mathematical ideas for seat racing

Here are a few practical and mathematical approaches to deal with the asymmetric (one-sided) noise in seat racing. The idea is to get closer to the true contribution of each rower despite the fact that errors like steering mistakes, crabs, or bad balance disproportionately hurt one crew more than they help another.

🧮 1. Use Robust Estimators
Problem: Least squares is sensitive to outliers (like a crab or bad steering run).

Fix: Use robust regression techniques such as:

Least absolute deviations (LAD): minimizes the sum of absolute errors, less sensitive to large outliers.

Huber loss or Tukey’s biweight: down-weights extreme residuals.

Quantile regression: fits the median instead of the mean — ideal if you assume most races are fair but some are skewed by one-sided errors.

🎲 2. Monte Carlo Simulation for Uncertainty
Problem: You don’t know how much any single bad race result skews the whole matrix.

Fix: Simulate race results with many different samples of assumed noise (including one-sided noise models like log-normal or clipped Gaussians), and look at confidence intervals for each rower’s score. This gives you a range of likely outcomes instead of one deterministic ranking.

🧠 3. Bayesian Inference
Problem: You want to include prior knowledge (e.g. you already know some athletes are stronger, or that a steering issue occurred).

Fix: Use a Bayesian model to infer rower contributions. You can:

Define prior distributions for rower abilities,

Add a likelihood function that models race outcomes and includes asymmetric error (e.g., skew-normal or exponential noise),

Then update your beliefs based on the race data.

🚤 4. Identify and Flag Anomalous Races
Problem: Some races are clearly "bad runs" — a boat crabs, steers wide, etc.

Fix:

After the race, look for statistical outliers (e.g., results > 2 std devs from the mean),

Or use known flags (e.g., coxswain reports, video review),

And exclude or down-weight those races from your matrix.

⚖️ 5. Weighted Averaging Across Race Segments
Problem: A single bad moment ruins the whole race time.

Fix: If you can segment each race (e.g. by GPS data or timing splits), calculate:

Median or trimmed mean of segment times (e.g., drop worst 10%),

Or only compare rower performance based on the most stable segments (e.g., middle 500m of a 1k).

🔄 6. Repeat Key Swaps
Problem: One bad swap shouldn't decide a rower’s fate.

Fix:

Repeat the same rower swap multiple times in different contexts (different boat lineups, different weather),

Then average the outcomes, or analyze variability to assess reliability of the result.