Efficient inference of rankings from multibody comparisons

Area of Science:

• Computational statistics
• Machine learning
• Sports analytics

Background:

• Many performance prediction models assume pairwise comparisons.
• Real-world contests often involve multiple entities per comparison (e.g., tournaments, games).
• The Plackett-Luce (PL) model handles multibody comparisons but faces computational challenges.

Purpose of the Study:

• To present an efficient implementation of the Plackett-Luce model for multibody comparisons.
• To validate the improved model's performance on synthetic and real-world data.
• To compare the predictive power of multibody PL models against projected pairwise models.

Main Methods:

• Developed an alternative, faster algorithm for computing Plackett-Luce rankings.
• Validated the algorithm using both simulated and actual datasets.
• Conducted cross-validation to assess predictive accuracy for unobserved comparisons.

Main Results:

• The new implementation significantly speeds up the computation of Plackett-Luce rankings.
• The Plackett-Luce model trained on multibody data shows superior predictive ability.
• Multibody comparison data leads to more accurate predictions than projected pairwise data.

Conclusions:

• Efficient Plackett-Luce modeling is crucial for analyzing complex competitive systems.
• Accounting for multibody comparisons directly improves prediction accuracy.
• The developed method enhances the applicability of the PL model to larger-scale problems.