The Science Behind Runningbrowser.com

Chapter 1

Effort

Physiological Background

Effort quantifies the metabolic cost of running at different intensities. The relationship between pace and physiological strain is non-linear: running slightly faster requires disproportionately more energy due to increased oxygen consumption, lactate accumulation, and neuromuscular fatigue.

At easy paces (Zone 1-2), the body primarily uses aerobic metabolism, efficiently burning fat and carbohydrates with minimal lactate buildup. As pace increases into threshold and VO2max territories (Zone 4-5), anaerobic contribution rises sharply, glycogen depletion accelerates, and recovery time extends significantly. [4]

The Effort value captures this non-linear relationship. The exact multipliers depend on your personal Lactate Threshold pace configured in Settings, which anchors the entire pace-effort curve to your fitness level.

Formula: Quality Days (Intervals/Tempo)

For workouts with quality distance (intervals, tempo runs), effort is calculated as a weighted average of the hard and easy portions:

Where:

E

Total Effort for the workout

E_h

Hard effort (from interval pace)

E_e

Easy effort (from easy pace, or default Z2 pace)

Q

Quality ratio (quality distance / total distance)

Formula: Easy Days (Pace-based)

For easy runs without quality distance, effort is derived directly from pace using linear interpolation on a personalized reference table:

LT = Lactate Threshold pace (configured in Settings)

Lactate Threshold & Table Generation

The pace-effort relationship is anchored to your Lactate Threshold (LT) pace. LT is the intensity at which lactate begins accumulating faster than it can be cleared - the boundary between sustainable aerobic effort and unsustainable anaerobic work.

At LT pace, effort is defined as 2.85. The table is then generated using exponential functions that model the physiological reality:

Above LT (Faster). Effort increases exponentially. Each second faster requires disproportionately more energy due to rising anaerobic contribution, lactate accumulation, and glycogen depletion.

Below LT (Slower). Effort decreases gradually. The body efficiently uses aerobic metabolism, burning fat with minimal lactate buildup. Recovery between efforts is quick.

Where Δt = difference in seconds from LT pace.

Reading the Effort scale

Effort has no unit: it multiplies distance. Its anchor is the threshold, where a kilometre counts 2.85. From there, every 10 seconds per kilometre slower lowers Effort by about 11%, and every 10 seconds faster raises it by about 19%. At the default paces (threshold 4:00, easy 5:10), a kilometre a minute faster than threshold counts as much as 6.3 easy kilometres.

The ends of the table

The pace-effort table runs from 60 seconds faster than your threshold (never faster than 2:30/km) to 90 seconds slower, in steps of 10 seconds. Between steps Effort is interpolated in a straight line, which sits a hair above the curve. Beyond the ends it keeps the end value: anything more than 90 seconds slower than threshold counts 1.01, anything more than 60 seconds faster counts 8.02. Very slow running and walking still count as load, just never less than that.

Per-Workout LT Storage

Each workout stores its own Lactate Threshold value at the time it was recorded. This ensures that effort calculations remain stable over time - even if you update your LT in settings later, historical workouts will continue using their original LT for calculations.

This is important because:

• Your LT improves with training - a 5:00/km run today represents different effort than the same pace 6 months ago
• Historical trends remain meaningful and comparable
• You can see how your fitness has progressed relative to your LT at each point in time

When viewing a workout's effort tooltip, you'll see which LT was used for the calculation (e.g., "LT: 3:42" or "LT: settings" if no specific LT was stored).

Updating LT for Workouts

In Settings, when you change your Lactate Threshold pace, you have control over which workouts receive the new value:

• Apply from date: Choose a specific date - the new LT will be applied to that date and all future workouts
• Apply to all workouts: Enable this toggle to update your entire training history with the new LT

If you don't specify a date, the new LT applies from today onwards by default.

Use cases:

• New user: Enable "Apply to all workouts" to set your LT across your entire history
• Fitness improvement: Set a new LT from today - past workouts keep their original LT, reflecting your fitness at that time
• Correcting a mistake: Use "Apply from date" to fix LT from when you made an error

Why Lactate Threshold Matters

Different runners have vastly different LT paces based on training history, genetics, and current fitness:

• Elite marathoner: LT around 3:00-3:15/km
• Competitive club runner: LT around 3:30-4:00/km
• Recreational runner: LT around 4:30-5:30/km
• Beginner: LT around 6:00-7:00/km or slower

By setting your personal LT pace in Settings, the effort calculations become meaningful for your fitness level. A 5:00/km pace might be easy recovery for an elite but threshold work for a beginner - the personalized table captures this difference.

