# Predicting the scoring time in hockey

## TL;DR

This paper introduces a Bayesian density estimator based on a weighted beta prime distribution to predict the time until the r-th goal in hockey, leveraging past performance data and expert opinions.

## Contribution

It proposes a novel Bayesian predictive density estimator for hockey scoring times using a gamma model and weighted beta prime distribution, outperforming existing methods.

## Key findings

- Estimator outperforms existing models in prediction accuracy.
- Efficient in both historical and current NHL seasons.
- Uses ancillary information like past performance and expert opinions.

## Abstract

In this paper, we propose a Bayesian predictive density estimator to predict the time until the r-th goal is scored in a hockey game, using ancillary information such as their performances in the past, points and specialists' opinions. To be more specific, we consider a gamma distribution as a waiting scoring model. The proposed density estimator belongs to an interesting new version of weighted beta prime distribution and outperforms the other estimator in the literature. The efficiency of our estimator is evaluated using frequentist risk along with measuring the prediction error from the old dataset, 2016-17, to the current season (2018-19) of the National Hockey League.