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Fitness scores and ideal conditions

Pace in ideal conditions, aerobic, interval and tempo scores, and what the trends can and cannot show.

Effort and Fatigue measure load: how hard a run was, and how much has built up. The fitness scores measure something else: what a run says about how fit you are. Two runs can carry the same load while one shows better fitness, so fitness is computed separately, with conditions credited as realistically as possible.

Pace in ideal conditions

A run's pace can be converted to flat, paved, windless, mild and dry conditions. Each condition adds a small, conservative cost c to the time; the speed in ideal conditions is the speed times all of them. The same costs credit conditions in the fitness scores and in the line added to Strava descriptions, while Effort keeps the effort model of the Conditions article.

videal = v · Π (1 + ck)
The cost of each condition, as a share of the time.
ConditionCost
windquadratic in wind ÷ speed (below): air resistance is about 4% of the energy of running, and forecast wind × 0.65 is the wind at a runner's height; only the wind above the Effort wind limit counts (Settings → Effort, 5 km/h by default)
hills0.16% per metre of climb per km: a route is taken as a loop, and descending gives back less than climbing costs; from the Effort climb limit (50 m by default)
terrain3% for a fully unpaved run, 8% when it is rough, in proportion
temperature0.3% per °C above 22 °C; 0.2% per °C below 5 °C (the Effort temperature limits, these by default)
rain or snow1% in rain, 4% in snow
cwind = 0.04 · (0.65 · w / v)2

Where:

w
wind speed from the weather forecast (m/s)
v
running speed (m/s)
0.04
the share of running's energy that goes into air resistance

Not counted: humidity, altitude, the wind's direction relative to the route, and point-to-point routes that drop more than they climb. [3] [7] [8]

The three fitness scores

Each week has three scores, shown in its summary with their trend:

Aerobic score. speed per heartbeat at the top of Z2, from your easy and long runs in zone 2 in ideal conditions, so weeks compare at the same heart rate. Faster there scores higher.

A = v / HR · 1000 · fcond

Interval score. the effort at interval pace, credited for conditions, for the structure of the session (rep length, and how dense the reps are) and for its heart rate (during the reps), as a rate per km of quality work, so volume does not move it.

Tempo score. how close the pace was to world-record pace for that distance, credited for conditions and squared. Tempo runs are also scaled by (165 / HR)², because the same pace at a lower heart rate is the fitness signal. Races count the result only, run at near-maximal heart rate anyway.

S = (tWR(d) / t · fcond)2 · 100 · (165 / HR)2

Weekly scores are shown as an index to each series’ first scored week in the recorded history, so fixed references such as 165 bpm cancel out. Changing the visible range does not change that reference.

The aerobic score in detail

Runs that count: easy and long runs logged in zone 2, with no secondary zone, a pace and an average heart rate. The week is read at the top of your Z2, as the Z2 pace line of the history chart: the pace in ideal conditions that the line through your Z2 runs of the last 3 weeks gives at that heart rate, so a harder or easier day does not move it. Without zones or enough runs, each run scores its speed per heartbeat, credited for conditions, and the week takes the average weighted by distance.

Example:

An easy run at 5:30/km and 140 bpm in ideal conditions: speed 3.03 m/s, so A = 3.03 / 140 · 1000 = 21.6. The same run at 135 bpm scores 22.4.

The interval score in detail

A session scores the Effort at its interval pace, credited for conditions, times a structure factor (longer repetitions and shorter recoveries are harder at the same pace) and by its heart rate: the same pace at fewer beats is fitter. It is a rate per km of quality work, so a 10 km session does not score more than a 4 km one at the same level.

fs = √(r / 400) · ρ / 0.5,  0.5 ≤ fs ≤ 2

Where:

r
repetition length (m)
ρ
time running fast ÷ (time running fast + recovery time)

The factor is 1 for 400 m repetitions with as much recovery as running and is held between 0.5 and 2, and then its square root is taken, so no structure counts more than about 1.4 times another. The week averages its sessions, weighted by quality distance.

The structure factor of some common sessions.
SessionDensityStructure factor
10 × 400 m at 3:40/km, 60 s recovery0.591.19
6 × 800 m at 3:45/km, 90 s recovery0.671.89
5 × 1000 m at 3:50/km, 90 s recovery0.722.00
3 × 2000 m at 4:00/km, 120 s recovery0.802.00
2 × 5000 m at 4:15/km, 180 s recovery0.882.00

The tempo score in detail

Tempo runs and races are compared with the men's world-record curve, which already holds how pace slows with distance. The record time for the run's distance is interpolated on a log–log scale between the points below; intensity is that time divided by yours.

The world-record reference behind the tempo score.
DistanceTime
400 m0:43
800 m1:40
1500 m3:26
3 km7:20
5 km12:35
10 km26:11
16.09 km44:23
21.1 km58:01
42.2 km2:01:39

Example:

A 10 km race in 45:00: intensity = 1571 / 2700 = 0.582, so S = 0.582² · 100 = 33.9 before conditions. A tempo run is also scaled by (165 / HR)².

An example

Two near-identical 10 km tempo runs, a week apart on the same loop:

Two tempo runs, as the app scores them.
Sep 26Oct 3
Distance and pace10 km · 4:01/km10.03 km · 3:59/km
Average heart rate167 bpm164 bpm
Climb, unpaved, temperature, wind77 m · 17% · 14 °C · 7.5 km/h76 m · 17% · 13 °C · 3 km/h
Pace in ideal conditions3:57/km3:55/km
Tempo score4345.3

Both carry the same Effort: the second run was faster, with less wind. Its tempo score is 5.4% higher, in line with its better speed per heartbeat (faster at 3 bpm lower), and only a little of that is explained by the calmer day.

Each week’s scores average its sessions; filler runs are left out, and a week without a session of a kind has no raw score for it: a gap, not a zero. Each series is indexed to its first scored week in the recorded history, fixed at 100 across all views. Missing aerobic and tempo indices use the available observed scores from the prior three calendar weeks. The overall trend averages the available indices, then smooths them over the current and two preceding calendar weeks before the display range is selected. The charts keep the same vertical scale across the 4–60-week views.

What the scores cannot see

  • Heart-rate errors: an optical sensor at the wrist can lock onto your cadence or lag at the start.
  • Runs logged in the wrong zone or category, which then count where they should not.
  • Treadmill paces, and GPS paces among tall buildings or under trees.
  • Humidity, altitude, illness, accumulated fatigue and the menstrual cycle, none of which is in the data.

Read the scores as trends over several weeks, not as a verdict on a single run.

Sources & further reading

Scientific References

These sources provide the scientific background discussed in this article. The formulas and coefficients used by Running Browser are described above, including their assumptions and limits.

  1. Pugh, L.G. (1971)

    The influence of wind resistance in running and walking and the mechanical efficiency of work against horizontal or vertical forces

    Journal of Physiology

  2. Minetti, A.E. et al. (2002)

    Energy cost of walking and running at extreme uphill and downhill slopes

    Journal of Applied Physiology

  3. Ely, M.R. et al. (2007)

    Impact of weather on marathon-running performance

    Medicine & Science in Sports & Exercise

View the complete bibliography

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