Special cases

• A quality session without an interval pace counts its hard part at Effort 3, just faster than threshold.
• Without an easy pace, the easy part of a quality session runs at the default Z2 pace from Settings.
• A planned run without a pace counts at the default Z2 pace, so the weeks ahead already show in Stress.
• An Effort you enter yourself replaces the whole calculation, conditions included.
• Rest days have no Effort. Strength work adds to Stress through its secondary distance (chapter 3).

Why pace, not heart rate

Effort comes from pace because pace is known before a run (a planned session has one) and means the same thing every day. Heart rate at a given pace rises with heat, humidity, dehydration, caffeine, poor sleep, illness and simply time on your feet (cardiac drift), so the same session can read very differently. Instead of letting those swings blur the load, the conditions that make a pace harder are counted one by one (chapter 2).

Heart rate is used where it carries a clear signal: speed per heartbeat on easy runs, and pace for the heart rate on tempo runs, as measures of fitness (chapter 5).

Chapter 2

Environmental Adjustments

The base effort assumes a flat, paved route in calm, mild weather. Five factors correct it for the conditions of the day. Each factor is 1 when its condition does not apply and grows with the extra cost; all of them can be tuned in Settings.

These adjustments raise Effort, with the effort model in Settings. The pace in ideal conditions and the fitness scores use separate, physically based costs: see chapter 5.

Wind Adjustment

Running against wind increases energy expenditure without a corresponding increase in pace. The wind adjustment compensates for this:

Where:

w

Wind speed (km/h)

t

Threshold (default: 5 km/h)

p

Percent increase per km/h (default: 1%)

Only applied when wind speed exceeds the threshold. Based on research showing approximately 4-8% increase in oxygen consumption per 10 km/h headwind. [3]

Elevation Gain Adjustment

Running uphill increases energy expenditure significantly. The elevation adjustment accounts for the additional effort required when a run has meaningful elevation gain:

Where:

gain

Total elevation gain (meters)

dist

Distance (km)

gain / dist

Elevation per km (m/km)

p

Percent increase per m/km (default: 1%)

Only applied when total elevation gain exceeds a threshold (default: 50m). The adjustment is proportional to elevation per km, meaning the same elevation gain over a shorter distance produces a higher adjustment.

Unpaved Terrain Adjustment

Trails, gravel and grass absorb part of every push-off and demand more stabilization than asphalt, so the same pace costs more energy. The share of the run on unpaved ground scales the adjustment linearly:

Where:

u

Share of the run on unpaved terrain (0-100%)

p

Percent increase for a fully unpaved run (default: 10%)

A run can also be marked rough (technical trail, roots, rocks, sand or mud). A fully unpaved rough run adds 25% by default instead of 10%, and its pace in ideal conditions gets more credit too.

Rain & Snow Adjustment

When the first weather icon is 🌧️, calculated effort increases by 5% by default. When it is ❄️, the default increase is 10%. Later icons do not trigger this adjustment: 🌧️💨 gets the rain increase, while ☀️🌧️ gets none.

These are adjustable model defaults. Change either percentage in Settings, or set it to 0 to disable it. This factor multiplies with the other environmental adjustments and also applies to weekly fitness scores. Manually entered effort takes precedence.

Temperature Adjustment

Running in extreme temperatures (hot or cold) increases physiological strain. The comfortable range is 5-22°C by default. Outside this range, effort is adjusted upward:

Where:

t

Temperature (°C)

range

Comfortable range (default: 5-22°C)

p

Percent increase per °C outside range (default: 1%)

If temperature is within the comfortable range, no adjustment is applied. Below the low threshold, the distance below is used. Above the high threshold, the distance above is used.

Combined Effort

The five factors are independent and multiply with the base effort, so a hilly trail run on a hot, windy day accumulates every correction:

• E_base comes from the quality-day formula or the pace table. Planned future days without a pace use your default Z2 pace from Settings, so upcoming training already counts toward projected stress.
• A manual effort wins: if you enter an effort yourself, it replaces the whole calculation, adjustments included.
• A factor without data (no wind recorded, no elevation) is 1 and leaves the effort unchanged.

