Polymarket Sentiment Agent: Let the LLM Read, Let the Math Decide

The core design principle

LLMs read language well and price probability badly. So the agent draws a hard line: the LLM only parses headlines into a sentiment label, never a price. A deterministic Python layer turns that label into a Bayesian posterior, and the signal is the gap between the posterior and the market-implied prior.

The separation is deliberate. Uncalibrated LLM price guesses are unreliable; calibrated Bayesian math is auditable and reproducible.

How a signal is formed

Headline
  → LLM labels sentiment
  → Bayesian update produces posterior probability
  → Edge = posterior − market-implied price
  → surface as a paper trade

Every number that touches a trade comes from the math layer, not the model. The LLM's output stays confined to what it's reliable at: reading tone and stance from text.

Serving it

A FastAPI backend exposes a status endpoint and the sentiment/posterior pipeline; a React front end inspects current signals. It runs in paper-trading mode because the goal is to test whether the Bayesian edge is real, not to move capital.

Why Bayesian, not a classifier

A posterior carries its own uncertainty. Instead of a point prediction, the agent reasons about how far a piece of news should move a belief relative to where the market already sits. When posterior and price agree, there's no edge and no trade, which is what you want from a signal generator.

Takeaway

The interesting engineering is boundary-drawing: give the LLM the narrow, language-shaped job it excels at and hand every probabilistic decision to explicit, testable math. Paper trading keeps the claims in check while the design gets validated.