Polymarket Brier Score

Calculate prediction accuracy for any Polymarket address. Brier Score measures how close a trader's positions were to the actual outcomes — independent of PnL, position size, or trading strategy.

Why Brier Score?

PnL tells you who made money. Brier Score tells you who predicted correctly.

• High PnL + Poor Brier → Market maker or arbitrageur (earns spread, not predictions)
• Low PnL + Good Brier → Accurate predictor with small positions or conservative sizing
• High PnL + Good Brier → Skilled predictor who also sizes well — the real signal

Trigger

User asks about prediction accuracy, Brier score, prediction quality, forecasting skill, or "how accurate is this trader".

Background

The Brier Score is a standard metric in forecasting (used by Metaculus, Good Judgment Project, etc.).

Formula: BS = (1/N) × Σ(forecast_probability - actual_outcome)²

• 0.0 = perfect prediction (always right with 100% confidence)
• 0.25 = no skill (equivalent to random 50/50 guessing)
• 0.5+ = worse than random

Lower is better.

Input

Same as polymarket-profile — accepts 0x address, username, or profile URL.

Execution

Step 1: Fetch Settled Positions

curl -s "https://data-api.polymarket.com/positions?user={ADDRESS}&sizeThreshold=0&limit=100&offset=0"

Paginate until all positions are fetched (same as polymarket-profile).

Filter to settled positions only: redeemable == true.

For each settled position, extract:

• outcome: "Yes" or "No" — the side the trader held
• avgPrice: the trader's average entry price = their implied probability forecast
• currentValue > 0: whether the market resolved in their favor (won) or not (lost)

Step 2: Determine Actual Outcome

For each settled position:

• If currentValue > 0 (won): the outcome the trader bet on did happen → actual = 1
• If currentValue == 0 (lost): the outcome the trader bet on did not happen → actual = 0

Step 3: Calculate Brier Score

For each settled position:

forecast = avgPrice  (what they paid = their implied probability)
squared_error = (forecast - actual)²

Then:

brier_score = sum(squared_error) / count(settled_positions)

Step 4: Calculate Calibration Breakdown (Optional, if ≥20 settled positions)

Group positions into probability buckets by avgPrice:

For each bucket:

• Count positions
• Average forecast probability
• Actual win rate (% that resolved in their favor)
• A well-calibrated trader's win rate should be close to their average forecast

Step 5: Output

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
  Brier Score: {ADDRESS_SHORT}
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

📊 Prediction Accuracy
  Brier Score:      {score} ({rating})
  Settled Markets:  {count}
  Correct:          {wins}/{total} ({win_rate}%)

📐 Calibration
  | Confidence | Positions | Avg Forecast | Actual Win% | Gap |
  |------------|-----------|-------------|-------------|-----|
  | High       | 12        | 87%         | 83%         | -4% |
  | Moderate   | 8         | 68%         | 62%         | -6% |
  | Coin flip  | 5         | 52%         | 60%         | +8% |
  | Contrarian | 3         | 28%         | 33%         | +5% |

💡 Interpretation
  {1-2 sentence plain language summary}

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
  Generated: {timestamp} | Data: Polymarket Public APIs
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Rating Scale

Notes

• Brier Score requires settled positions. Accounts with mostly open positions will have a small sample size — flag this: "Based on N settled markets. Score reliability increases with more data."
• If fewer than 5 settled positions, output: "Not enough settled data for a meaningful Brier Score."
• avgPrice is used as the probability forecast. This is a simplification — traders who DCA (buy at multiple prices) will have a blended avgPrice. Acceptable for v0.2.
• SPLIT positions should be excluded from Brier calculation. SPLIT is a market-neutral operation (buy both sides), not a directional prediction. Identify via polymarket-profile's activity data if available, otherwise include all positions with a note.
• This score is independent of position size. A $10 bet and a $10,000 bet on the same market at the same price contribute equally. This is intentional — we're measuring prediction skill, not bankroll management.