Where the Conditions Come From

The adjustments are only as good as the data behind them. For runs synced from Strava , most of it is filled in automatically:

• Elevation gain comes from Strava, as recorded by your watch or phone.
• Wind speed and temperature come from Open-Meteo: the hourly values at the run's start point, for the middle hour of the run.
• Weather icons and unpaved terrain are not part of Strava's data; add them when you edit the workout.
• Runs without GPS (treadmill, manual entries) get no weather lookup, so wind and temperature stay empty unless you enter them.

Every value can be corrected in the workout. When you edit the run on Strava later, distance, pace, heart rate and elevation are updated, but wind and temperature keep their first imported (or corrected) values.

Why these defaults

• Wind, nothing up to 5 km/h, then 1% per km/h. On a loop or an out-and-back a light breeze gives back on one side most of what it takes on the other; a stronger wind costs more against you than it returns behind you.
• Elevation, from 50 m of climbing, 1% per metre per km. The threshold ignores the small rises every route has and the noise in GPS altitude; a route climbing 10 m every kilometre costs about 10% more.
• Unpaved terrain, 10% for a fully unpaved run. Grass, gravel and forest paths absorb part of every stride and ask more of the ankles; sand costs far more, firm dirt less. 10% is a middle value for park and trail running.
• Rain and snow, 5% and 10%. Wet clothes and shoes weigh more, footing is less sure and strides shorten; snow adds a soft, uneven surface.
• Temperature, nothing from 5 to 22 °C, then 1% per degree. Endurance is best in cool weather, around 10 °C for a marathon, and falls off on both sides: in the heat blood goes to the skin to shed heat and the heart rate drifts up; in the cold muscles are stiffer and clothing heavier.

[3] [7] [8]

Tuning the model to yourself

Every threshold and percentage can be changed in Settings. A runner used to the heat can raise the upper temperature or lower its percentage; a confident trail runner can lower the unpaved percentage; a percentage of 0 switches a factor off.

Conditions are stored with each run and Effort is computed when it is shown, so a change in Settings applies to every run, past ones included. The threshold is the exception: each run keeps its own (chapter 1).

Two ways of counting conditions

This chapter counts conditions generously, because Effort measures load: how hard the day was on the body, and erring high keeps Stress on the cautious side. The pace in ideal conditions (chapter 5) counts them sparingly, because it credits fitness, and erring low keeps the fitness scores honest.

Chapter 3

Stress (Training Load)

Physiological Background

Training stress accumulates over time and dissipates through recovery. This follows the fitness-fatigue model (Banister, 1975), where each workout adds to both fitness and fatigue, but fatigue decays faster than fitness gains. [1]

The Stress metric represents accumulated fatigue from recent training, with more recent workouts contributing more heavily. This helps identify:

• Overreaching risk - when stress climbs too high
• Taper effectiveness - stress should drop before races
• Training consistency - stable stress indicates regular training
• Recovery status - how much fatigue remains from recent work

Formula

Stress is calculated as the weighted sum of training load over the past 21 days, with exponentially decaying weights: [2]

Where:

d_i

Distance in meters on day i

E_i

Effort value on day i

s_i

Secondary distance (strength work) on day i

D_i

Decay factor for day i

Decay Factors

The decay factors model how fatigue dissipates over time. As in the fitness-fatigue model, fatigue fades exponentially: every day a workout keeps the same share (87%) of the weight it had the day before. Today's workout has full impact (1.0), while a workout from 20 days ago contributes only about 7% of its original load: [1]

Where:

i

Days ago (0 = today, up to 20)

0.135

Decay rate per day: a time constant of about 7.4 days, so a workout's weight halves roughly every 5 days

The decay curve follows research on glycogen replenishment, muscle repair, and neuromuscular recovery. Most acute fatigue clears within 7 days, but residual effects persist for 2-3 weeks.

A rule of thumb

If every day were the same, Stress would settle at one day's load times the sum of the 21 decay factors, 7.46. A day's load is its kilometres times its Effort, so with the week spread evenly:

Real weeks are not even: a long run yesterday weighs more than one six days ago, so daily Stress swings around this level (figure 3.2). Still, it says what a week of training settles into.

How fast Stress responds

After a lasting change in training, Stress covers about 65% of the way to its new level in one week, 90% in two and all of it in three, when the oldest days leave the window. The other way round, a week off takes away about 65% of it. That is why a taper of two or three weeks lowers Stress clearly, while fitness, built over months, holds.

