weighted-liquidity-pools-fact-spot-price

Spot price: Pair prices depend on both balances and weights.

Scope: {"collection":"defi","dataAsOf":"2026-10-02","blockHeight":null}

## Sources

- [Weighted Math](https://docs.balancer.fi/concepts/explore-available-balancer-pools/weighted-pool/weighted-math.html) — Balancer. Unequal-weight AMM invariant and spot price. Locator: Invariant; Spot price; Swap equations. Retrieved: 2026-10-02T18:53:19.859Z.
- [Add/Remove Liquidity Types](https://docs.balancer.fi/concepts/vault/add-remove-liquidity-types.html) — Balancer. Economics of proportional and non-proportional joins/exits. Locator: Unbalanced; Single token exact out; Proportional. Retrieved: 2026-10-02T18:53:19.923Z.

## Revision history

- 2026-10-02: First publication after primary-source research and separate automated verification.

## Cite this entry

Degrees of Satoshi editorial project. “Weighted liquidity pools: why every AMM is not fifty-fifty.” Published 2026-10-02; updated 2026-10-02. https://degreesofsatoshi.com/encyclopedia/weighted-liquidity-pools/