Development Metrics

The Development page turns running, heart-rate, elevation, temperature, and race-result history into athlete-specific trends. These are field estimates for comparing an athlete with their own earlier data. They are not lab measurements, diagnoses, or universal scores for comparing different athletes.

Three principles apply throughout the page:

• Past only: an aerobic observation is scored against runs recorded before that week. The current run never helps define its own expected value.
• Like with like: variable efforts and unsupported activity types are removed, and pace, grade, and heat are accounted for only when the data supports doing so.
• Show the uncertainty: sparse data, extrapolation, and missing context are surfaced instead of silently producing a precise-looking number.

Metric summary

Aerobic pace and cardiac cost

Why the model does not use a simple HR-to-speed ratio

A raw heart rate / speed ratio changes with pace even when fitness has not changed because heart rate has a substantial non-zero intercept. Instead, rslts.run fits the athlete’s own relationship between steady running speed and heart rate:

expected HR = intercept + speed effect + optional heat effect

The relationship between heart rate and submaximal running velocity is supported in controlled running research, but the estimate shown here is an rslts.run field model rather than a laboratory protocol. See Higher Precision of Heart Rate Compared with VO2 to Predict Exercise Intensity in Endurance-Trained Runners.

Which runs are eligible

The model uses steady outdoor road runs with usable heart-rate and speed samples. It excludes trail and treadmill activity types, highly variable efforts, implausible heart rate or speed, and routes whose climbing cannot be normalized reliably. Open Review aerobic run selection on the Development page to see the decision for every run.

Each eligible run contributes one standardized measurement segment:

1. The first 10 minutes of running are treated as warm-up and are not measured.
2. Running time from 10 to 60 minutes is divided into five-minute chunks. A chunk needs at least four minutes of usable samples and no more than 8% pace variation.
3. The earliest qualifying chunk whose average speed is within 5% of the immediately preceding qualifying chunk becomes the measurement window. In a continuously steady run, this is normally minutes 15–20.
4. Clean pace is the time-weighted median speed and clean heart rate is the time-weighted mean HR inside that five-minute window.

This prevents warm-up HR, late-run cardiac drift, cooldowns, and workout structure from being blended into a single run-level value. Open Review aerobic run selection to see the chosen window, sample coverage, adjustments, and exclusion reason for each run. Weekly values use the median behavior of that week’s qualifying runs.

Past baseline and reference heart rate

Each week first tries an 84-day baseline of earlier runs. If that history cannot support a valid speed/heart-rate fit, it can fall back to 168 days. At least eight earlier runs and a meaningful spread of speeds are required. A robust second fit removes extreme heart-rate or GPS residuals.

The reference heart rate is a display anchor, chosen from clean-run heart rates available before the displayed history and rounded to 5 bpm. It is then frozen for the chart. If a newer athlete does not have eight earlier runs at the start of the range, the anchor is frozen immediately before the first week with enough prior history; earlier weeks remain unscored. A later run can therefore never move the anchor used to display an earlier estimate. The anchor is not a training-zone prescription. Aerobic pace is the speed implied at that reference heart rate after applying the week’s median cardiac residual.

Cardiac cost is the median percentage difference between observed heart rate and the past model’s expected heart rate at the same speed. A value of -3% means the week’s qualifying runs required about 3% less heart rate than expected from the earlier baseline. A positive value means higher cost.

Grade normalization

When at least 70% of eligible samples have usable elevation and distance context, local grade is estimated over a centered 60-second window. Speed is converted to a level-equivalent value using the grade energy-cost relationship from Minetti and colleagues. The adjustment is deliberately bounded, and trail runs remain excluded because surface and technical difficulty are not captured by grade alone.

Research basis: Energy cost of walking and running at extreme uphill and downhill slopes.

Temperature normalization

Temperature is adjusted only when the athlete’s own earlier runs can estimate a plausible heat response independently from speed. The fit requires at least 12 earlier runs, at least an 8°C spread in warm conditions, sufficient temperature coverage in the current week, and an estimated response between 0 and 1.5 bpm per °C. Only temperatures above the 12°C cool reference add heat load. If those checks fail, the ordinary speed/heart-rate model is used.

This adjustment uses recorded activity temperature, which may reflect a device sensor or an upstream platform. It does not currently account for humidity, sun, wind, hydration, acclimation, or sensor placement. Heat-related cardiovascular drift is well established; see Cardiovascular drift during heat stress: implications for exercise prescription.

