Intervals.icu estimates FTP by looking for max efforts in rides and using those to place you on a power curve. So its similar to using 95% of FTP or 2 x 8m average but any max effort of 60s or more will do. The curve is modelled using Mortons 3P power model and that is used to get your 60 min critical power (FTP). The estimated value decays if you reduce your training load and stays the same if you maintain it.
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Intervals.icu keeps TSB on the same day. So TSB today = todays CTL - todays ATL i.e. it shows the TSB after your training for the day. I am not sure if I should change that or not …
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Yeh, you are probably right. When I wrote the response, the key point I wanted to get across was that the TSS impact on CTL and ATL was related to an exponential decay function and not a straight divisor. I did a quick Google search and assumed that a particular blogger had it correct. I now seem to recall that the denominator (and/or numerator) is the sum of the exponential decay). I’ll look forward to your corrected formula. FYI: I didn’t find it in Allen/Coggan/McGregor’s recent book.
FWIW: I have using the PMC charts of TP Premium and WKO4 since early 2016. As an “older” athlete (61), I have found that I need to set ATL at 14 days (ironically, the default setting, if I recall correctly, back then) to get a more realistic TSB. I have found this particularly important during heavy ramp phases (e.g. last 30 days of 6.0, which is a lot for an older athlete) and leading to tapers for A/B events/races.
In all honesty, I wasn’t sure where the exponential formula came from. When I first started trying to create this spreadsheet I found a couple of references to it on some forums but when I couldn’t get it to match WKO4 I asked on their Facebook group. Apparently it’s actually as simple as this:
Today’s CTL = Yesterday’s CTL + (Today’s TSS - Yesterday’s CTL) / 42
Today’s ATL = Yesterday’s ATL + (Today’s TSS - Yesterday’s ATL) / 7
Great, this matches WKO4 to multiple decimal places…
Needless to say, a quick internet search found this article from 2016:
Good to know that even trainingpeaks/WKO doesn’t even know which formula to use.
It doesn’t really make that much difference to the outcome though, and you are quite correct in saying that the constant drives how much of a decay there is in CTL/ATL and the numbers you choose can be influenced by age etc.
Mike
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Pretty sure it came from Bannister’s impulse response model.
Yes, they simplified Bannister’s model and its discussed in Training and Racing book but no formula is given (#ExerciseForReader). If you can’t recall from college math (#thisMathMajorForgot), search “exponentially weighted moving average” and that basic formula is all over the Internet.
Thanks.
Memory like a sieve for anything useful like that.
Mike
I’d like to get the current week to show both completed and remaining planned TSS but that’ll need a little bit more thought…
Mike
Heh I was actually trying to do the same thing today. Almost needs a counter that subtracts up to 7 as the week passes.
I’ve changed the Weekly TSS tables to only count planned TSS if it’s in the future and Actual TSS if it’s in the past or on today.
Not perfect because I haven’t come up with a way of including planned TSS on today but only if there isn’t an Actual TSS value…
Link at the top of the topic updated if you want to download it again.
Mike
I saw a response from Andy Coggan to a question on another forum regarding ATL and its variation with increased age & he said he’d experimented and, when he was 57, set his ATL time constant to 10 days, & that seemed about right for him. Is there a simple way to change the ATL time constant in the worksheet?
You certainly can: Use the green boxes shown below to adjust the constants.
The blue and pink boxes are your starting CTL and ATL.
Mike
Thanks for the advice. Great spreadsheet & love the charting!
If this formula offends any mathematically-inclined people, note that it is:
Today’s CTL = (1-k) * Yesterday’s CTL + k * Today’s TSS, where k = 1/42
This is just the iterative form of an exponential moving average, as you said.
Out of interest, why would that be considered a better form of the equation?
(I’m not a mathematician, obviously)
Mike
awesome thanks for the sheet. A cool new toy to play with 
also as a sidenote to intervals.icu, I put in my data and it’s cool to see how the trainerroad training plan keeps me perfectly in their green “optimal” training zone 
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Cheers,
I might have to add that feature too. Handy as a visual aid when planning.
Mike
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They reference this paper:
https://www.tandfonline.com/doi/abs/10.1080/00140139608964484
Which is an interesting read just by itself.
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Your form seems to be popular with economists. Mine (which is just rearranging terms) is more appealing to me, at least, because it’s more closely related to how you would write the non-iterative forms. (You can equivalently write CTL as a weighted sum or integral of TSS, without reference past CTL values. That’s how you normally see the Bannister impulse-response model written.)
Incidentally, WKO4 may be using a constant of (1 - exp(-1/42)) rather than your (1/42). I think that would be more typical for this kind of formula.
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Thanks
They don’t. I asked on the user group because I couldn’t get the exponential form to match WKO. It was confirmed that they use the simpler form as did Coggan’s original spreadsheet.
Mike
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Thats interesting. Have you seen any commentary on 1/42 vs the exp version? Why one over the other?