climbing-grades

A Bayesian analysis of the climbing grade scale.

The accompanying manuscript (manuscript/ms-jqas-r1.tex) fits a Bayesian dynamic Bradley-Terry model to ascent data from thecrag.com for sport, trad and bouldering grades in Australia, New Zealand and Germany. The central inferential target is the slope parameter m, which describes the multiplicative increase in difficulty (d = exp(m)) per unit of grade.

Repository layout

data/processed/        Pre-cleaned ascent and route RDS files (per country)
R/                     Analysis pipeline (data prep, Stan inference, plotting)
results/{aus,nz,germany}/   Per-analysis outputs: posterior draws, diagnostics, figures, processing tables
manuscript/            LaTeX sources for the manuscript, supplement and response document
logs/                  Stdout/stderr from the run-*.R scripts (created on first run)

R dependencies

The inference scripts require: rstan, lubridate, stringr, xtable, knitr, tidyr. The package tidyjson is referenced by R/thecrag-json.R for the original JSON-to-RDS conversion of raw thecrag.com exports, but is loaded lazily so the inference pipeline runs without it once the RDS files in data/processed/ are in place.

Reproducing the analyses

The Stan models are defined in R/climbing-stan.R. Two variants are provided:

• Fixed-w (default) — the Wiener-process step SD is fixed at w = 0.5 grade units per month. This was used for all 20 main analyses.
• Joint-w — w is estimated jointly with m and the climber-grade trajectories under a HalfNormal(0, 1) prior. Selected with run.stan.climbing.model(d, estimate.w=TRUE).

The 20 main analyses are driven by R/create-all-notebooks.R, which iterates over rows of R/config.csv and renders R/bayesian-climbing-analysis.Rmd for each configuration.

For the JQAS revision we added several focused, reproducible scripts that run a single configuration and write outputs (posterior draws, convergence diagnostics, posterior figure) to the corresponding results/ directory.

Script	What it does	Reviewer comment addressed
R/run-aus-sport-diagnostics.R	Headline AUS Sport per-session run with R-hat / ESS / divergence diagnostics captured	#2 (MCMC diagnostics)
R/run-aus-sport-thresholds.R	Threshold sensitivity: AUS Sport per-session at min.ascents = 50 and 100 (≥30 already done)	#4 (threshold sensitivity)
R/run-aus-sport-every-attempt.R	AUS Sport per-session restricted to climbers who appear to log every attempt (≤5% ticks, ≤5% lonely redpoints)	#9 (every-attempt logger subset)
R/run-aus-sport-estimate-w.R	AUS Sport per-session with joint estimation of the Wiener-process step SD w (Gamma(2, 4) prior)	#3 (Wiener variance treatment)
R/run-aus-sport-prior-sensitivity.R	AUS Sport per-session re-fit under three alternative priors on m (tighter / wider lognormal, Gamma(2, 4))	#2 (prior justification / sensitivity)

Each script is self-contained and writes its log to logs/. To run any of them from the repository root:

mkdir -p logs
Rscript R/run-aus-sport-diagnostics.R   > logs/aus-sport-diagnostics.log   2>&1 &
Rscript R/run-aus-sport-thresholds.R    > logs/aus-sport-thresholds.log    2>&1 &
Rscript R/run-aus-sport-every-attempt.R > logs/aus-sport-every-attempt.log 2>&1 &
Rscript R/run-aus-sport-estimate-w.R    > logs/aus-sport-estimate-w.log    2>&1 &

A single AUS Sport per-session run takes roughly 80-150 minutes on a 4-core machine with 4 parallel chains; smaller datasets (NZ Trad, Germany Sport-FR) finish in under a minute. Each run also writes per-chain Stan CSVs to logs/stan-<run-name>-chain_<i>.csv so that partial draws can be inspected while the run is in flight.

Output naming convention

Each run writes to results/<country>/ with a file stem of the form

ascents-from-<startDate>-to-<endDate>-minAscents<n>-minFails<k>-<gear>-<grade.type>[-tl][-session][-estimateW]

where -tl indicates the tickprop / lonely-redpoint logging-quality filter was applied, -session indicates session-aggregated data, and -estimateW indicates the joint-w model. The four file suffixes that follow this stem are: .rds (posterior draws), -data.rds (preprocessed data), -diagnostics.rds (convergence summary), and -posterior.png (figure).

Building the manuscript

cd manuscript
pdflatex ms-jqas-r1
bibtex   ms-jqas-r1
makeglossaries ms-jqas-r1
pdflatex ms-jqas-r1
pdflatex ms-jqas-r1

pdflatex supplement-jqas
bibtex   supplement-jqas
pdflatex supplement-jqas
pdflatex supplement-jqas

pdflatex response-to-reviewers
pdflatex response-to-reviewers