A functional data approach to model score difference process in professional basketball games
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Bibliographic record
Abstract
In this paper, we investigate the progress of score difference (between home and away teams) in professional basketball games employing functional data analysis (FDA). The observed score difference is viewed as the realization of the latent intensity process, which is assumed to be continuous. There are two major advantages of modeling the latent score difference intensity process using FDA: (1) it allows for arbitrary dependent structure among score change increments. This removes potential model mis-specifications and accommodates momentum which is often observed in sports games. (2) further statistical inferences using FDA estimates will not suffer from inconsistency due to the issue of having a continuous model yet discretely sampled data. Based on the FDA estimates, we define and numerically characterize momentum in basketball games and demonstrate its importance in predicting game outcomes.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it