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Who is the Greatest Athlete of All Times:
A Probabilistic Rating Model (2021)

S. Yoon., M. Chang., Y. Oh., S. Yoo.

2021 International Mathematical Modeling Competition National Winner

To achieve this objective, we first identified factors that would affect determining the greatness of an athlete. These included: the number of matches, aggregated number of points, or strength of the opponent. Building the foundation to finding the GOAT of our chosen individual sport, we first examined the results of the 2018 Grand Slam tournaments. Giving each of the participants an individual rating, we were able to conclude that the great-est women’s tennis player of 2018 was Simona Halep, which was a natural result looking at the provided dataset.


To extend our model from the previous approach, we selected Men’s individual Epee Fencing for our Individual sport, and data was collected from the Olympics since 1932. We made substantial improvements upon the previous Tennis model, firstly developing a Performance Probability Distribution Function (PPDF) to represent an individual’s skill at that particular time. We then developed a Performance Indicator to quantify the performance of an athlete at each match. We used the Maximum Likelihood Estimate (MLE) method to estimate each PPDF that fitted its corresponding performance indicators. Suitable modifications were made to guarantee accuracy of the PPDFs, such as modifying the Rating Deviation of athletes during a period of non-observation by the model. (i.e. the 4 years between each Olympic)

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