Volume 13, Issue 4

Applying Google’s PageRank model to sports is a popular concept in contemporary sports ranking. However, there is limited evidence that rankings generated with PageRank models do well at predicting the winners of playoffs series. In this paper, we use a PageRank model to predict the outcomes of the 2008–2016 NHL playoffs. Unlike previous studies that use a uniform personalization vector, we incorporate Corsi statistics into a personalization vector, use a nine-fold cross validation to identify tuning parameters, and evaluate the prediction accuracy of the tuned model. We found our ratings had a 70% accuracy for predicting the outcome of playoff series, outperforming the Colley, Massey, Bradley-Terry, Maher, and Generalized Markov models by 5%. The implication of our results is that fitting parameter values and adding a personalization vector can lead to improved performance when using PageRank models.

The Pythagorean win expectancy model developed by Bill James remains one of the most celebrated results in sports analytics. Many have extended the application of this model from its original use in baseball to other sports. Others have shown technical scoring conditions that imply the equivalence of win probability and the Pythagorean model. However, no explanation has been offered for why different sports yield different results beyond “that’s what the data say.” This article presents a theoretical analysis of the Pythagorean model by first deducing an exact within-team equation relating win percentage to seasonal scoring records, and then reconciling mathematically this result with the Pythagorean model which is cross-sectional across teams in a league. We derive a complete decomposition of the Pythagorean coefficient γ in terms of the exact model, and show that γ captures two key quantities – average points per game, and the average margins of victory and defeat – that together explain why different sports yield different results. We demonstrate this decomposition using the past decade of seasonal results from MLB baseball, NBA basketball, NFL football, and NHL hockey, and show that the data do reflect the properties deduced in our analysis.