Bibliographic record
Abstract
In Canada and in some of the northern states of the USA, there is a general excitement each spring, not only with the change in weather but also with the advent of the Stanley Cup Playoffs. A popular activity among friends and co-workers is the participation in a Stanley Cup Playoff pool. A common Stanley Cup Playoff pool proceeds along the following lines. Among K drafters (participants in the pool), an order is determined from which drafter 1 selects a hockey player from any of the 16 teams in the National Hockey League (NHL) that have qualified for the Stanley Cup Playoffs. Drafter 2 then selects a player but is not allowed to select the player chosen by drafter 1. The drafting continues until the first round is complete (i.e., drafterK has made a selection). The order of drafting is then reversed for the second round, and the process continues form rounds. At the completion of the draft, each drafter has selected a lineup of m players where each player accumulates points (i.e., goals plus assists) during the playoffs. The drafter whose lineup has the greatest number of total points is declared the winner. Typically, a monetary prize is given to the winner. Now, the question arises as to how one should select hockey players. Clearly, players who are able to generate lots of points in a game have some appeal. However, this must be tempered by the strength of a player’s team. For example, a weak team is likely to be eliminated early in the Stanley Cup Playoffs, and therefore, a good player on a weak team may not be as valuable as a weaker player on a stronger team. One might also consider the effect of the “eggs in one basket” syndrome. By choosing players predominantly from one team, a drafter’s success is greatly influenced by the success of the team. It is fair to say that it is not obvious how to best select hockey players in a draft. Although we have not come across any previous work concerning drafting in hockey pools, there is a considerable literature on the related problems of rating sports teams and predicting the outcome of sporting events. For example, Berry, Reese, and Larkey (1999) compare players of different eras in the sports of professional hockey, golf, and baseball. Carlin (1996) uses point spreads to estimate prediction probabilities for the NCAA basketball tournament. More generally, the volume edited by Bennett (1998) covers a wide range of topics related to statistical issues in sport. This paper considers a statistical approach to the player selection problem in play- off hockey pools. More detail on all aspects of the proposed approach can be found in Summers (2005). In section 15.2, some statistical modelling is proposed for the number of points scored and the number of games played by hockey players. Together with Sportsbook odds, subjective probabilities, connected graphs, Newton-Raphson optimization, and simulation, expectations concerning the total points by lineups are obtained. A key point is that the expectations are calculated in advance of the draft so that drafting may be done in real time. Friends and co-workers may not be entirely understanding if they need to wait long periods of time for a drafter to make a selection. In section 15.3, an optimality criterion is introduced for the selection of hockey players, and the optimality criterion is a simple function of the expectations derived in section 15.2. In section 15.4, we conduct a simulation study to assess the proposed selection strategy against some common ad-hoc strategies. We observe that the proposed selection strategy is arguably the best strategy. The results of an actual Stanley Cup playoff pool using our methodology are reported in section 15.5. We conclude with a short discussion in section 15.6.
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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 | 0.004 | 0.019 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.013 | 0.002 |
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".