- What: Probability and odds are two ways of expressing the same thing — a YES share at 65¢ means the market assigns 65% probability; converting between formats is the foundation of every profitable trade.
- Why it matters: If you can't translate market prices into probabilities and compare them to your own estimates, you can't identify whether a trade has positive expected value.
- Key formula: Edge = Your probability estimate − Market implied probability. Any positive edge, sized with Kelly Criterion, is a mathematically sound bet.
- Bottom line: Track your Brier score over 100+ trades — if it's below 0.20, your probability estimates are well-calibrated and your edge is real, not lucky.
Implied Probability
In a binary prediction market, the YES share price is the implied probability. There is no conversion needed:
This elegant property is what makes prediction markets so powerful as forecasting tools — the probability estimate is always real-time, and always backed by real money. Compare this to traditional polls, where "probability" is either unstated or estimated by a model.
Expected Value (EV)
Expected Value is the mathematical expectation of a trade — how much you should expect to win (or lose) on average per dollar bet, given your true probability estimate.
Market: YES at 62¢. You estimate true probability = 75%.
Profit if YES resolves YES = $1.00 − $0.62 = $0.38 per share
Cost if YES resolves NO = $0.62 per share
EV = (0.75 × $0.38) − (0.25 × $0.62) = $0.285 − $0.155 = +$0.13 per share
→ At 100 shares ($62 invested), expected profit = +$13. Positive EV — buy YES.
The Kelly Criterion
The Kelly Criterion, developed by mathematician John Kelly Jr. at Bell Labs in 1956, defines the optimal fraction of your bankroll to wager in order to maximise long-run geometric growth while preventing ruin.
For Polymarket, b = (1 − market_price) / market_price (the odds the market offers).
YES price: 60¢. Your true probability estimate: 75%.
Net odds b = (1 − 0.60) / 0.60 = 0.667
f* = (0.75 × 0.667 − 0.25) / 0.667 = (0.500 − 0.25) / 0.667 = 37.5% of bankroll
→ With a $1,000 bankroll, optimal bet = $375. Half-Kelly = $187.50 (recommended in practice).
Why Use Half-Kelly?
Full Kelly is mathematically optimal only if your probability estimate is perfectly calibrated. In practice, probability estimates are uncertain. Using half-Kelly reduces short-term drawdowns significantly while sacrificing only ~25% of long-run growth rate — a worthwhile trade-off.
Brier Scores: Measuring Forecast Accuracy
A Brier score measures the accuracy of probabilistic predictions. It is the standard metric used by Metaculus, Good Judgment, and prediction market researchers to compare forecasters.
| Brier Score | Interpretation |
|---|---|
| 0.00 | Perfect forecaster — impossible in practice |
| 0.05–0.15 | Expert-level calibration (top superforecasters) |
| 0.20–0.25 | Average participant — no better than 50/50 |
| 0.25 | Baseline: always predict 50% for everything |
| >0.25 | Actively harmful — worse than saying "I don't know" |
Calibration: The Most Important Skill
Calibration means your stated probabilities match the actual frequencies. If you say 70% on 100 different events, roughly 70 of them should happen. Most people are systematically overconfident: when they say 90%, the event happens only ~70% of the time.
To improve calibration:
- Keep a forecast log with exact probability estimates before each event resolves.
- Calculate your Brier score monthly and look for systematic over/underconfidence.
- Use reference classes as anchors before adding event-specific information.
- Prefer base-rate data from Good Judgment Open and Metaculus to calibrate your intuition.
Frequently Asked Questions
What is implied probability in prediction markets?
Implied probability is the market's consensus estimate of an event's likelihood, expressed as a percentage. It equals the contract price × 100. A YES contract at $0.68 implies 68% probability. If you believe the true probability is higher, that gap is your trading edge.
How do I calculate the Kelly Criterion for a Polymarket bet?
Use the formula: f* = (p × b − q) / b, where p = your estimated probability, q = 1−p, and b = (1−price)/price (net payout odds). For YES at 60¢ with estimated true prob of 75%: b = 0.667, f* = 37.5% of bankroll. Use half-Kelly (18.75%) in practice.
What is a Brier Score and how do I improve it?
The Brier Score measures forecast accuracy: BS = mean squared error of your probability estimates vs. actual outcomes. Lower is better (0 = perfect, 0.25 = random). Improve it by: logging all predictions with exact probabilities, computing monthly scores, using base rates as anchors before adding event-specific information, and correcting for overconfidence bias.
What is the difference between EV and win rate?
Win rate measures how often you're right. EV measures how much you make on average. A 40% win rate with a 3:1 payout is more profitable than a 70% win rate with a 0.5:1 payout. Professional traders optimise for EV, not for feeling right often. On Polymarket, this means buying low-probability events that are still underpriced — not just obvious frontrunners.
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