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    Education·9 min read

    The Math Behind Prediction Market Pricing

    Expected value, the Kelly criterion, and calibration: the three concepts that separate profitable prediction market traders from everyone else.

    The Math That Matters

    You don't need a PhD to trade prediction markets. But understanding three key concepts will put you ahead of 90% of traders.

    Most prediction market traders lose money. Not because they're bad at predicting outcomes. Many of them are actually quite good at estimating probabilities. They lose because they don't understand how to turn a probability edge into a profitable trading strategy.

    The gap between "I think this will happen" and "I should bet X dollars at Y price" is filled by math. Not complicated math, either. You don't need calculus or statistics degrees. Just three concepts that, once you internalize them, change how you think about every trade.

    1Expected value: the only number that matters

    Expected value (EV) is the average outcome if you made the same bet thousands of times. It's the single most important concept in prediction market trading.

    The Expected Value Formula

    EV = (P(win) × profit) − (P(lose) × cost)

    Positive EV Example

    You think there's a 75% chance an event happens. YES is priced at $0.60.

    EV = (0.75 × $0.40) − (0.25 × $0.60)

    EV = +$0.15 per share

    Negative EV Example

    You think there's a 60% chance. YES is priced at $0.65.

    EV = (0.60 × $0.35) − (0.40 × $0.65)

    EV = −$0.05 per share

    The rule is simple: only take trades with positive expected value. If your probability estimate says the market is underpriced, buy. If it says the market is overpriced, sell (or buy NO). If the price matches your estimate, skip it. There's no edge.

    A positive EV trade can still lose. That's fine. Over hundreds of trades, positive EV compounds into real profit. One bad outcome doesn't mean the decision was wrong.

    2The Kelly criterion: how much to bet

    Knowing a trade has positive EV tells you whether to bet. The Kelly criterion tells you how much. It's a formula that maximizes long-term growth while avoiding ruin.

    The Kelly Formula for Prediction Markets

    f* = (p × b − q) / b

    f* = fraction of bankrollp = your probabilityq = 1 − pb = payout odds

    Let's say you have a $10,000 bankroll. You estimate an event has a 70% chance of happening, and YES is priced at $0.55. The payout odds are ($1.00 − $0.55) / $0.55 = 0.818.

    Worked example

    f* = (0.70 × 0.818 − 0.30) / 0.818

    f* = (0.573 − 0.30) / 0.818

    f* = 0.273 / 0.818

    f* = 0.334 → bet 33.4% of bankroll ($3,340)

    Use fractional Kelly in practice

    Full Kelly is aggressive. Most professional traders use quarter Kelly (divide by 4) or half Kelly (divide by 2). In the example above, quarter Kelly would be $835. This sacrifices some theoretical growth rate in exchange for much smoother returns and less risk of ruin. At ClydeScan, we use quarter Kelly as our default.

    3Calibration: are you actually good at this?

    Both EV and Kelly depend on your probability estimate being accurate. If you consistently estimate 70% for events that actually happen 50% of the time, you'll lose money no matter how good your math is.

    Calibration measures whether your confidence levels match reality. A well-calibrated forecaster who says "70% likely" should be right about 70% of the time, not 90%, not 50%.

    You say 90% → it happens 92% of the timeWell calibrated
    You say 70% → it happens 71% of the timeWell calibrated
    You say 70% → it happens 50% of the timeOverconfident
    You say 50% → it happens 75% of the timeUnderconfident

    How to check your calibration

    Track every prediction you make with your confidence level. After 50+ predictions, group them by confidence bucket (60-70%, 70-80%, etc.) and check how often you were actually right. Most people discover they're overconfident, saying 80% when they should say 65%. Knowing this lets you adjust.

    4Putting it together: a real example

    Let's walk through a complete decision. Market: "Will the US unemployment rate for March be under 4.0%?" Price: $0.55 (YES).

    Decision Framework

    Step 1: Estimate probability

    BLS data shows unemployment has been 3.7-3.9% for the last 6 months. Economic indicators remain stable. No major layoff events. We estimate 78% chance it stays under 4.0%.

    Step 2: Calculate EV

    EV = (0.78 × $0.45) − (0.22 × $0.55) = $0.351 − $0.121 = +$0.23

    Step 3: Size with Kelly (quarter)

    Full Kelly = (0.78 × 0.818 − 0.22) / 0.818 = 51% → Quarter Kelly = 12.8% of bankroll

    Step 4: Check calibration adjustment

    Historical calibration data shows we're 3% overconfident in economic markets. Adjusted probability: 75%. Recalculated Kelly: 10.2%.

    This is the exact decision framework our system runs on every single trade. The numbers change, but the process is always: estimate → calculate EV → size with Kelly → adjust for calibration.

    5Why most traders skip the math (and lose)

    Most retail prediction market traders bet based on vibes. "I feel pretty confident about this" becomes a $500 bet. "This seems likely" becomes all-in. There's no framework, no sizing discipline, no calibration tracking.

    The math isn't hard. A spreadsheet or even back-of-napkin calculations will get you 80% of the way there. The hard part is consistently applying it, which is exactly why automation helps. A bot doesn't get excited about a trade and oversize it. A bot doesn't skip the EV calculation because "this one is obvious."

    The difference between a profitable prediction market trader and an unprofitable one isn't better predictions. It's better math applied to similar predictions.

    EV > 0Only positive EV trades
    ¼ KellyConservative sizing
    50+Trades to check calibration

    Math built in, no spreadsheets needed

    ClydeScan calculates EV, applies Kelly sizing, and tracks calibration automatically on every trade.