FALL 2025

AUTHOR

Ryan Saito, Saint John’s High School

ABSTRACT

This paper offers a simulation-based framework for predicting placements in official World Cube Association (WCA) competitions. Currently, the WCA uses psych-sheet rankings, which only present a competitor’s best average of five (Ao5) and singular solve. Our goal is to create a simulation framework that uses recent performance to estimate realistic placement probabilities. We construct kernel density estimates (Gaussian KDEs with an adaptive bandwidth based on the coefficient of variation) for each competitor using their most recent twenty-five official solves, and optionally csTimer practice solves. Then, we use percentile sampling and bootstrap Ao5s to make synthetic solves across 100-1000 tournament iterations.

We also created an open-source app that shows each competitor’s probability of advancing, their expected rank, and a KDE distribution with 95% confidence and prediction intervals. We tested this tool at the Saint John’s Warm Up 2025, where it correctly predicted the podium of the competition with 80% accuracy (12 out of 15 places) and had 33% of the predictions exactly correct (5 out of 15 places). At the Rubik’s World Championships in 2025, the tool also correctly predicted the entire podium for the 3×3 event. Practically, the tool lets competitors and organizers set expectations, evaluate consistencies, and make decisions about training, seeding, and round cutoffs based on the data. It is also accessible to spectators and enthusiasts.