The Bradley‑Terry model offers a clean way to turn head‑to‑head choices into probabilistic rankings. Instead of demanding absolute scores, it asks annotators which of two items is better, then infers hidden latent strengths for each item. When two items share equal strength the win probability is ½; larger strength gaps push the odds toward the stronger item. Its logistic‑style form lets engineers embed it in binary toolkits.

Practitioners collect counts wᵢⱼ of wins for item i over j and fit the model by maximum likelihood estimation. The log‑likelihood aggregates each pair’s contribution, and gradient descent adjusts βᵢ based on the difference between observed wins and expected wins. This iterative correction drives latent scores until predicted pairwise probabilities mirror the empirical data. The approach scales gracefully to thousands of items in practice.

Because only relative strengths matter, the model normalises one β to zero or forces the sum to a constant, yielding a coherent global ranking from noisy local judgments. Data scientists use this bridge to leverage cheap comparative labels in recommendation systems, search ranking, and evaluation of language‑model outputs, turning scattered preferences into actionable orderings. This capability improves model alignment with human preferences.