Chess Multiverse
Error Explorer.
The definitive research platform for analyzing human decision errors, time pressure blunders, and opening complexities across elite chess.
Error Explorer
Filter deep into critical blunders, inaccuracies, and time-pressure collapses.
Opening Atlas
Discover which opening systems produce the highest rate of catastrophic errors.
Event Explorer
Analyze tournament-level macro statistics and evaluation loss aggregates.
Player Profiles
Investigate individual player vulnerability profiles and opening weaknesses.
Research Dashboard
Statistical visualizations natively rendered via DuckDB SQL aggregations.
Methodology
Explore the mathematics and derivation layers behind CMEED v1.0 metrics.
Opening Atlas
Aggregation of error frequencies and evaluation drops categorized by ECO.
💡 Click on an ECO Code to instantly view all specific errors in the Explorer.
| ECO | Opening Family | Errors Logged | Blunder % | Avg Eval Loss | Pressure % | CMX-ODI |
|---|
Event Explorer
Macro-level error analysis across major tournaments and broadcasts.
💡 Click on a Tournament Name to filter the Error Explorer.
| Tournament / Event | Year | Errors Logged | Blunders | Avg Eval Loss | Pressure % |
|---|
Player Profiles
Investigate individual player vulnerability profiles.
💡 Click on a Player Name to filter the Error Explorer.
| Player | Peak ELO | Errors | Blunders | Avg Loss | Panic Avg | Top Opening |
|---|
Research Dashboard
Statistical visualizations natively rendered via DuckDB SQL aggregations.
Mathematical Framework & Derivations
The theoretical foundation and derived metrics powering CMEED v1.0.
1. Expected Score Loss (ESL)
Standard engine evaluations (measured in pawns) do not linearly correlate with game outcomes. A +2.0 advantage is massive at the grandmaster level, but the difference between +6.0 and +8.0 is negligible. To quantify human error accurately, CMEED converts raw engine evaluations into an Expected Score (ES) using a logistic function, representing the probability of winning.
Where \(k = 2.2\) is the scaling constant calibrated for elite human play. The Expected Score Loss (ESL) isolates the exact probabilistic damage a human makes in a single decision by calculating the delta between the optimal engine continuation and the played move:
This yields a percentage (0% to 100%) representing the exact amount of winning probability the player discarded.
2. Opening Danger Index (ODI)
The ODI is a proprietary composite metric designed to measure the inherent volatility and psychological difficulty of specific chess openings (categorized by ECO). It is a weighted sum of five normalized variables:
- \(w_1 = 0.28\): Error Volume \((E / E_{max})\) — Frequency of critical errors in this line.
- \(w_2 = 0.22\): Blunder Density \((B / E)\) — The ratio of severe blunders to total errors.
- \(w_3 = 0.24\): Evaluation Magnitude \((\min(\bar{\Delta e} / 4, 1))\) — Average evaluation drop, capped at 4.0 pawns.
- \(w_4 = 0.14\): Player Diversity \((P / P_{max})\) — Ensures the errors are systemic to the opening, not isolated to a single player's bad tournament.
- \(w_5 = 0.12\): Time Pressure Frequency — The percentage of errors occurring with under 60 seconds on the clock.
3. Panic Index (Time-Pressure Collapse)
To isolate cognitive collapse from general positional misunderstanding, the Panic Index evaluates specific evaluation hemorrhage when the human clock parameter \(t\) drops below critical thresholds. Given a set of moves \(M\), the Panic Index is the arithmetic mean of evaluation drops strictly where \(t < 60\) seconds:
This allows researchers to profile which players maintain cognitive stability under extreme time distress and which openings induce the highest rate of clock-management failure.
4. Reproducible Reference Analysis (Tutorials)
CMEED is designed for strict empirical reproducibility. The following case studies demonstrate how a researcher can utilize the Error Explorer and DuckDB query engine to rapidly validate behavioral hypotheses regarding elite cognitive degradation.
Academic Citations
This project yields two distinct academic outputs. Depending on your use case, please cite the dataset, the software, or both: