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[1] C茅sar A Morales. A mathematics-based new penalty area in football: tackling ping. Journal of sports sciences, 34(24):2233鈥?237, 2016.
[2] Luca Pappalardo and et al. A public data set of spatio-temporal match events in soccer competitions. Scientific data, 6(1):1鈥?5, 2019.: https://doi.org/10.6084/m9.figshare.c.4415000
[3] David Sumpter. Mathematical modelling of football, 2020.: https://uppsala.instructure.com/courses/28112
[4] David Sumpter. Soccermatics: Mathematical Adventures in the Beautiful Game Pro-Edition. Bloomsbury Publishing, 2017. 238鈥?41.
[5] Wikipedia contributors. Logistic regression 鈥?Wikipedia, the free encyclopedia, 2022.: https://en.wikipedia.org/wiki/Logistic_regression
[6] MathWorks. glmfit: Fit generalized linear regression model. 2022.: https://www.mathworks.com/help/stats/glmfit.html
