Is the Overtime Period in an NHL Game Long Enough? An Example for Teaching Estimation and Hypothesis Testing in the Presence of Censored Data
Bibliographic record
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.060 | 0.190 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.009 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.004 | 0.008 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".