Is the Overtime Period in an NHL Game Long Enough? An Example for Teaching Estimation and Hypothesis Testing in the Presence of Censored Data

Abstract

This note outlines an approach for introducing students to estimation and hypothesis testing with censored data using a National Hockey League example. We consider the effects of extending the overtime period in a regular season game beyond its current length of five minutes. The rationale for this change is that more games would be decided on the basis of four-on-four play rather than on a shootout. In order to make this assessment, we must estimate the parameter of the exponential distribution. We used data from the 281 NHL games that went to overtime during the 2005–2006 season. Of these, more than half went to a shootout and hence these potential observations of the time to a goal are censored and must be taken into account in the estimation. For more advanced students, we offer the mechanics of a likelihood ratio test to confirm that four-on-four play in overtime is a much different game than five-on-five in regulation play.

KEY WORDS:

• Likelihood estimates
• Statistics in sports