Open Access Te Herenga Waka-Victoria University of Wellington
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A Novel Framework for Constructing Sport-Based Rating Systems

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posted on 2021-12-09, 07:02 authored by Ankit Patel

This doctoral thesis examines the multivariate nature of sporting performances, expressed as performance on context specific tasks, to develop a novel framework for constructing sport-based rating systems, also referred to as scoring models. The intent of this framework is to produce reliable, robust, intuitive, and transparent ratings, regarded as meaningful, for performance prevalent in the sport player and team evaluation environment. In this thesis, Bracewell’s (2003) definition of a rating as an elegant form of dimension reduction is extended. Specifically, ratings are an elegant and excessive form of dimension reduction whereby a single numerical value provides an objective interpretation of performance.  The data, provided by numerous vendors, is a summary of actions and performances completed by an individual during the evaluation period. A literature review of rating systems to measure performance, revealed a set of common methodologies, which were applied to produce a set of rating systems that were used as pilot studies to garner a set of learnings and limitations surrounding the current literature.  By reviewing rating methodologies and developing rating systems a set of limitations and communalities surrounding the current literature were identified and used to develop a novel framework for constructing sport-based rating systems which output measures of both team and player-level performance. The proposed framework adopts a multi-objective ensembling strategy and implements five key communalities present within many rating methodologies. These communalities are the application of 1) dimension reduction and feature selection techniques, 2) feature engineering tasks, 3) a multi-objective framework, 4) time-based variables and 5) an ensembling procedure to produce an overall rating.  An ensemble approach is adopted because it assumed that sporting performances are a function of the significant traits affecting performance. Therefore, performance is defined as performance=f(〖trait〗_1,…,〖trait〗_n). Moreover, the framework is a form of model stacking where information from multiple models is combined to generate a more informative model. Rating systems built using this approach provide a meaningful quantitative interpretation performance during an evaluation period. These ratings measure the quality of performance during a specific time-interval, known as the evaluation period.  The framework introduces a methodical approach for constructing rating systems within the sporting domain, which produce meaningful ratings. Meaningful ratings must 1) yield good performance when data is drawn from a wide range of probability distributions that are largely unaffected by outliers, small departures from model assumptions and small sample sizes (robust), 2) be accurate and produce highly informative predictions which are well-calibrated and sharp (reliable), 3) be interpretable and easy to communicate and (transparent), and 4) relate to real-world observable outcomes (intuitive).  The framework is developed to construct meaningful rating systems within the sporting industry to evaluate team and player performances. The approach was tested and validated by constructing both team and individual player-based rating systems within the cricketing context. The results of these systems were found to be meaningful, in that, they produced reliable, robust, transparent, and intuitive ratings. This ratings framework is not restricted within the sport of cricket to evaluate players and teams’ performances and is applicable in any sporting code where a summary of multivariate data is necessary to understand performance.  Common model evaluation metrics were found to be limited and lacked applicability when evaluating the effectiveness of meaningful ratings, therefore a novel evaluation metric was developed. The constructed metric applies a distance and magnitude-based metrics derived from the spherical scoring rule methodology. The distance and magnitude-based spherical (DMS) metric applies an analytical hierarchy process to assess the effectiveness of meaningful sport-based ratings and accounts for forecasting difficulty on a time basis. The DMS performance metric quantifies elements of the decision-making process by 1) evaluating the distance between ratings reported by the modeller and the actual outcome or the modellers ‘true’ beliefs, 2) providing an indication of “good” ratings, 3) accounting for the context and the forecasting difficulty to which the ratings are being applied, and 4) capturing the introduction of any subjective human bias within sport-based rating systems. The DMS metric is shown to outperform conventional model evaluation metrics such as the log-loss, in specific sporting scenarios of varying difficulty.


Copyright Date


Date of Award



Te Herenga Waka—Victoria University of Wellington

Rights License

Author Retains Copyright

Degree Discipline

Statistics and Operations Research

Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level


Degree Name

Doctor of Philosophy

ANZSRC Type Of Activity code


Victoria University of Wellington Item Type

Awarded Doctoral Thesis



Victoria University of Wellington School

School of Mathematics and Statistics


Bracewell, Paul; Liu, Ivy