DV-PMI · Probability weighting
Probability Weighting Index (PWI)
Updated 2026-06-15
As of 2026-06-15, the PWI stands at 1.017 with a 52-week rolling z-score of +1.59. Alpha = 1.0 corresponds to rational pricing; values below 1 are the classical inverse-S weighting documented in Tversky and Kahneman (1992). The 13-week moving average is 0.708 and the index is computed from 1,037,734 non-bot trades this week.
Light line: weekly alpha. Bold line: 13-week moving average. An alpha of 1.0 would mean the market prices binary outcomes rationally.
Components (weighted averages across non-bot wallets)
| Component | Latest value | What it captures |
|---|---|---|
| Trade-weighted mean calibration error | 0.0184 | Absolute gap between trade price and realized frequency |
| Trade-weighted longshot fraction | 0.2869 | Share of trades at prices below 10% |
52-week rolling statistics
| Statistic | Value |
|---|---|
| Mean | 0.803 |
| SD | 0.135 |
| Min | 0.534 |
| Max | 1.034 |
| Observations | 52 |
Methodology
Each week, a one-parameter Prelec weighting function w(p) = exp(-(-log p)^alpha) is fit by weighted nonlinear least squares separately to each wallet class (active retail, sophisticated, casual, one-shot, bot). The PWI is the trade-count-weighted mean of the alphas across all non-bot wallet classes that week. Bots are excluded (trades_per_day > 50 OR n_trades > 1000) so the index reflects human probability weighting rather than algorithmic liquidity provision.
Interpretation: an alpha of 1.0 corresponds to rational pricing with no probability distortion. An alpha below 1 is the classical inverse-S weighting (small probabilities over-weighted, mid probabilities under-weighted) documented in Tversky and Kahneman (1992). An alpha above 1 implies the rarer opposite pattern. The 52-week rolling z-score requires at least 13 non-null observations and is blank before that.
Data
pwi_history.csv (163 weeks, from 2023-02-27) · pwi_latest.json · pwi_timeseries.json
Cite this index
@misc{dellavedova2026pwi,
title = {Probability Weighting Index},
author = {Della Vedova, Joshua},
year = {2026},
url = {https://jdellavedova.com/pwi}
}