# G-Elo: Generalization of the Elo algorithm by modelling the discretized margin of victory

arXiv: https://arxiv.org/abs/2010.11187 · HTML: https://mlsanity.com/paper/2010.11187/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2020.

## Built on by (most cited first, 6 of 6)

- [Simplified Kalman filter for online rating: one-fits-all approach](https://mlsanity.com/paper/2104.14012/) (2021)
- [Stochastic analysis of the Elo rating algorithm in round-robin tournaments](https://mlsanity.com/paper/2212.12015/) (2022)
- [FIFA ranking: Evaluation and path forward](https://mlsanity.com/paper/2201.00691/) (2021)
- [FIVB ranking: Misstep in the right direction](https://mlsanity.com/paper/2408.01603/) (2024)
- [New insights into Elo algorithm for practitioners and statisticians](https://mlsanity.com/paper/2604.03840/) (2026)
- [Score-Driven Rating System for Sports](https://mlsanity.com/paper/2604.09143/) (2026)

## Abstract (arXiv)

In this work we develop a new algorithm for rating of teams (or players) in one-on-one games by exploiting the observed difference of the game-points (such as goals), also known as a margin of victory (MOV). Our objective is to obtain the Elo-style algorithm whose operation is simple to implement and to understand intuitively. This is done in three steps: first, we define the probabilistic model between the teams' skills and the discretized MOV variable: this generalizes the model underpinning the Elo algorithm, where the MOV variable is discretized into three categories (win/loss/draw). Second, with the formal probabilistic model at hand, the optimization required by the maximum likelihood rule is implemented via stochastic gradient; this yields simple on-line equations for the rating updates which are identical in their general form to those characteristic of the Elo algorithm: the main difference lies in the way the scores and the expected scores are defined. Third, we propose a simple method to estimate the coefficients of the model, and thus define the operation of the algorithm; it is done in a closed form using the historical data so the algorithm is tailored to the sport of interest and the coefficients defining its operation are determined in entirely transparent manner. The alternative, optimization-based strategy to find the coefficients is also presented. We show numerical examples based on the results of the association football of the English Premier League and the American football of the National Football League.