The Science Behind the Prediction

Minetti Energy Model

Running uphill costs more energy. Running downhill costs less — but not as much less as you might expect, because your muscles work hard to brake on steep descents. A 2017 systematic review in Sports Medicine confirmed the biomechanical and physiological framework behind graded running, cataloguing how metabolic cost, muscle contraction patterns, and energy dissipation change with slope. In 2025, Looney, Hoogkamer & Kram pooled individual data from 26 studies (n=487 runners) into the largest cross-validation of graded running models to date, testing four equations head-to-head against measured metabolic rates across extreme slopes.

The energy model that underpins every grade adjustment in this tool comes from Minetti et al.'s original 2002 treadmill study — the 5th-degree polynomial that maps metabolic cost from −45% to +45% grade. The 2025 cross-validation showed it remains accurate on flat and downhill terrain; on steep uphills, newer models narrow the error margin, but the Minetti curve continues to be the standard reference across the field with over 500 citations.

Grade Adjusted Pace

Grade Adjusted Pace asks a simple question: if you ran this hilly segment on flat ground at the same level of effort, how fast would you be going? The Minetti curve gives us the answer — the ratio of flat metabolic cost to graded metabolic cost tells us exactly how much to adjust your pace for any slope.

This is how we build your runner profile from Strava data, and how we apply that profile to your race course. Every split prediction is a GAP calculation: your trained effort, translated honestly to the specific terrain ahead of you.

Recency-Weighted Runner Profile

Your fitness today is not the same as your fitness six months ago. Recent training runs are weighted more heavily than older ones using an exponential decay function — runs older than about six weeks contribute proportionally less to your pace profile. This means your prediction reflects who you are now, not a stale snapshot from last season.

Pa:HR Aerobic Decoupling

For a well-recovered, aerobically fit runner, the ratio of pace to heart rate stays stable across the full duration of a run — the body works at the same relative effort from start to finish. When fatigue accumulates or aerobic fitness is underdeveloped, heart rate drifts upward as pace drops: the second half of the run becomes progressively less efficient. This drift is called aerobic decoupling, and its magnitude is a sensitive marker of both fitness and recovery status.

Pa:HR decoupling is computed as the difference in aerobic efficiency — pace divided by heart rate — between the first and second halves of each run, expressed as a percentage. A 2022 analysis of 82,303 marathon runners in Sports Medicine found that both the magnitude and the onset of internal-to-external workload decoupling significantly predict marathon performance, reducing prediction error by 20% when added to critical-speed models. This tool computes Pa:HR for each synced Strava run and displays a trend across your last twelve activities — available only when heart rate consent is granted, since it requires continuous HR data.

Riegel Fatigue Adjustment

Race performance scales as a power law with distance — the longer the race, the more your pace degrades due to cumulative physiological fatigue. A 2024 mathematical analysis in the European Journal of Applied Physiology formally proved this power-law model outperforms the competing critical-power model across 2,571 runners and 5,805 cyclists, and showed it produces safer pacing strategies. Separately, a 2016 study of 2,303 recreational runners confirmed the formula works well up to a half marathon and calibrated the fatigue exponent for non-elite athletes.

The underlying relationship was first quantified by Peter Riegel in 1981. When your race is significantly longer than your longest training runs, we apply a Riegel adjustment to account for the fatigue premium above what GAP alone can see. The adjustment is modest — it compounds at about 6% per doubling of distance — but on an ultramarathon it can add meaningful time to the prediction.

Weather & Altitude Corrections

Heat slows you down. High altitude does too. A landmark 2021 study in Medicine & Science in Sports & Exercise analysed 1,258 endurance races across 84 locations and 42 countries spanning 1936–2019 — the largest dataset of its kind. It confirmed that optimal performance occurs between 7.5–15°C WBGT, with each degree above that costing roughly 0.2–1.1% depending on event distance. A 2025 study of six World Marathon Majors further corroborated the temperature–performance link and raised the question of climate change impacts on future race scheduling.

Our temperature corrections build on the foundational work of Ely et al. (2007), which quantified the progressive slowing of marathon performance as wet-bulb globe temperature rises from 5°C to 25°C. The Steadman heat index is applied when temperature and humidity combine to create meaningful thermal load. Altitude corrections begin above 900 metres, where oxygen delivery starts to measurably decline in non-acclimatised runners — a threshold consistent with a 2025 meta-analysis of 13 altitude training RCTs confirming that altitude significantly alters hematological markers and endurance performance.

Terrain Confidence

No model should pretend to know more than it does. If your race contains terrain significantly harder or more mountainous than anything in your training history, GAP extrapolation becomes less reliable — and you deserve to know that. The confidence system measures three things: how much of the race course falls outside your trained grade range, how much of it is in the hardest effort zones, and how far the race distance exceeds your longest training runs.

When confidence is medium or low, the prediction is shown with an uncertainty range rather than a single number. The goal is not to discourage you — it's to give you an honest picture of what the model can and cannot see.