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Advanced Methods for Ranking Individuals by Group Comparison

Learn about new exponential and Bradley-Terry models for ranking individuals in group comparisons, using regularized least square and maximum likelihood approaches. Understand the iterative calculation methods and how to estimate individual strengths effectively. Compare and optimize theoretical vs. actual team performances.

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Advanced Methods for Ranking Individuals by Group Comparison

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  1. Ranking individuals by group comparison • New exponentiel model • Two methods for calculations • Regularized least square • Maximum likelihood

  2. Ranking individuals by group comparison • Bradley-Terry model • k individuals, m competitions • I+ and I- opposing teams • p vector of individual strengths

  3. Ranking individuals by group comparison • Estimated by minimizing log likelihood • Iterative approach • May only find local minimum, not global

  4. Ranking individuals by group comparison • Definitions: • v vector of individual strengths • T is theoretical team performance • Y is actual team performance

  5. Ranking individuals by group comparison

  6. Ranking individuals by group comparison • New exponential model can be derived • The old model

  7. Ranking individuals by group comparison • New exponential model can be derived • The old model

  8. Regularized least square

  9. Regularized least square

  10. Regularized least square

  11. Regularized least square

  12. Maximum Likelihood

  13. Maximum Likelihood

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