I'm sure someone will chime in with a lot more knowledge than me but-

(1) I remember reading that ctl and atl are "exponentially weighted rolling averages".

(2) The daily pmc just gives you a snapshot of where you are and the percent change over the last 7/ 28/ 90/ 365 days. At least that is mine, could be the way it is set up. The big pmc gives you options for date ranges, activity type, and if you plan future workouts you can model your ctl and plan a peak.

That is correct. Default time constants are 42 and 15 d, respectively, although you can (and should) tweak them (the ATL time constant, anyway...although it too is adjustable, the CTL time constant doesn't really matter) so that the output of the PMC best matches your actual responses.

Also note that to make use of the PMC approach, you need to set your FTP correctly, and keep on top of any changes...Strava, for example, doesn't let you do that (it just retrospectively applies the set FTP to *all* prior workouts), which is why their version of my Performance Manager approach is fatally flawed

Andrew Coggan wrote:

Default time constants are 42 and 15 d, respectively,

some dude on TP said 7 for ATL :-)

http://home.trainingpeaks.com/...-performance-manager

did it change ?

ATL and CTL are exponentially weighted moving averages of the daily TSS values with default time constants of 1/7 days^-1 and 1/42 days^-1 respectively. You can modify the time constants if you like.

In lay terms, CTL indicates training loads for past few months (hence why it's termed "chronic") and ATL indicates training loads over the past few weeks (hence why it's termed "acute").

They are not simple rolling averages of TSS values over the past 7 and 42 days.

With a simple rolling average over X days, the TSS values for the past X days are evenly weighted in the calculation of the average. If you think about it, that doesn't make much sense as it suggests that:
- a ride X days ago would contribute equally to today's acute and chronic training load (and stress balance) as does today's ride
- that a ride X+1 or X + Y days ago doesn't contribute at all to to today's acute and chronic training loads. Why should a ride 8 days ago have no impact on ATL while a ride 7 days ago has the same weighting as today's ride?

With an EMWA function, the daily TSS values are weighted differently and all values back to the beginning of time are included, with more recent values weighted more than prior values. That should make intuitive sense as a ride done yesterday should have a greater impact on today's numbers than a ride done a week, or a month or a year ago would.

The time constant (a positive fractional value between 0 and 1) dictates the rate of decay in the weighting function, and the decay occurs more rapidly the higher the time constant. So while a ride on a day a year ago still contributes to today's ATL and CTL - the decay in weighting with the default time constant means its contribution will be negligible.

However a ride a few days ago will be weighted more highly in the calculation of ATL than it will for CTL, while a ride 30 days ago will be weighted more in the calculation of CTL than ATL.

Easy calculation of EMWA is explained in this item:
http://stats.stackexchange.com/questions/44650/a-simpler-way-to-calculate-exponentially-weighted-moving-average



To calculate today's ATL (or CTL) - simply multiply the difference between today's TSS and yesterday's ATL (or CTL) by the ATL (or CTL) time constant and add it to yesterday's ATL (or CTL) value.

Today's TSB is simply yesterday's CTL minus yesterday's ATL.

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http://www.cyclecoach.com
http://www.aerocoach.com.au

Thank you for this! Exactly what I needed.the straight average did not make sense And hence my confusion.

This was very helpful. Thanks again.

Quick question. Does a workout stop contributing to atl after 7 days? Or does it keep getting added in but with the chronic training load time constant?

All rides going back in time contribute to ATL, and ATL is always calculated using the ATL time constant.

It's an infinite time series sum.

The weighting applied to TSS values for days going back in time is as follows, with only the past 31 days plotted (it goes on all the way back to the big bang):



Hence for calculating today's ATL, then it is the weighted average of each day's TSS going back forever in time, with the weighting for each day as shown in the above chart.

For calculating ATL, then today's TSS counts for 1/7 (14.3%) of the total weighting applied.
.
Yesterday's TSS is assigned a weighting of (1/7) x (1-1/7)^1 = 12.2%

Day -2 weighting is (1/7) x (1-1/7)^2 = 10.5%

Day -3 weighting is (1/7) x (1-1/7)^3 = 9.0%

and so on back in time forever more.

As you can see from the chart, for a time constant of 1/7, the weighting starts much higher and drops off much more rapidly than when the TC is 1/42.


For CTL, today's TSS is given a weighting of (1/42) x (1-1/42)^0 = 2.38%

Yesterday's weighting is (1/42) x (1-1/42)^1 = 2.32%

Day -2 weighting is (1/42) x (1-1/42)^2 = 2.27%

Day -3 weighting is (1/42) x (1-1/42)^3 = 2.21%

and so on back in time forever more.


So including today, the past 7 days of TSS is weighted such that it contributes to 66% of today's ATL value but only 15.5% of today's CTL value.

Past 14 days: the daily TSS comprises 88.4% of the total weighting for ATL and 28.6% for CTL.

Past 21 days: 96.1% ATL, 39.7% CTL

Past 60 days: 99.99% ATL, 76.4% CTL

Past 120 days: 99.999999% ATL, 94.5% CTL

As you can see, the total sum of the daily weightings converges to 100% as you approach infinite number of days before today, but the ATL weighting approaches 100% more rapidly than the CTL weighting.

---

http://www.cyclecoach.com
http://www.aerocoach.com.au

That dude was right. 15 d is what you get when you convert the 7 d time constant to 3 half-lives, thus covering 87.5% adaptation.

Sorry for the confusion!

Again. Makes sense from a phisiological perspective. Thanks for the detailed responses.