Methodology

How Polara produces institutional-grade probabilistic signals from forecaster activity.

1. Overview

Polara is a real-money binary prediction market for European macro events. Forecasters stake euros on YES/NO outcomes. The platform aggregates their positions into the Skill-Weighted Probability (SWP) — a single, auditable signal used for institutional analysis.

Unlike gambling platforms, Polara rewards forecasters who demonstrate sustained calibration over time. The more accurate your historical track record, the more your current positions influence the SWP.

2. LMSR Pricing Mechanism

Polara uses the Logarithmic Market Scoring Rule (LMSR) to price shares and determine payouts. The cost to move the market from state q to q' is:

C(q) = b × ln(e^(q_yes/b) + e^(q_no/b))

The liquidity parameter b is volume-dynamic, scaling from 300 (new market) to 1,500 (high-volume market):

b(V) = 300 + 1200 × (1 − exp(−0.0000347 × V))

where V is total volume in euros. Half-saturation is reached at €20,000 volume (b ≈ 900). This ensures early forecasters face lower slippage while deep markets maintain tighter spreads.

3. Skill-Weighted Probability (SWP)

The SWP is the primary signal. It weights each forecaster's implied probability by their skill score:

SWP = Σ(w_i × p_i) / Σw_i
w_i = CS_i × ln(1 + n_i)

where CS_i is the forecaster's Calibration Score (0–100) and n_i is their total prediction count. New forecasters receive a bootstrap prior of CS = 60 until they accumulate enough settled predictions.

The SWP is distinct from the LMSR price: it reflects who is forecasting, not just the aggregate position sizes.

4. Forecaster Scoring

Each forecaster's accuracy is measured using the Brier Score:

BS = (f − o)²

where f is the forecast probability (0–1) and o is the outcome (0 or 1). Lower is better; a random forecaster scores 0.25 on average.

The Time-Weighted Brier Score (TWBS) discounts early forecasts that were revised:

TWBS = BS × (1 − 0.30 × τ)

Calibration Score summarises performance over all settled predictions:

CS = (1 − avg_BS) × 100

Badge tiers

Superforecaster
CS ≥ 85, 50+ predictions
Senior Expert
CS ≥ 80, 30+ predictions
Expert
CS ≥ 70, 15+ predictions
Analyst
CS ≥ 55, 5+ predictions
Novice
< 5 predictions

5. Settlement Protocol

When a market's lock time passes, it enters the settling stage. Settlement follows a 4-stage process:

  1. Automated — system resolves against the linked source URL
  2. Retry — if source is unavailable, system retries after 24h
  3. Manual override — admin confirms outcome from official data
  4. Cancel — if outcome cannot be determined, market is cancelled and all positions refunded at cost

On settlement, winning shares pay €1.00 each. A 2% platform fee is deducted on the buy side at time of trade.

6. Known Limitations

  • Low volume — early markets have thin liquidity; b-value adjusts automatically
  • Binary-only structure — complex continuous outcomes are approximated as YES/NO thresholds
  • Bootstrap CS prior — new forecasters start at CS 60; this may over-weight newcomers initially
  • No short selling — forecasters can only buy YES or NO, not exit positions before settlement