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  "id": "weighted-liquidity-pools",
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  "collection": "defi",
  "title": "Weighted liquidity pools: why every AMM is not fifty-fifty",
  "description": "Understand how unequal pool weights change inventory and spot-price calculations without turning a pool into a guaranteed portfolio.",
  "aliases": [
    "Balancer weighted pool 80 20 explained",
    "Balancer 80 20 pool price calculation"
  ],
  "dates": {
    "published": "2026-10-02",
    "modified": "2026-10-02",
    "verified": "2026-10-02T19:18:00.092Z",
    "dataAsOf": "2026-10-02"
  },
  "authorship": {
    "publisher": "Degrees of Satoshi editorial project",
    "process": "AI-assisted research and drafting with a separate automated source-verification pass; no external expert or named human review is implied."
  },
  "quickAnswer": {
    "text": "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.",
    "claimId": "weighted-liquidity-pools-quick-answer",
    "sourceIds": [
      "x425-defi-balancer-weighted"
    ]
  },
  "keyFacts": [
    {
      "label": "Weights",
      "value": "Normalized asset weights sum to one.",
      "sourceIds": [
        "x425-defi-balancer-weighted"
      ],
      "id": "weights",
      "claimId": "weighted-liquidity-pools-fact-weights"
    },
    {
      "label": "Invariant",
      "value": "The weighted invariant multiplies balances raised to their respective weights.",
      "sourceIds": [
        "x425-defi-balancer-weighted"
      ],
      "id": "invariant",
      "claimId": "weighted-liquidity-pools-fact-invariant"
    },
    {
      "label": "Spot price",
      "value": "Pair prices depend on both balances and weights.",
      "sourceIds": [
        "x425-defi-balancer-weighted"
      ],
      "id": "spot-price",
      "claimId": "weighted-liquidity-pools-fact-spot-price"
    }
  ],
  "prerequisites": [
    "automated-market-makers"
  ],
  "sections": [
    {
      "id": "example",
      "heading": "Normalize balances before comparing",
      "sourceIds": [
        "x425-defi-balancer-weighted"
      ],
      "paragraphs": [
        "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."
      ]
    },
    {
      "id": "invariant",
      "heading": "Weights change how inventory responds",
      "sourceIds": [
        "x425-defi-balancer-weighted"
      ],
      "paragraphs": [
        "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."
      ]
    },
    {
      "id": "join",
      "heading": "Read the pool and join method",
      "sourceIds": [
        "x425-defi-balancer-joins",
        "x425-defi-balancer-weighted"
      ],
      "paragraphs": [
        "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."
      ]
    }
  ],
  "faq": [
    {
      "question": "Does an 80/20 pool mean I must hold exactly four times as many A tokens?",
      "answer": "No. Weights interact with relative prices. Token counts alone do not specify the value proportions when the assets have different prices.",
      "sourceIds": [
        "x425-defi-balancer-weighted"
      ]
    }
  ],
  "claims": [
    {
      "id": "weighted-liquidity-pools-quick-answer",
      "articleSlug": "weighted-liquidity-pools",
      "statement": "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.",
      "sourceIds": [
        "source-44508aa15cf95cd2"
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      "sourceLocators": [
        {
          "sourceId": "source-44508aa15cf95cd2",
          "locator": "Invariant; Spot price; Swap equations"
        }
      ],
      "scope": {
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        "checkedAt": "2026-10-02T19:18:00.092Z",
        "reviewer": "Independent automated verification — Codex root, separate from the DeFi drafting agent",
        "notes": [
          "Checked Balancer weighted invariant and normalized weights; 80/0.8 and 20/0.2 both equal100, giving the stated marginal ratio before fees."
        ]
      }
    },
    {
      "id": "weighted-liquidity-pools-fact-weights",
      "articleSlug": "weighted-liquidity-pools",
      "statement": "Weights: Normalized asset weights sum to one.",
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        "source-44508aa15cf95cd2"
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        "notes": [
          "Checked Balancer weighted invariant and normalized weights; 80/0.8 and 20/0.2 both equal100, giving the stated marginal ratio before fees."
        ]
      }
    },
    {
      "id": "weighted-liquidity-pools-fact-invariant",
      "articleSlug": "weighted-liquidity-pools",
      "statement": "Invariant: The weighted invariant multiplies balances raised to their respective weights.",
      "sourceIds": [
        "source-44508aa15cf95cd2"
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      "sourceLocators": [
        {
          "sourceId": "source-44508aa15cf95cd2",
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        "notes": [
          "Checked Balancer weighted invariant and normalized weights; 80/0.8 and 20/0.2 both equal100, giving the stated marginal ratio before fees."
        ]
      }
    },
    {
      "id": "weighted-liquidity-pools-fact-spot-price",
      "articleSlug": "weighted-liquidity-pools",
      "statement": "Spot price: Pair prices depend on both balances and weights.",
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        "source-44508aa15cf95cd2"
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        "notes": [
          "Checked Balancer weighted invariant and normalized weights; 80/0.8 and 20/0.2 both equal100, giving the stated marginal ratio before fees."
        ]
      }
    }
  ],
  "sources": [
    {
      "id": "x425-defi-balancer-weighted",
      "label": "Weighted Math",
      "publisher": "Balancer",
      "url": "https://docs.balancer.fi/concepts/explore-available-balancer-pools/weighted-pool/weighted-math.html",
      "locator": "Invariant; Spot price; Swap equations",
      "note": "Unequal-weight AMM invariant and spot price.",
      "version": "Documentation retrieved for the 2026-10-02 editorial scope; content hash recorded",
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    {
      "id": "x425-defi-balancer-joins",
      "label": "Add/Remove Liquidity Types",
      "publisher": "Balancer",
      "url": "https://docs.balancer.fi/concepts/vault/add-remove-liquidity-types.html",
      "locator": "Unbalanced; Single token exact out; Proportional",
      "note": "Economics of proportional and non-proportional joins/exits.",
      "version": "Documentation retrieved for the 2026-10-02 editorial scope; content hash recorded",
      "checkedAt": "2026-10-02T18:53:19.923Z",
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  "related": {
    "articles": [
      "single-sided-pool-deposits",
      "constant-product-pools",
      "impermanent-loss",
      "lp-fee-break-even",
      "stableswap-pools"
    ],
    "dossiers": [],
    "wallets": []
  },
  "revisionHistory": [
    {
      "date": "2026-10-02",
      "kind": "published",
      "summary": "First publication after primary-source research and separate automated verification."
    }
  ],
  "citation": "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/"
}