Ranking individuals by group comparison

New exponentiel model Two methods for calculations

Regularized least square Maximum likelihood

Ranking individuals by group comparison

Bradley-Terry model k individuals, m competitions I+ and I- opposing teams p vector of individual strengths

Ranking individuals by group comparison

Estimated by minimizing log likelihood Iterative approach May only find local minimum, not global

Ranking individuals by group comparison

Definitions: v vector of individual strengths T is theoretical team performance

Y is actual team performance

Ranking individuals by group comparison

Ranking individuals by group comparison

New exponential model can be derived

The old model

Ranking individuals by group comparison

New exponential model can be derived

The old model

Regularized least square

Regularized least square

Regularized least square

Regularized least square

Maximum Likelihood

Maximum Likelihood