TSS and IF calculation??

NP and IF have no relationship to duration. You could have identical NP and IF numbers for a 5 minute ride or a 5 hour ride. TSS is the only computation that integrates intensity and duration. And, your calculations appear to be correct.

frenchyge said:

Ok, I thought I had a good handle on these two items, but it is apparent that I don't understand again. :o

peakscoachinggroup.comPowerTrainingChapter.pdfOpen ↗
Page 9 of Andy's power training document describes an analogy for TSS as "TSS = exercise duration x average power x a power-dependent intensity weighting factor" which makes perfect sense to me - basically the total work done, with an intensity factor applied.

Then, on page 10, in the 8-step process for calculating TSS, things change.
Steps 1-4: Calculate NP
Step 5: Divide NP by LT power to determine IF
Step 6: Multiply NP x duration to obtain normalized work performed - Edit: Great so far, same as first two factors in the analogy above.
Step 7: Multiply step 6 by the IF from step 5 - Edit: okay, there's the third factor from the analogy above, so we're done, right?
Step 8: Divide step 7 by the amount of work that could be performed in one hour at threshold power and multiply by 100 to determine TSS points - Edit: Here's where my world starts to shake. See below.

So, per the 8-steps, the TSS formula becomes:

(NP x workout duration x IF) / (LT pwr x 1 hr) --- rearranging terms and substituting IF for [NP / LT pwr], you get:

(IF)^2 x workout duration in hours x 100 = TSS score.

IF-squared? Is that right? 😕 I thought IF was the factor that corrects my workout specific power (NP) to an equivalent amount of LT power?

So: 1) ride 1 hr at LT pwr = 100 TSS points. 2) ride 30-min at LT pwr = 50 TSS points. 3) ride 1 hr at half of LT-pwr = 25 TSS points? The TSS values within Cycling Peaks software support this, but I sure didn't expect it. I thought the fourth-order normalizing process built into the IF calculation took care of the exponentially increasing difficulty of generating the higher power, but now it appears that it gets squared again to reflect the need for recovery? I'm hoping that Andy or someone can explain or show me where I did something wrong. 😕

Well if it helps unconfuse things any, I can tell you that your algebraic derivation and conclusions are correct. Now, let's see if I can clearly explain why IF ends up being squared in the calculation of TSS when you use the reduced formula...

For starters, realize that we have a pretty good handle on the relationship between exercise intensity and metabolic strain, which can be approximated by a 4th order equation. Perhaps a slightly greater or lesser exponent would come closer to the truth, or perhaps an exponential rather than a power equation would be a better description of reality, but as it is being applied in the calculation of normalized power, it doesn't really matter: over a rather broad range of potential exponents/equations that might be used to fit metabolic data (e.g., blood lactate responses), the value for normalized power that you arrive at doesn't vary much. IOW, the calculation of normalized power is rather insensitive to the precise value that you use to weight the data in an attempt to correct for metabolic non-linearities.

In contrast to the situation above, we really don't know precisely how exercise intensity and exercise duration interact to cause a particular level of physiological strain (stress being the imposed load, strain being the response to that load). About all we can really say is that there is some sort of interaction there. So, to calculate a "training stress score" I simply assumed that they interacted in some manner, and hence (as you would in statistics) multiplied the virtual work performed (i.e., normalized power x duration in seconds) by the intensity of that work relative to your functional threshold power. IOW, the calculation of TSS parsimoniously assumes a linear interaction between (virtual) work and intensity, largely because it would be difficult, if not impossible, to truly justify any other formulation.

So how do you get from a linear interaction to a squared relationship? That's really just by happenstance, as a result of expressing the data relative to a TSS of 100 as assigned to an hour of exercise at functional threshold power. IOW, the squaring of IF isn't inherently included in the calculations, but comes of out simplifying the math (which in the process eliminates the concept of work, virtual or actual, entirely).

The good news is that applications such as the "Training Manager" aren't overly particular as to precisely how you quantify the overall training load, although they do require that you do. So, while in the future it may (or may not) be possible to significantly improve upon TSS, we can still put our powermeter data to use right now to better describe, and thus prescribe, training....

