## Usage

Step-by-step

1. Upload PGN files:

   • Upload the PGN of the player you want to analyze (suspect).
   • Upload a PGN from a reference group (same rating, similar time control, etc.).Software already comes with some small dataset from 3+0 blitz games around some ELOs.

2. Configure analysis parameters:

   • Player name: exact name to analyze.
   • Exclude name: optional, to skip that name from reference group.
   • Stockfish depth: usually between 6 and 20.
   • Opening plies to skip: e.g. 6 to ignore book moves.
   • CPU cores: how many workers to use in parallel.

3. Analyze results across the 9 statistical tabs:

   • Segmentation & KS
   • Histograms + QQ Plots
   • Fligner-Killeen
   • Mann–Whitney U
   • Control Chart
   • Bayesian Win-Rate + CP
   • Time vs. deviation
   • Robust Z-Score
   • Advantage Analysis

Statistical Tests Implemented

Method	Description
Game Phase Segmentation	Splits the analysis by opening, middlegame, and endgame
Kolmogorov-Smirnov Test	Compares cumulative CP-Loss distributions (ks_2samp())
Histograms + QQ Plots	Visual distribution comparison (go.Histogram(), stats.norm.ppf())
Fligner-Killeen Test	Tests variance homogeneity (stats.fligner())
Mann-Whitney U Test	Compares medians between groups (stats.mannwhitneyu())
Control Charts	Tracks CP-Loss trends over time (np.nanpercentile())
Bayesian Win-Rate	Models win-rate with uncertainty (scipy.stats.beta.cdf())
Time vs Deviation	Analyzes clock usage irregularities (re.search())
Robust Z-Score	Outlier detection via median absolute deviation (np.median(), etc.)
Advantage Analysis	CP-Loss grouped by position status (winning, equal, losing)

Statistical Test Descriptions

Test / Tab	Purpose
Segmentation & KS Test	Splits CP-loss into opening, middlegame, and endgame and compares distributions. Performs a Kolmogorov–Smirnov (KS) test on the full CP-loss distribution to detect distributional shifts between the suspect and reference players.
Histograms + QQ Plots	Compares the shape of log-transformed CP-loss distributions using overlaid histograms and QQ-plots to identify deviations from normality and mismatches in spread.
Fligner–Killeen Test	Evaluates variance homogeneity between suspect and reference groups. Useful to detect inconsistent behavior or variance inflation, often seen in engine-assisted play.
Mann–Whitney U Test	A non-parametric test to compare medians of CP-loss values. Checks if suspect performance is statistically better (lower CP-loss) than the reference group.
Control Chart	Visualizes suspect's CP-loss per game, overlaid with mean and percentile bounds (10th, 90th) from the reference group. Helps detect temporal anomalies or streaks of high precision.
Bayesian Win-Rate	Computes a Bayesian posterior probability that the suspect's win-rate is legitimate given expected win probability. Overlaid with CP-loss evolution for dual metric tracking.
Time vs. Deviation	Plots mean move time vs. standard deviation for each game to detect suspicious consistency in move timings. Engine users often play with unnatural regularity.
Robust Z-Score	Applies a robust outlier detection using median absolute deviation (MAD) on log(CP-loss + 1). Flags games with statistically extreme precision.
Advantage-based Analysis	Groups moves into equal, winning, or losing positions (±150 centipawns) and compares CP-loss across these categories. Helps reveal inconsistent accuracy depending on the position type.