What counts

• Runs: distance in metres times Effort.
• Strength and other training: its secondary distance in metres, added as it is, so 1,000 m of secondary distance weighs like a kilometre at Effort 1.0.
• Planned runs: at their planned pace, or the default Z2 pace without one, so you see where a plan takes your Stress before you run it.
• Several workouts on one day: all of them.

When Stress is shown

Stress needs an entry on each of the last 15 days: a run, other training or a rest day. With gaps the app shows nothing rather than a number that would read too low, since a missing day may be a run that was never logged. Log rest days as workouts in the Rest category; plan templates do it for you. Stress is rounded to whole numbers.

Interpreting Stress Values

Note: These ranges are individual. Athletes with years of training may handle higher stress, while beginners should stay conservative. Track your personal patterns over time.

Using Stress for Race Preparation

These metrics help you plan training load during peak phases leading up to a race. The key principle: avoid exceeding stress levels significantly higher than your previous training peaks.

When building toward a goal race:

1. Review your stress values from previous successful training blocks
2. Use those peaks as a ceiling - don't exceed them by more than 10-15%
3. Build gradually toward that ceiling over several weeks
4. Allow stress to drop during taper (typically 30-50% reduction)

Pushing stress far beyond what your body has previously handled increases injury risk and often leads to arriving at race day fatigued rather than fresh. Progressive overload means small, sustainable increases - not dramatic jumps that overwhelm your recovery capacity.

Chapter 4

Planning a training block

Plan templates turn a goal, a race date and how you train today into a block where every session is planned. The rules are deterministic: the same inputs always give the same plan, and the tables and the figure in this chapter come from the code that builds it.

Starting from current fitness

Everything is anchored on a threshold pace T: the pace of a race lasting about 55 minutes. It comes from, in order: the threshold you set in Settings; your most recent race in the log (3–25 km, in the last 14 weeks, never a marathon); the current race pace you enter for the goal (not for the marathon, whose pace is no proxy for threshold); or a conservative estimate. The target pace is never used: training follows the fitness you have, and the target stays the race goal. When the threshold is estimated from a performance, adding the plan saves it in Settings.

Where:

t(d)

race time (s) over a distance d in km

d_T

the distance covered in 55 minutes (3300 s) at threshold pace

1.06

Riegel's fatigue exponent: going twice as far takes a little more than twice as long

Every training pace follows from T by the same model: 3K, 5K, 10K, half-marathon and marathon pace, the marathon a further 2% slower since few runners hold the predicted pace that long. From a 4:00/km threshold: 3K 3:39, 5K 3:46, 10K 3:55, half marathon 4:06, marathon 4:22. Easy pace is the one in Settings and never speeds up because the goal is faster. [5] [6]

Fitness may improve during the block, but conservatively: about 0.3% of T per build week, at most 4%, and never past the target. A target further away is noted as ambitious; the workouts stay realistic and the race itself is planned at the target.

Periods and recovery weeks

A block runs through Base (aerobic development), Build (threshold work), Specific (race-specific work) and a Taper, in proportions that depend on the goal: the marathon gives more weeks to base and specific work, the 10K more to building threshold. Base building is all base, without a taper.

After two or three loading weeks comes a lighter week (every two for runners under 30 km a week), never in the first three weeks or just before the taper. It runs at 80–90% of the level it interrupts, and its key session is about 30% smaller too. A race closer than the usual block gets a shorter one (at least four weeks); a race further away a longer, gentler one.

Weekly volume

Week one is your current volume. Each loading week adds a modest step that gets smaller as volume grows: 6% below 25 km a week, 5% up to 50 km, 4% up to 80 km and 3% above, never more than 10%. A block stretched over more weeks spreads the same growth more gently.

Peak volume has two ceilings, never targets: 1.25 to 1.45 times the starting volume depending on the goal, and about 18 km per training day plus 10 (20 for the marathon), so six days with a rest day hold around 118 km. The days are always yours to choose; picking more than you have been running holds the volume for two weeks per added day, so frequency and volume don't rise together.

Long runs

The long run is sized by you, not by the race distance: a share of the week that falls as training days rise (35% at three days to 26% at seven) and eases off above 60 km a week. That gives roughly 9–10 km at 30 km a week, 15 km at 50, 18–19 km at 70 and 22 km at 90, for a 5K runner as much as for a marathoner; the marathon adds 4 points of the week and the half marathon 2.