[quote="frenchyge"]
Page 9 of Andy's power training document describes an analogy for TSS as "TSS = exercise duration x average power x a power-dependent intensity weighting factor" which makes perfect sense to me - basically the total work done, with an intensity factor applied.

[snip]

Step 8: Divide step 7 by the amount of work that could be performed in one hour at threshold power and multiply by 100 to determine TSS points - Edit: [i]Here's where my world starts to shake. See below.[/QUOTE]
I think the breakdown is between what you quote from p 9, which is an absolute measure of training (duration x intensity x weighting factor) and the result of the page 10 calculation which is the absolute value normalized by what is essentially a 1 hr TT (times 100). As you observe, it is this normalization that introduces the additional IF factor. I believe it wouldn't matter for an individual if the normalization step were left out; though it would make it harder to compare workouts between different riders.

acoggan said:

So how do you get from a linear interaction to a squared relationship? That's really just by happenstance, as a result of expressing the data relative to a TSS of 100 as assigned to an hour of exercise at functional threshold power. IOW, the squaring of IF isn't inherently included in the calculations, but comes of out simplifying the math (which in the process eliminates the concept of work, virtual or actual, entirely).

Andy, thanks for that explanation. It does help. Wouldn't the presence of the IF factor already serve to "right-size" the TSS points without having the "100 points per [enter personal LTpwr value here x 3600] kJ" conversion there as well? In the current calculation, halving the duration halves the strain, whereas halving the intensity produces a quartering of the strain. Does that correlate to your experience or other modelling?

I had originally set up a training plan spreadsheet using your typical IF values of .8 for L2 and .9 for L3 and then mulitplying them by the number of minutes per week to determine TSS per week. I was quite shocked by how the TSS values from my first couple endurance rides matched up against my plan. :eek:

acoggan said:

The good news is that applications such as the "Training Manager" aren't overly particular as to precisely how you quantify the overall training load, although they do require that you do. So, while in the future it may (or may not) be possible to significantly improve upon TSS, we can still put our powermeter data to use right now to better describe, and thus prescribe, training....

I think many of us are anxiously awaiting this tool. 🙂

asgelle said:

I think the breakdown is between what you quote from p 9, which is an absolute measure of training (duration x intensity x weighting factor) and the result of the page 10 calculation which is the absolute value normalized by what is essentially a 1 hr TT (times 100). As you observe, it is this normalization that introduces the additional IF factor. I believe it wouldn't matter for an individual if the normalization step were left out; though it would make it harder to compare workouts between different riders.

Since the IF is already personalized to the individual by dividing by the LTpwr, I didn't notice the effect that personalizing the size of a "TSS point" would have on the overall relationship.

In other words, if I increase my LT power, then not only does a particular workout become relatively "less intense" (ie, lower IF than the same workout from a month earlier), but my TSS points become bigger as well. If my LT pwr is 250W, then my TSS points are worth (250x3600)/100 = 9000 kJ/point. But if I increase LT pwr to 300W then my TSS points are 10,800 kJ/point. Both effects serve to reduce TSS, and the combined effect is where the squaring comes in. It's all becoming clear now.... 🙂

Hey everyone,

I pulled out this thread for educational purposes 🙄.

I just can't completely grasp all of the formula's/calculations. I would like to figure out my IF, TSS, and CTL. I did some searching and found a couple of formula's posted by some of you wizzard's on here. I've never used any spreadsheet's or WKO+'s, so I'm trying it out on paper.

What I got so far :
Yesterday I did a high L3/low L4 2x20 session. So my calculation of TSS is:
91% * 91% * .33 * 100 = 27 TSS (???)

I was at 91% of my FTP, and .33 is 20 minutes.

My 2nd 20 min. interval was at 90%. So the TSS for that was 26.