Confidence interval and extrapolation

The shaded 80% interval is formed by repeatedly resampling both the past baseline runs and the current week’s runs, refitting the model, and taking the central 80% of valid estimates. It describes sensitivity to the available runs; it does not include every source of measurement or model error.

A triangle means the selected reference heart rate implies a speed outside the speeds observed in the past baseline. That estimate is an extrapolation and should be read more cautiously.

The confidence label also checks evidence quality rather than run count alone. It considers:

• the number of baseline and current runs;
• residual model error in bpm;
• the spread of speeds represented in the past baseline;
• steady-window sample coverage;
• reference-heart-rate extrapolation; and
• the relative width of the bootstrap interval.

The page names the reason when confidence is reduced. A pace change is called improved or declined only when confidence is at least medium and its magnitude exceeds the larger of 1% or half the current uncertainty-band width. Otherwise it is labeled stable or uncertain. The comparison period is normally 10–16 weeks before the current four-week summary.

Durability

Durability measures the percentage change in heart rate / speed from the steady 10–20 minute reference window to a steady 10-minute window ending at 45, 60, or 90 minutes. Both windows need at least six minutes of usable samples, low within-window pace variability, and average speeds within 5% of each other. The Finish option compares early and late eligible chunks when a standardized checkpoint is unavailable, so its timing varies by run length.

A positive value means heart-rate cost rose later in the run; lower values indicate less deterioration at a matched pace. Hydration, heat, fueling, terrain, fatigue, and sensor quality can all affect a single run, so the weekly median and longer trend are more useful than one point.

Research context: The Importance of ‘Durability’ in the Physiological Profiling of Endurance Athletes and Cardiovascular drift during heat stress.

Training base

Training base is descriptive context rather than a fitness model. Weekly bars total running duration or distance and report run count, active days, and longest run. The summary compares the latest 28 days with the preceding 28 days. More volume is not automatically better; interpret it alongside durability, aerobic response, recovery, and the athlete’s plan.

Race form and critical speed

With two or more supported race distances in the preceding year, critical speed is the slope of the linear distance-time model:

distance = critical speed × time + finite-distance capacity

The fastest result at each supported distance is used. With only one supported result, the page shows a VDOT-based approximation and labels it as such; it is not a fitted critical-speed measurement. Race conditions, course accuracy, tactics, and whether the result was truly maximal all influence the estimate.

Research example: Calculation of Critical Speed from Raw Training Data in Recreational Marathon Runners.

Retrospective race validation

Validation asks whether the aerobic trend available before a race moves with later race performance:

1. Each supported race is paired with aerobic observations from the preceding 35 days. Race day and later observations are never used.
2. The pre-race aerobic value is the median of those observations. The race is converted to a distance-normalized, race-equivalent critical-speed approximation.
3. A race less than 35 days after the previous scored race is shown as a hollow context point but excluded from validation. This keeps scored pre-race windows independent instead of reusing the same aerobic observations.
4. Both series are indexed to their first pair at 100 so races at different distances can share one chart.
5. Spearman’s rank correlation describes whether higher aerobic rankings tend to accompany higher race-form rankings. Five independent pairs are required before a strength label is shown.
6. After five independent pairs, paired bootstrap resampling adds a central 80% range around the correlation. A wide range is a warning that the apparent relationship is not yet stable.
7. Direction agreement ignores changes smaller than 0.5% and reports how often the remaining consecutive changes move in the same direction.
8. Starting with the third independent pair, the prediction uses only earlier independent pairs to calibrate the athlete’s race-to-aerobic ratio. The displayed error is the median absolute speed error from those past-only predictions, with an 80% bootstrap range once enough predictions exist. Median signed bias shows whether predictions tend to be systematically fast or slow.

Correlation is descriptive, not causal, and a handful of races can produce an unstable value. Course, weather, tactics, competition, and race effort are not normalized. See the NIST explanation of Spearman rank correlation.

Reading changes responsibly

• Trend lines use a padded local y-axis rather than an automatic zero baseline so meaningful longitudinal movement remains visible. The minimum span prevents tiny changes from filling the chart; read the numeric labels and uncertainty alongside the apparent slope. Weekly workload bars remain anchored at zero.
• Prefer multi-week direction over a single point.
• Check confidence, run count, model error, pace spread, the shaded interval, and extrapolation markers.
• Use the run audit to identify missing temperature/elevation context or excluded runs.
• Treat abrupt changes as a prompt to inspect training, illness, weather, sensors, and data quality.
• Use race validation to learn how well the aerobic estimate tracks this athlete; do not assume the relationship is equally strong for everyone.