It starts from your longest run of the last four weeks and grows by about 10% a loading week (1–2 km, 2.5 for the marathon), never jumping to meet the share. It never takes more than 40% of the week, or longer than 2:30 at long-run pace (2:45 for the marathon). In marathon-specific weeks every other long run finishes at marathon pace, from 4 km growing to 12; late in a half-marathon block some carry 3–6 km at half-marathon pace. 5K, 10K and base long runs stay aerobic.

Key sessions

Each goal has a small library of sessions per period, rotated week by week instead of one session repeated with more reps. 5K: hills, threshold cruise intervals and controlled 400s, then 600–800 m at 5K pace, then 1000 m reps, 400 m at 3K effort and a 1200-1000-800-600 ladder. 10K: tempo and threshold cruise intervals, then 1–2 km reps at 10K pace. Half marathon: threshold, then blocks at half-marathon pace. Marathon: threshold, then marathon-pace blocks and continuous marathon pace.

The hard part of a session scales with your weekly volume, within limits per effort. Warm-up and cool-down add 2–5 km, and recoveries suit the session: short jogs between threshold reps, longer ones between 5K reps.

A second key session is planned only at six or seven training days and at least 50 km a week, on a day at least two days from both the main session and the long run, and only when neither carries big race-pace work. Together the two stay within 16% of the week.

The session library

These are the sessions each goal rotates through, period by period. The table shows their shape; the number of repetitions and the length of continuous runs follow from your weekly volume (table 4.2).

The week, and rest days

Sessions go on your training days by priority: the long run on Sunday (else Saturday, else your last training day), the main session at least two days from it (Tuesday first), easy runs on the other days, a recovery run right after a hard day from five days a week, and strides (short, relaxed accelerations) on one easy run from four days a week. A final check keeps hard sessions at least 48 hours apart and at most two a week. The rest days you choose are logged as rest.

A week from the sample block

Week 7 of the sample block in figure 4.1 is a Specific week of 51.1 km on four days; its race week follows. Each session's pace is its average, warm-up and cool-down included; the description names the hard part.

Taper and race week

The taper is distance-specific: the race week for 5K and 10K, two weeks for the half marathon (85%, then 50% of the peak) and three for the marathon (80%, 65%, 35%). Intensity stays: race week keeps a short sharpener at race rhythm (4 × 400 m at 5K pace, 4 × 600 m at 10K pace, 2 × 1600 m at half-marathon pace, or 3 km at marathon pace), at least three days before the race, and nothing the day before.

Notes, never blocks

A plan is always generated; what deserves a second look is noted: a target faster than one block can bring, volume or training days low for the goal, a long run over 40% of its week, a week rising more than 12%, long daily runs on few days (with a suggestion of one more day, never more than six), and a threshold that was estimated rather than set.

From template to log

• Every session becomes a planned workout in your log, with its distance, paces, zones and a title, and counts toward Effort and Stress like any planned run.
• The other days are logged as rest days, so Stress keeps its history (chapter 3).
• Days already gone this week are left alone. Planned workouts that are not done yet are replaced, unless you choose to keep them alongside; completed runs and runs from Strava are never replaced.
• Each session stores the threshold it was planned with, so its Effort stays put if your threshold changes later.
• Everything stays editable: move, change or delete sessions like any other workout.

Chapter 5

Fitness scores and ideal conditions

Effort and Stress 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 chapter 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 on easy and long runs in zone 2, weighted by distance and credited for conditions. Faster at the same heart rate, or as fast at a lower one, scores higher.

Interval score. quality distance times the effort at interval pace, credited for conditions and for the session's structure (rep length, and how dense the reps are). It does not use heart rate: a session's average mixes warm-up, reps and recoveries.

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.

Weekly scores are shown as an index to the first scored week of the chosen window, so fixed references such as 165 bpm cancel out.

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. Each scores its speed per heartbeat, credited for conditions, and the week takes the average weighted by distance, so a long run counts more than a short one.

The interval score in detail

A session scores its quality distance times the Effort at its interval pace, credited for conditions, times a structure factor: longer repetitions and shorter recoveries are harder at the same pace.

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, so no structure more than doubles or halves a session. The week takes the average of its sessions.

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.

An example

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

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.

Weeks, indexes and trends

Each week's scores average its sessions; filler runs are left out, and a week without a session of a kind has no score for it: a gap, not a zero. The trend chart shows every week as an index, the first scored week of the chosen window being 100, and the week summary compares the week with the average of the three before it.

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.