Is my TSS 53 ??
(Sorry for my ignorance :o)

The other things are:

daveryanwyoming said:

- Normalized Power using 30 second smoothing and pwr^4 averaging
- Intensity Factor = NP/FTP
- TSS = IF^2*hours*100
- CTL = CTL(d-1) + [TSS-CTL(d-1)]*[1 - exp^(-1/42)]
- ATL = ATL(d-1) + [TSS-ATL(d-1)]*[1 - exp^(-1/7)]
- TSB = CTL-ATL

(thanks Dave)
I'm not exactly sure how to use these formula's.

Thank you for any help with my stupidity 🙂,

-Greg

gman0482 said:

What I got so far :
Yesterday I did a high L3/low L4 2x20 session. So my calculation of TSS is:
91% * 91% * .33 * 100 = 27 TSS (???)

I was at 91% of my FTP, and .33 is 20 minutes.

My 2nd 20 min. interval was at 90%. So the TSS for that was 26.

Is my TSS 53 ??
(Sorry for my ignorance :o)

First TSS isn't additive across segments, IOW:

TSS(interval 1) + TSS (interval 2) + TSS (rest) does not in general equal total TSS for the workout.

That's one of the stickier points of the TSS concept but one most of us accept even though in the end CTL and ATL rely on averages of TSS that implicitly rely on addition.

So you need to estimate IF for the entire workout, not segment by segment and you should include all warmup, cooldown and rest time between intervals.

So assuming 10 minutes of WU, 5 minutes rest between efforts and 10 minutes CD all at 0.6 your IF would be ~ 0.82 for 1.08 hours giving you a TSS of ~73

-Dave

Heh, good times.... Thanks for digging that up. 🙂

Greg, your guess was pretty close, but Dave's right. NP and TSS are tough to do on paper. It's a lot easier when the computer does the heavy lifting for you. If you want to post your warmup, cooldown and rest durations and approximate % of FTP for those, someone (or me) will tell you what the TSS would be.

Thanks "wizzards" 🙂,

Ok, my warmup was 15 min at 59%, my rest was 5 min @ 64% and my cooldown was 10 min @ 55%. Besides TSS, these formula's do have a rather complicated process (at least for me anyways).

I need a product-key # to authorize my Excel, so I'll purchase it tomorrow. WKO+ is on my list as well, right after Alex's plan 😉. I figure I have alot of time with my KK computer before next season, to make a decision between a PT or SRM.

Thanks, you all are huge help as always gentlemen,

-Greg

70 min workout
IF = .81
TSS = 77

Also, this might save you some $$ on MS Excel if you're interested: OpenOffice.org - The Free and Open Productivity Suite 😎

This is great, thank you.

When you get OO up and running you might try the scripts contained in this zip folder.

The 'gym TSS spreadsheet' estimates TSS without the 30 second averaging for workouts like the one you described. It works pretty well as long as the time segments are at least a couple of minutes long like they were in your 2x20 example.

The 'simple PMC Predictor' lets you play with different workout plans in terms of individual ride TSS and see the impact on ATL, CTL and TSB.

You'll need to unzip the files, but they should run in OO without modification.

-Dave

Beautiful....

Once again, your help is massive.

ooops, the zip file I posted has the newer (2007) Excel format, try the older version files in here...

Dave,

For some reason when I try to unzip it, it gives me a message "This is the first data disk, please insert last data disk". It pops up endlessly. I don't know what I'm doing wrong.

Thanks,
-Greg

frenchyge said:

Also, this might save you some $$ on MS Excel if you're interested: OpenOffice.org - The Free and Open Productivity Suite 😎

[FONT="Arial"]We'll see how long this sticks around after the acquisition by Oracle...[/FONT]

Sorry Greg, no idea. I just downloaded the file and opened it on two other computers (not the pc I used to zip and upload the file) and both opened the spreadsheets just fine. I expect it has something to do with the unzip program you're using. I haven't seen the error message you posted since the command line pkzip days and floppy disks.

-Dave

gman0482 said:

Dave,

For some reason when I try to unzip it, it gives me a message "This is the first data disk, please insert last data disk". It pops up endlessly. I don't know what I'm doing wrong.

Thanks,
-Greg