A recent thread got me interested in power normalization algorithms so today I decided to compare a couple for myself. I used Coggan’s normalized power (CNP) as well as an exponentially weighted moving average (EWMA). For the EWMA I used a time constant that yields a half-life value of ~30s (alpha =0.0465).

**CNP**

1) starting at 30 seconds, calculate a 30 second rolling average for power

2) raise the values obtained in step 1 to the 4th power

3) take the average of all the values obtained in step 2

4) take the 4th root of the number obtained in step 3

**EWMA**

**The Challenge**

Warm-up followed by a work period that includes 2x10min work periods that both average 250W -but differ significantly in the amount of strain. Furthermore, the efforts were bracketed with 5min@250W for calibration purposes. All efforts were preceded with 5min@150W to establish baseline.

**The Results – Heart rate**

**Power Normalizations**

**Summary Statistics**

Code:

**Workload**
Average 198.1
Std Dev 52.3
%RSD 26.4
**30s Average**
Average 198.1
Std Dev 50.1
%RSD 25.3
**EWMA**
Average 198.1
Std Dev 44.7
%RSD 22.5
**Normalized Power**
217.0
**Heart Rate**
Average 139.8
Std Dev 16.1
%RSD 11.5

Correlation coefficients

Code:

Correl HR-30s 0.673678
Correl HR-EWMA 0.872638
Correl HR-Workload 0.721307

**Conclusions**

Obviously a straight 30s moving average of workload does not correlate as well with physiological stress as does the EWMA. The plot of EWMA is very similar to the HR response plot indicating that this algorithm really does approximate real-time physiological strain well. Interestingly, you can see that HR remains the ultimate normalizer, as the %RSD of that measurement is the smallest. It is almost humorous that the EWMA of power seems to be a backwards calculation of HR; a measure that some power disciples want to completely ignore.

However, Coggan’s normalized power does a very good job at increasing the strain estimate of variable workouts as confirmed by the HR-Power calibration plot show below (done last month). The entire workout yielded an average HR of 139.8bpm, which agrees well with the NP of 217W unlike the average power of 198.1W.

Both algorithms have their advantages. EWMP better matches instantaneous strain, and is more elegant, however, CNP matches strain over the course of the entire workout very well.

ElJ I suggest you use try the EWMA algorithm as a normalization protocol in your most excellent TT optimization program. The syntax is actually easier than NP.