A Lipschitz–Wasserstein Framework for Modeling Reaction-Time Distributions in Video Game Design
Year: 2026
Type: article
Abstract: We present a novel framework for modeling reaction time distributions in the context of video games aimed at providing a performance tool to support the design of new levels. Modern games generate rich behavioral telemetry (including reaction times, success rates, and interaction patterns) that can be leveraged to understand player behavior and inform adaptive game design. Given a set of general parameters describing a newly designed level, the framework predicts the corresponding reaction time distribution, offering actionable insight during the design process. To address this problem, we employ a combination of statistical fitting via maximum likelihood estimation, weighted approximations, and Lipschitz-based estimators in Wasserstein space. This mathematical framework establishes the groundwork for future AI-based extensions, using metric-space learning to predict distributions for unseen level configurations. The methodology provides theoretical guarantees under mild mathematical assumptions, ensuring bounded estimation errors through the assumption of Lipschitz continuity. Three approaches are proposed, all grounded in a Lipschitz characterization of the metric model parameters, which embeds the vector representation of levels into the 1-Wasserstein space of reaction time distributions. The practical applicability of the framework is demonstrated on a dataset of 480 gameplay observations across 24 participants and 20 distinct trials, testing all three fitting procedures on a set of representative examples.
Source: Axioms
Institution: Universitat Politècnica de València
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Funder: Generalitat Valenciana
Award: G6219168559
OpenAlex ID: W7165146896