Ranking of Contract Bridge Players
Y. Wang (TU Delft - Electrical Engineering, Mathematics and Computer Science)
R.J. Fokkink – Mentor (TU Delft - Applied Probability)
Huijuan Wang – Graduation committee member (TU Delft - Multimedia Computing)
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Abstract
Contract bridge is a challenging card game that combines strategic bidding, teamwork, and probabilistic outcomes. This thesis develops a rigorous mathematical framework for analyzing duplicate bridge tournaments, with a focus on fair and accurate player ranking. We introduce a threshold ranking model that extends the classic Bradley–Terry model by incorporating a tie parameter, allowing us to model the non-negligible probability of tied scores in bridge results. We derive theoretical results for this model, notably, we prove that the total match-points and number of tied boards are sufficient statistics for the estimation of players’ skill levels and the tie parameter. Using both a reference dataset from literature and the results of the 2024 China National Bridge Championship, we demonstrate that our model can reliably estimate skill parameters: the inferred rankings align with actual tournament outcomes and distinguish the strongest and weakest pairs. To complement the parametric model, we employ a fuzzy logic approach to categorize board-by-board performance into qualitative grades (“Excellent”, “Good”, etc.) and compute aggregate fuzzy performance scores. This provides an additional lens to evaluate each pair’s consistency and tendency for extreme results. The combined analysis yields a richer understanding of performance: while the statistical model emphasizes overall consistency and head-to-head advantages, the fuzzy analysis highlights variability and exceptional highs or lows. Our results show that both methods concur on the identification of top performers, reinforcing confidence in the findings, and together they reveal nuanced differences among closely ranked competitors. These insights further confirm the fairness of the duplicate format (skill prevails in the long run) while quantifying the impact of chance and strategic diversity on interim rankings.
In summary, the contributions of this thesis are: (1) a new tie-aware mathematical model for ranking players in duplicate bridge, supported by theoretical guarantees and validated by empirical data; (2) the integration of fuzzy logic metrics into bridge performance evaluation, offering practical measures of consistency; and (3) a comprehensive case study on championship data illustrating how our methods can be applied to draw meaningful conclusions about player abilities and game dynamics. This work not only advances the methodology for analyzing bridge tournaments but also provides tools and perspectives that can inform the design of fair competition systems and the training of competitive bridge players.