We introduce several new sports team rating models based on the gradient descent algorithm. More precisely, the models can be formulated by maximising the likelihood of match results observed using a single step of this optimisation heuristic. The proposed framework is inspired by the prominent Elo rating system, and yields an iterative version of ordinal logistic regression, as well as different variants of Poisson regression-based models. This construction makes the update equations easy to interpret, and adjusts ratings once new match results are observed. Thus, it naturally handles temporal changes in team strength. Moreover, a study of association football data indicates that the new models yield more accurate forecasts and are less computationally demanding than corresponding methods that jointly optimise the likelihood for the whole set of matches.

我们介绍了基于梯度下降算法的几个新的运动队评分模型。更准确地说，可以通过使用此优化试探法的单个步骤最大化观察到的匹配结果的可能性来制定模型。拟议的框架受到著名的Elo评级系统的启发，并产生了有序逻辑回归的迭代版本，以及基于Poisson回归模型的不同变体。这种结构使更新方程式易于解释，并且一旦观察到新的匹配结果，就可以调整等级。因此，它自然可以处理团队实力的暂时变化。而且，