Normalized Power (NP)

Normalized Power (NP) converts a variable power profile into a single equivalent steady intensity. Intuitively, it tries to answer:

• If I rode at a constant power with the same physiological cost, what constant power would that be?

Compared to average power, NP is more sensitive to high-intensity surges, making it useful for estimating training load (e.g., power-based TSS).

Why NP exists

Physiology shows that intensity and physiological cost (glycogen use, lactate accumulation, hormonal stress) are not linear; the cost rises disproportionately at higher intensities.

Linear vs. exponential

• Linear view (average power): riding 1 hour at 200 W has the same average as “30 min at 100 W + 30 min at 300 W” (both average to 200 W).
• Physiological view (NP): 300 W causes much more stress than 100 W “gives back”. The latter often feels closer to a steady ~260–270 W effort.

NP amplifies high-power segments via a fourth-power weighting, which is intended to better approximate metabolic cost than a simple average.

How Trainingload.ai computes NP

Trainingload.ai follows the common NP definition: compute a 30-second rolling average, raise to the 4th power, average, then take the 4th root.

P_smooth(t) = (1/30) * sum_{i=0..29} P(t-i)
NP = 4th_root( (1/N) * sum_{j=1..N} (P_smooth(j))^4 )

Where:

• $P(t)$ is instantaneous power at time $t$
• $P_{smooth}(t)$ is the 30-second rolling average at time $t$
• $N$ is the number of samples

Typical Use Cases

1. Race analysis

• Criterium: frequent accelerations often make NP much higher than average power. NP better reflects how hard the race was.
• Time trial / triathlon: NP should be close to average power due to steadier pacing. If NP is much higher, pacing was likely too variable.

2. Training load (TSS)

NP is a key input to TSS (Training Stress Score).

IF = NP / FTP
TSS ∝ Duration_sec * NP * IF

Using NP helps TSS capture the load of variable workouts (intervals) more realistically than average power alone.

Trainingload.ai advice:

1. Less meaningful for short durations: below ~20 minutes, NP can be noisy because physiology may not reach a steady state. For sprint sessions, use max power, average power, and interval-level metrics instead.
2. Don’t “game” NP: on recovery rides, don’t add sprints just to inflate NP. The goal is low intensity; NP should match the purpose of the session.
3. Check VI: view it alongside VI (Variability Index): VI = NP / Avg Power. Higher VI means a more variable effort.

Limitations

• Depends on reliable power data: dropouts and device errors affect results.
• Sensitive to windowing and sampling: different sampling rates/interpolation can slightly change NP.
• Captures “cost intensity”, not fatigue directly: NP doesn’t directly equal recovery needs or muscle damage.

Related docs

• Variability Index
• Training Stress Score
• Intensity Factor