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<p>Time pressure and positional ambiguity are two fundamental cognitive constraints that threaten human performance in sequential decision systems such as chess. However, the interactive and nonlinear nature of these factors has not yet been sufficiently quantified. In this study, 39,922 ply-level positions from blitz games of seven elite chess players on the Lichess platform were analysed using Stockfish&#xa0;14.1 engine evaluation to examine how blunder probability varies across time pressure and positional ambiguity regimes. Cluster-robust logistic regression and histogram-based gradient boosting (HGB) models were applied comparatively and game phase included as a control variable. Permutation importance and SHAP values were used for explainability analyses. The findings reveal that blunder probability amplifies nonlinearly under the joint effect of low remaining time and high engine evaluation gap which is a pattern formally confirmed by restricted cubic spline regression (<InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\Delta \text {AIC} = 58.32\)</EquationSource></InlineEquation> relative to a log-linear baseline). The proposed Amplification Index (<span>AmpInd</span>), defined as the exponentiated interaction coefficient between extreme time pressure and positional ambiguity, showed an additional error multiplier of approximately 5.1% at a 300&#xa0;cp ambiguity level under the sub-10-second regime. This estimate remained stable across four model specifications including game phase control, sensitivity analysis, and mixed effects modeling. The HGB model achieved the highest discriminative performance (AUC <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(= 0.806\)</EquationSource></InlineEquation>), and explainability analyses confirmed positional ambiguity and time pressure as the dominant determinants of model decisions. These results demonstrate that human errors are not random but concentrate under specific combinations of cognitive constraints. We offer a quantitative framework for context-sensitive error modeling and provide generalizable findings that can form the basis for developing adaptive decision support systems in human-centered AI research.</p>

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Interpretable machine learning analysis of nonlinear error amplification under time pressure and positional ambiguity in elite blitz chess

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  • 出版模式：

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  • 发表日期：

    2026年6月26日

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  • Ali Cüvitoğlu

摘要

Time pressure and positional ambiguity are two fundamental cognitive constraints that threaten human performance in sequential decision systems such as chess. However, the interactive and nonlinear nature of these factors has not yet been sufficiently quantified. In this study, 39,922 ply-level positions from blitz games of seven elite chess players on the Lichess platform were analysed using Stockfish 14.1 engine evaluation to examine how blunder probability varies across time pressure and positional ambiguity regimes. Cluster-robust logistic regression and histogram-based gradient boosting (HGB) models were applied comparatively and game phase included as a control variable. Permutation importance and SHAP values were used for explainability analyses. The findings reveal that blunder probability amplifies nonlinearly under the joint effect of low remaining time and high engine evaluation gap which is a pattern formally confirmed by restricted cubic spline regression (\(\Delta \text {AIC} = 58.32\) relative to a log-linear baseline). The proposed Amplification Index (AmpInd), defined as the exponentiated interaction coefficient between extreme time pressure and positional ambiguity, showed an additional error multiplier of approximately 5.1% at a 300 cp ambiguity level under the sub-10-second regime. This estimate remained stable across four model specifications including game phase control, sensitivity analysis, and mixed effects modeling. The HGB model achieved the highest discriminative performance (AUC \(= 0.806\)), and explainability analyses confirmed positional ambiguity and time pressure as the dominant determinants of model decisions. These results demonstrate that human errors are not random but concentrate under specific combinations of cognitive constraints. We offer a quantitative framework for context-sensitive error modeling and provide generalizable findings that can form the basis for developing adaptive decision support systems in human-centered AI research.