How fractal complexity distorts distance and elevation gain in trail and mountain running: The case for course measurement standardization
Bibliographic record
Abstract
This study investigates how fractal complexity affects Trail and mountain running (TMR) race course measurements at varying GPS resolutions and emphasizes the need for standardized course measurement protocols. GPX files from 34 UTMB World Series race courses, including final events in Chamonix, were analyzed. Horizontal distance, elevation gain, km-effort, and fractal complexity were computed at varying GPS spatial resolutions (0.2–100 m). Elevation data were refined using a 20-cm resolution Digital Elevation Model (DEM) to ensure consistency across the dataset. The courses were systematically resampled and compared to assess the effects of spatial resolution on race measurements and classifications. The findings reveal that a decrease in GPS spatial resolution significantly reduces measured distances and elevation gains. Discrepancies in kilometer-effort reached up to 14% (mean = 7.0%, SD = 3.8%), horizontal distance up to 6.3% (mean = 2.9%, SD = 1.5%), and elevation gain up to 32% (mean = 14.0%, SD = 9.5%). Adopting a 1-m resolution, chosen for its practical balance between capturing terrain complexity at a human scale and computational efficiency, would enhance the reliability of distance, elevation gain, and km-effort calculations, ensuring fairer race classifications and improved comparability across events.
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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 | 0.018 | 0.112 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".