Metrics, in plain words
How Inertial computes fitness and freshness
Fitness is a 42-day exponentially weighted average of your daily training load. Fatigue is the same average over 7 days. Freshness is fitness minus fatigue. Days you did not run contribute a load of zero, so the decay is part of the model rather than a gap in it.
| What | Number | The qualifier |
|---|---|---|
| Fitness time constant | 42 days | alpha = 1 - e^(-1/42), about 0.0235 |
| Fatigue time constant | 7 days | alpha = 1 - e^(-1/7), about 0.1331 |
| Freshness | fitness minus fatigue | negative in a hard block, positive in a taper |
| Rest days | load 0, not skipped | the decay is the model |
The formula
Two exponentially weighted moving averages over the same daily series.
alpha = 1 - e^(-1 / timeConstant)
value = value + alpha x (todayLoad - value)Fitness uses a time constant of 42 days. Fatigue uses 7. Freshness is fitness minus fatigue. Your daily load is the sum of every run that day, bucketed by your local calendar date rather than by UTC.
| Line | Time constant | Weight on today |
|---|---|---|
| fitness | 42 days | 2.4% |
| fatigue | 7 days | 13.3% |
| freshness | derived | fitness minus fatigue |
Why rest days are zeros, not gaps
A day with no run contributes a load of zero to both averages. That pulls both lines down, quickly for fatigue and slowly for fitness.
This is the whole mechanism of a taper. Cut volume and fatigue falls in about a week while fitness barely moves, so freshness climbs. Skip the zeros and the model cannot express that at all.
What this gets wrong
It is not fitness. It is a smoothed picture of how much you have been training. Swap long easy runs for short sharp ones and this number falls while your 5K time improves. That is the model behaving correctly and the name misleading you, which we wrote about at length.
It inherits every error in training load. Wrong heart-rate zones bend both lines the same way.
The time constants are conventions. 42 and 7 come from the widely used formulation, not from a study of you. Busso's work showed the right constants vary between athletes and over a season.
What we show you
Two lines and a number, with the label saying what they are. We do not convert freshness into a traffic light or tell you whether to train today. The model does not know about your sleep, your job, or the fact that you are getting a cold.
Sources
- Banister EW, Calvert TW. Planning for future performance. Can J Appl Sport Sci 5(3):170-176, 1980 primary
- Busso T. Variable dose-response relationship between exercise training and performance. Med Sci Sports Exerc 35(7):1188-1195, 2003 primary
- Coggan A, Allen H. Training and Racing with a Power Meter — the CTL/ATL/TSB formulation reference
Changelog
- — First published.