TrueSkill Through Time: Reliable Initial Skill Estimates and Historical Comparability with Julia , Python , and R

Abstract

Knowing how individual abilities change is essential in a wide range of activities. The most widely used skill estimators in industry and academia (such as Elo and TrueSkill) propagate information in only one direction, from the past to the future, preventing them from obtaining reliable initial estimates and ensuring comparability between estimates distant in time and space. In contrast, the model TrueSkill Through Time (TTT) propagates all historical information throughout a single causal network, providing estimates with low uncertainty at any given time, enabling reliable initial skill estimates, and ensuring historical comparability. Although the TTT model was published more than a decade ago, it was not available until now in the programming languages with the largest communities. Here we offer the first software for Julia, Python, and R, accompanied by a detailed overview for the general public and an in-depth scientific explanation. After illustrating its basic mode of use, we show how to estimate the learning curves of historical players of the Association of Tennis Professionals. Analytical approximation methods and message-passing algorithms allow inference to be solved efficiently using any low-end computer, even in causal networks with millions of nodes and irregular structures.