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Algorithm Explanation & Scientific Basis

Deep dive into our pace calculation algorithms, environmental adjustment formulas, and the scientific basis for race phase strategies.

Environment Lab Algorithm

The Environment Lab uses the GAP (Grade Adjusted Pace) algorithm to account for the effects of temperature, slope, wind, and surface type on pace, helping you maintain the same physiological intensity under different environmental conditions.

Core Formula

Padj = Pbase × (1 + temp_factor + slope_factor + wind_factor + surface_factor)

P_adj = Adjusted pace, P_base = Base pace, all factors are relative adjustments

Temperature Correction

Temperature significantly affects running performance. We correct based on heat stress index:

temp_factor = 0 (if 10°C ≤ T ≤ 15°C)
temp_factor = (T - 15) × 0.006 (if T > 15°C)
temp_factor = (10 - T) × 0.002 (if T < 10°C)
  • Optimal range: 10-15°C, no correction needed
  • High temperature (>15°C): +0.6% pace per degree above 15°C
  • Low temperature (<10°C): +0.2% pace per degree below 10°C

Slope Correction (GAP Algorithm)

Slope is a key factor affecting pace. We use the GAP (Grade Adjusted Pace) algorithm for correction:

slope_factor = (gain / distance) × 6.0 (uphill)
slope_factor = -(loss / distance) × 3.5 (downhill)
  • Uphill: Each 1m elevation gain ≈ 6m on flat ground, significantly increases pace
  • Downhill: Each 1m elevation loss ≈ -3.5m on flat ground, reduces pace accordingly

Wind Correction

Wind effects on pace:

wind_factor = (wind / 10) × 0.03 (headwind, wind > 0)
wind_factor = -(|wind| / 10) × 0.012 (tailwind, wind < 0)

Surface Type Correction

Correction factors for different surface types:

Asphalt
× 1.0
Track
× 0.98
Cobblestone
× 1.05
Trail
× 1.15

Pace Strategy Algorithms

We use a multiplier model to calculate different pace strategies. Each strategy adjusts the multiplier for each segment to change pace distribution while keeping total finish time constant.

Multiplier Model

p0 = T / Σ(di × mi)
pi = p0 × mi
ti = pi × di

p₀ = Base pace, pᵢ = Pace for segment i, mᵢ = Multiplier for segment i, dᵢ = Distance for segment i, tᵢ = Time for segment i, T = Total time, n = Number of segments

Even Split Pace

All segments have a multiplier of 1, maintaining consistent pace throughout.

mi = 1 (for all segments)

Negative Split Pace

Slightly slower in the first half, gradually increasing pace in the second half. Multiplier decreases linearly from start to finish.

x = (i / (n - 1)) × 2 - 1 (maps to [-1, 1])
mi = 1 + (-x) × amplitude

Amplitude is calculated based on strength parameter, limited to 0.02-0.08 range to avoid extreme adjustments

Slight Positive Split Pace

Slightly faster in the first half, allowing controlled pace decrease in the second half. Multiplier increases linearly from start to finish.

x = (i / (n - 1)) × 2 - 1
mi = 1 + x × amplitude

Ten-Ten-Ten Strategy

Conservative first 10 miles (16.1 km), steady middle section, slightly faster last 10 km (6.2 mi). Suitable for experienced runners.

mi = 1 + amplitude (first 10 miles)
mi = 1 (middle section)
mi = 1 - amplitude (last 10 km)

What is RPE?

RPE (Rating of Perceived Exertion) describes how hard an effort feels by integrating heart rate, breathing, muscular fatigue, and thermal stress. This tool uses the Borg RPE framework, a widely validated method in endurance sports science.

Learn more: Borg (1982)

Why race phases instead of constant pace?

Endurance races are not experienced at a constant effort. Athletes naturally regulate pace across distinct phases as fatigue, energy availability, and perceived effort change over time.

Learn more: Tucker et al. (2009)

Why time-based phases?

Perceived exertion scales more consistently with relative race progress (% of total time) than with fixed distance. Effort regulation is strongly influenced by how much of the race is expected to remain.

Learn more: Eston et al. (2007)

How should I use this?

Use pace targets as external structure and RPE as an internal feedback check. When both align, pacing is likely appropriate. When they diverge, effort perception should guide adjustment.

Learn more: Noakes (2007)

Race Phases Strategy

A four-phase strategy designed specifically for marathon (42.195km), based on human physiological responses and race realities:

Start (0-3.1mi)
-3.5s / unit
Cruise (3.1-18.6mi)
0s (target pace)
Decision (18.6-23.6mi)
+2s / unit
Final (23.6-26.2mi)
-5s / unit

Race Phases can be combined with user-selected pace strategies (e.g., negative split, slight positive split). Strategy adjustments are applied at 50% intensity on top of the phase base.

References & Scientific Basis

This algorithm is based on research in exercise physiology, environmental science, and marathon training practices. Main references include the GAP (Grade Adjusted Pace) algorithm, heat stress index models, and extensive analysis of marathon race data.

Authoritative References