Methodology

Overview

The RPI is a hierarchical Bayesian latent-strength model fitted by Markov Chain Monte Carlo (NUTS) over every recorded race in a multi-season window. Each crew has a posterior distribution over its true skill, not a point estimate — so every published rating comes with a 90% credible interval reflecting how much data has actually constrained that crew.

Crucially, the model fits every team's skill jointly from the whole race graph. League and club strengths are themselves parameters the model learns, so beating a strong-league crew lifts you automatically — no hand-tuned bonuses required.

The model

Every crew has a latent skill θ in units of seconds-per-500m of pace. For each race we observe pace residuals around a race-level intercept α_r:

where θ_eff includes a per-team distance specialization term, α_r is anchored to a per-distance-bucket baseline pace μ_pace[d] (so the model can't silently absorb cluster strength into the intercept), and σ_effective scales with race type, conditions, importance tier, and distance bucket.

The display rating shown across the site is RPI = 1500 + 50 × E[θ], with the 90% credible interval drawn from the posterior's 5th and 95th percentiles.

Hierarchical priors

Skill is partially pooled at multiple levels — global → league → club → boat-class — so crews with sparse data borrow strength from their peers:

Teams with NULL league fall back to a country-scoped pseudo-league (e.g. __unknown_USA) so the pool isn't corrupted by mixing across continents.

Likelihood components

The Plackett-Luce term is invariant to α_r: it depends only on the order of θ values within a race, so it provides a gradient that always pushes θ_winner > θ_loser even when the pace likelihood's rank signal is corrupted by noisy conditions.

Distance & event-level handling

Race distances are bucketed into four physical categories — short sprint (<1600m), standard sprint (1600–2200m), medium (2200–3500m), and head race (≥3500m). Each bucket has its own learned noise multiplier:

An event’s level shrinks or inflates the per-race noise, so a national title pulls the posterior harder than a local regatta. Level is curated per event — it used to be guessed from keywords in the regatta’s name, which is why “Head of the Charles” and “Head of the Hooch” scored alike:

Tiers come from a structured events.tiercolumn when curated, with a keyword fallback for events that haven't been tagged yet.

Cross-season AR(1) dynamics

Rather than a hard carry-forward at season boundaries, the model uses a learned autoregressive transition between seasons:

α_AR ~ Beta(4, 2) has a prior mean around 0.67, but the posterior is data-driven — programs with high roster turnover learn a lower α, programs with stable crews learn a higher α. Single-season fits skip the AR block entirely.

Inference

The full posterior is sampled with the No-U-Turn Sampler (NUTS) via NumPyro/JAX, running 4 chains of 2 500 warmup + 1 000 samples each with a dense mass matrix on the scalar hyperparameter block. A typical mens-V8 fit takes 1–3 minutes on CPU and converges to max R̂ < 1.05 with zero divergences.

Posterior summaries (mean, SD, 5th and 95th percentiles) are persisted to team_rpi_posterior; the joint sample matrix lands in team_rpi_posterior_samples so the head-to-head matchup endpoint can draw correlated (θ_A, θ_B) pairs and report calibrated win probabilities and margin credible intervals.

Reading a rating

Every leaderboard rating shows the posterior mean (the single best guess) plus a confidence chip — HIGH, MED, or LOW — driven by the posterior SD. Crews with fewer than 4 rated results in the current season are flagged as provisional: their posterior is mostly the league prior, not their own evidence, so we surface that uncertainty rather than dressing it up as a confident pick.

Backtest accuracy

We score the model on every pairwise outcome in the rated record — 13,209 of them: every pair of crews in every race, priced on the rating each held going in. The calibration table on the landing page reads directly off those buckets. When the model says 70–80%, the favourite wins 79% of the time; at 90–100% it wins 94%. Every bucket lands within about two points, and where it misses it is mildly under-confident, which is the direction to miss in.

Each pair is priced on the last rating published strictly before its race, so no result is scored against a posterior it helped produce. The ratings behind it are still fitted on the full season, so this is not a strict forward-only walk-forward (which we have running offline at ~68% on a 28-day single holdout). On a 3-year training window any single race contributes <1% of the total evidence, so the bias is small relative to the gain in practicality: measuring fresh predictions doesn't require an MCMC refit queue.

Known limitations

• Joint cross-boat-class fits with shared club_effect are infrastructure-ready but currently run per-class in production for compute economy. The joint mode needs ≥2 000/2 000 MCMC samples for convergence on the ~5 000-parameter joint posterior.
• Roster changes within a season are not modeled. Mid-season swaps still appear as the same crew identity.
• Lane bias and course-specific effects are not modeled — pace-margin within each race already cancels course mean, but lane-by-lane variation is folded into σ.
• Within-season recency weighting was trialed and reverted: on this 3-year horizon, the AR(1) cross-season decay plus equal-weight within-season produced the best holdout accuracy.
• Event level is curated, with no keyword fallback. An event nobody has classified counts as local rather than being scored on how its name is spelled.