An analysis of curling using a three-dimensional Markov model
Bibliographic record
Abstract
Using data from 1,199 matches containing 10,933 ends in the Canadian Men’s Curling Championships, we developed both a three-dimensional empirical state space model and three-dimensional homogeneous and heterogeneous Markov models to estimate win probabilities throughout a curling match. The Markovian win probabilities were derived from the observed scoring probabilities using recursive logic. These win probabilities allowed us to answer questions regarding optimal curling strategy. When presented with the choice to score 1 point or blanking an end, we conclude that teams holding the hammer should choose to blank the end in most situations. Looking at empirical results of conceded matches, we conclude that concession behavior is consistent with a psychological win probability threshold of 2.57%. However, we also find that teams frequently concede when their win probability at time of concession is, in fact, much higher than this threshold. This is true particularly after the 9th end, suggesting that teams are conceding matches when they have up to a 15% chance of winning.
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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 | 0.007 | 0.025 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
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".