Methodology
Construction, data sources, and reproducibility notes for each published index.
Data source
All indices derive from the universe of resolved Polymarket trades on the Polygon blockchain, November 2022 to present (640M trades across 1.98M wallets as of the latest snapshot, of which a subset have resolved markets and enter the Prelec and calibration aggregations). Trades are deduplicated against the Paradigm events index and joined against the Polymarket market-to-outcome mapping.
The framework applies to any binary prediction market with public settlement data. Kalshi integration is contingent on wallet-level data access and is planned for a future release.
Wallet classification
Wallets are partitioned into five exclusive classes using Paper 1’s rule: algorithmic (more than 50 trades per active day or more than 1,000 total trades), sophisticated (more than $10K volume AND HHI less than 0.5 AND span more than 30 days), active retail (10 to 1,000 trades), casual (2 to 9 trades), and one-shot (single trade).
Indices
Probability Weighting Index (PWI)
Composite z-score of two weekly moments: mean calibration error (absolute gap between price and realized frequency, pooled across all trades) and longshot fraction (share of trades at prices below 10%). Positive PWI indicates elevated probability distortion; negative indicates compressed distortion.
Market Calibration Curve
Twenty price bins from 2.5% to 97.5%; for each bin we report the realized win rate across all non-bot trades in the pooled sample, with a binomial confidence interval. A one-parameter Prelec function (w(p) = exp(-(-log p)^alpha)) is fit by weighted nonlinear least squares with weights proportional to trade counts. Reports alpha and the fit R-squared.
Execution Edge Monitor
Weekly Prelec alpha fit separately for each wallet class. The index value is alpha(algorithmic) minus alpha(active retail) each week. A behavioral proxy for the algorithmic-retail execution divergence documented in Paper 1 (algorithmic wallets capture −4.25 bps effective spread; active retail pays +11.68 bps).
Private Information Index (PII)
Wallet-level excess accuracy (accuracy - max(p, 1-p)) with a one-sided binomial z-test. Flagging threshold is z > 2.326 (p < 0.01) with positive excess accuracy. Holm-Bonferroni and Benjamini-Hochberg family-wise and false-discovery-rate corrections reported separately. Sub-populations are split by the MNPI taxonomy (vote, action, performance, stochastic), ordered by a priori MNPI risk.
Algorithmic Share of Participation
Weekly share of counterparty events (each match contributes one maker and one taker) attributable to wallets in the algorithmic class. Counting both sides keeps the human side of the market visible: maker-only attribution would assign roughly 95% to algorithms.
Longshot / Favorite Price Gap
Realized win rate in the longshot price band (prices below 10%) minus the band midpoint (5%). Positive values indicate longshots are underpriced; negative values indicate the traditional favorite-longshot bias. Favorite-side gap is planned for a future release.
Market Efficiency Trend
Weekly R-squared of the one-parameter Prelec fit applied to active retail trades. Higher values mean the week's calibration gap is well-described by a single behavioral parameter; lower values indicate idiosyncratic shocks dominate.
Rolling statistics
Each weekly index is published with 4-, 13-, and 52-week moving averages and a 52-week rolling z-score. The z-score requires at least 13 non-null observations before reporting. The "notable movements" block on the landing page fires whenever the absolute z-score exceeds 1.0.
Refresh schedule
Indices refresh every Sunday at 22:00 Pacific time. The pipeline extracts new Polygon blocks via Alchemy, updates the processed-trade panel, re-runs all aggregations, and pushes the updated CSVs and JSONs to the public repository. Each refresh is tagged with a semantic version; each tag is archived to Zenodo with a permanent DOI.
Reproducibility
All aggregation code is in the public repository, with pinned dependencies in requirements.txt. The processed trade panel is derived from public blockchain data and is regenerable end-to-end. The CHANGELOG records every methodology change with date and rationale; breaking changes to any published column trigger a major version bump and a one-release deprecation window.
Daubert mapping
Each index design is mapped to the four Rule 702 factors. Testable: every index reports an explicit null and the test statistic is recomputable. Known error rate: permutation- validated false positive rates for the PII; bootstrap confidence intervals for the calibration and PWI. Peer review: each index is grounded in a working paper (see the research page) and in previously peer-reviewed primitives. General acceptance: the primitives (Kyle 1985, Glosten-Milgrom 1985, Fama 1972, Anand et al. 2012, Tversky-Kahneman 1992, Prelec 1998) are standard in the literature.