Having a little information can be a dangerous proposition. Lately I've been reading up on things like TSS (Training Stress Score), NP (Normalized Power), and IF (Intensity Factor). I have a powertap and no coach, so I get to experiment with some stuff.
See, I'm an engineer, which means that I am naturally curious about the equations that come with having a powermeter. In case you didn't get the memo, there's a lot more that you can do with a powermeter than just measure power. The biggest thing that's in vogue at the moment is this thing called WKO+, which is a software program developed by a guy named Hunter Allen which takes all that raw powermeter data, condenses each ride into a single number, then does stuff with that number. The number is the so-called TSS, or Training Stress Score. You can read about this elsewhere, but basically it's a number that quantifies how hard your ride was.
I hate to do stuff with numbers that I don't understand. It drives me up the wall to, say, look at an insurance reimbursement summary because it's got a number added to a bunch of zeros that equal to zero. Not kidding. I can show you the paper. It's even got plus signs and equal signs between all the numbers. Anyway...
So, I hate to do stuff involving numbers that I don't understand. First off, the whole concept of TSS starts with the concept of NP, or Normalized Power. This is your power as a function of time, smoothed out using a smoothing function, raised to the fourth power, averaged, and 4th-rooted. Still following? Basically it means that there is some function, call it the "Stress Function", which is directly proportional to Power raised to the fourth. This is actually supported by some data, so it's not all bullshit here. Basically then, normalized power is the constant power which, if sustained for the time of the workout, results in the average of the stress function. Nobody's following now, but I'll plow ahead anyway. I have no issue with this at all. Makes perfect sense to me.
TSS is basically the amount of energy the rider expends during the ride, "corrected" by an "intensity factor", which is a function of the normalized power described above. I happen to think that the TSS concept is wrong.
The first clue is that a three hour ride at endurance pace will net the same TSS as a one hour ride at time trial pace. Maybe, but consider this: take two identical riders. Set them on an every-other-day training schedule at 100 TSS per workout. So far so good. Now, Rider 1 does his 100 TSS as a three hour endurance ride, every other day while Rider 2 does his 100 TSS sessions as a one hour at threshold interval set. Let them do this for a month, give them a few days off and then set them against each other in a time trail. Which one wins? My money's on the guy who did threshold intervals for a month.
But TSS doesn't reflect this at all. If you look at a plot of their TSS, it is identical. You'd think that they are training identically. But it's been well documented by Friel and others that interval training is much better for training racing efforts than just riding around for a few hours.
So here's what I propose. TSS, when it's normalized to the rider's functional threshold power, becomes the equation: TSS = T*IF^2, where T is time in hours and IF is "intensity factor" which is NP/FTP. Let's go back to the original derivation of NP. NP is the constant power which produces the same average "stress function" value as the raw power function. The whole point of TSS is to incorporate training "volume" with intensity. Andrew Coggan says on the Wattage Forum that "work" (derived by multiplying NP with time) is the volume component and IF is the intensity; he multiplies these together because he can't really think of anything better to do to combine them. The big problem with describing his formula in this manner is that IF and work energy are not independent. They are both dependent on NP. This is sort of a problem if your starting point is assuming that "volume" and "intensity" are independent concepts.
Now imagine a new TSS* formula which simply multiplies the average "stress function" value, which is proportional to NP^4, and time. Normalize it by dividing it by the average stress function value at FTP and you get TSS* = T*IF^4, where T is time in hours. Let's put it to the test:
Rider 1:
TSS* = 3hr*0.6^4 = 39%
Rider 2:
TSS* = 1hr*1^4 = 100%
Isn't this more of what we expect? Rider 1, following his 3 hour, endurance ride schedule, will be vastly undertrained (61% less) compared to Rider 2. This isn't a new concept: Coggan himself considered this formulation briefly after noting that data for time-to-exhaustion vs. power (which is kind of like the TSS concept) followed a near 4th power law form. He dismisses this out of hand though for some reason involving the hypothetical seeming equivalence between the recovery time from a 12 hour ride and a track pursuit effort.
Food for thought anyway. Myself, I am keeping track of both TSS and TSS* and will see how well each correlates to my form through the season.
PS. If you don't know who Andrew Coggan and Hunter Allen are, they wrote a fairly widely read book about training with a powermeter.
Thursday, November 26, 2009
Subscribe to:
Post Comments (Atom)
3 comments:
Brian,
Some food for thought on Thanksgiving:
Training stress score /= training performance score.
Andrew,
Thanks for responding! Can you expand on your comment?
The whole point of training for me is for performance. I can tell for myself when I need to recover; I don't need a score to tell me that. I need a quantification of how well my training is adapting me for racing. TSS seems ill suited for that.
I read some of your original concepts on the Wattage forum back in 2003 when you were still developing the system. I thought you discarded the IF^4 model a bit flippantly.
Whether you realize it or not, when you developed the NP model, you developed a "stress function" which is proportional to IF^4. And then you discard it out of hand in favor of the IF^2 model when you developed the TSS.
TSS isn't measuring training performance though. Since that is related to goals, and cannot therefore be isolated in a single metric.
Whilst you've said the 1hour guy will win, and he almost certainly will win a ~1hour TT. It's nowhere near as certain as who'll win the 100mile TT or the 12 hour TT? (I don't know if you have these in your part of the world, but come to Britain, there's loads of TT's that long, on good fast courses.)
Certainly simply measuring TSS as a whole will give you little idea of who'll win, but I don't think completely devaluing the longer workouts make any more sense.
I think, rather like dividing up Running and Cycling CTL's as a triathlete has to, an improvement on TSS should look to divide up the power zones that have been trained, so a score that is specific to the needs of the event being trained can be achieved.
Post a Comment