Bayesian Mispricing: The Spec in Plain English
You don't need a statistics degree to understand how this scanner works. You need one idea: two independent opinions are more valuable than one.
That's the whole thing. Let me show you how it plays out.
Start Here: What Is a Mispricing?
Polymarket is a prediction market where you trade YES or NO shares on real-world events. If a market trades at 60 cents, the crowd thinks there's a 60% chance the event resolves YES.
A mispricing is when that 60% is wrong — when the real probability is materially different from what the crowd is pricing. If the true probability is 70%, you can buy YES at 60 and expect to profit over time. That's the edge.
The problem is: how do you know the true probability? You don't. But you can build a reasonable estimate by combining multiple independent signals. The more independent the signals — and the more they agree — the more confident you can be.
Two Signals
The scanner uses two agents.
Agent A is a price comparison. Kalshi often lists the same question as Polymarket. When it does, Kalshi's price is an independent crowd estimate from a completely different pool of traders. If Polymarket says 55% and Kalshi says 68%, you have two crowds disagreeing. That disagreement is information.
How much weight you give the Kalshi signal depends on volume. If Kalshi has ten times more money on the question, it carries a lot of weight. If it's a thin Kalshi market with light trading, the signal is weaker. The math uses a log-scale volume ratio: higher volume relative to the Polymarket market = higher confidence weight, capped at 75%.
Agent B is an AI probability estimate. Claude Haiku reads the market question and produces an independent probability estimate with a confidence score. It's drawing on what it knows about the event, base rates, and context. Claude is limited to a 50% max confidence weight — it can never be the only voice. It's a second opinion, not a verdict.
If there's no Kalshi match, Agent A goes silent. Agent B always runs.
The Blend (Bayesian Update)
Here's the key move. The market price — 55¢ in our example — is the starting point. The prior. We trust the crowd's base estimate.
Then we update it with each signal.
The formula is a weighted average: new estimate = (1 − confidence) × prior + confidence × signal.
So if Agent A (Kalshi at 68¢) has 40% confidence, and Agent B (Claude at 62¢) has 35% confidence, the math produces a posterior somewhere above 55¢ — pulled in the direction both signals are pointing.
If the two signals disagree with each other, they partially cancel out. If they both point the same way, the effect is stronger. The swarm output is the weighted average of the posterior estimates from both agents.
Flagging the Edge
The scanner calculates the gap between the swarm's probability and the Polymarket price.
- Gap ≥ 5pp → FLAGGED
- Gap ≥ 8pp → HIGH CONFIDENCE
A 5pp edge on a market trading at 55¢ means the swarm thinks it's worth 60¢ (or 50¢ in the other direction). That's meaningful. Over enough similar trades, a consistent 5pp edge compounds.
A HIGH CONFIDENCE flag at 8pp means both signals strongly agree the market is mispriced. Pro subscribers get an alert email when these appear.
Kelly Sizing
Once you have an edge, the natural question is: how much do I bet?
Kelly criterion answers that. The formula takes your probability estimate, the market price (which determines your payout), and tells you the mathematically optimal fraction of your bankroll to risk.
The scanner uses quarter-Kelly — that's 25% of the full Kelly fraction. Full Kelly is theoretically optimal but aggressive. Quarter-Kelly gives you most of the long-run growth while dramatically cutting variance. You win slower, you stay in the game longer.
There's also a hard cap: no single bet exceeds 5% of bankroll, regardless of the Kelly output. And a 2% transaction cost is already baked in — that covers Polymarket's fee plus expected slippage.
The number you see in the tool (e.g., 3.2%) is your suggested position size as a percent of your trading bankroll.
What You Actually Do With This
You see a market flagged at +9pp YES. The scanner says the swarm thinks it's 73% and Polymarket is at 64%.
Before you trade, you ask: does this make sense? Is there something I know that explains the gap? Is there a news event that moved Kalshi more than Polymarket, or vice versa? Is the question worded differently on the two platforms in a way that might cause artificial divergence?
If the gap holds up under scrutiny, you have a researched edge. You size per the Kelly number and you track your results.
The scanner finds the candidates. You make the final call.
That's the whole system. Two independent signals, Bayesian blend, Kelly sizing, human judgment at the end.
Find the gap. Trade the gap.