TLDR Tech / Crypto
How Polymarket Prices Beliefs: The Math Behind LMSR
LMSR (Logarithmic Market Scoring Rule) is the automated market maker backbone of Polymarket, solving the thin-liquidity problem that renders traditional order books unworkable for niche prediction markets by having the protocol itself always quote prices. The pricing mechanism is mathematically equivalent to the softmax function used in neural network classifiers, guaranteeing that all outcome probabilities remain valid and sum to 1.0 regardless of trade flow. The liquidity parameter b directly bounds market maker loss at b x ln(n), capping the subsidy needed to bootstrap liquidity – a binary market with b=100,000 carries a maximum loss exposure of roughly $69,315. For traders, edge is formally quantified but sequential self-induced price impact degrades average fill quality, meaning position sizing must account for both informational conviction and effective market depth.
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