Originally Posted by
aaronmcd
Hey I got a question. I'm trying to use a spreadsheet to calculate ATL, CTL & TSB.
When I look online, I find the same general formula for ATL & CTL, but I can't find a consistent time constant and I would rather not take the time going through derivations. I find these three constants popping up:
(1) ATL constant = 1/7, CTL constant = 1/42
(2) ATL constant = 2/(7+1), CTL constant = 2/(42+1)
(3) ATL constant = exp(-1/7), CTL constant = exp(-1/42)
I don't know how to compute exponentially weighted averages. Number 3 seems way off - seems too close to one.
Number one seems best. Starting out with extreme negative, balancing out to +/- 10 most of the time, and being negative most of march with a low of -32 last Saturday.
Edit:
Also wondering what's a good range of TSB to hit during recovery.
Using (1), last three blocks recoveries I hit barely positive (then hovered around 0 for the whole block), +25 recovery (decreased steadily to ~0 through block), and +10 recovery (most of last block was negative).
(3) is correct. the time constant is 42 and 7, not exp(-1/42). If you think about it, exp(-1/42) ought to be correct as CTL is primarily stuff from the previous 42 days, with stuff from the last day matter little. Therefore, the contribution from the previous day should account for most of the new number. exp(-1/7) should be less as the more recent events are weighted more.
THe actual expression are as follows
ATL (today) = ATL(yesterday) * (exp (-1/7)) + TSS (today) * (1-exp(-1/7))
CTL (today) = CTL(yesterday) * (exp (-1/42)) + TSS (today) * (1-exp(-1/42))
also, one last note, for globecanvas's point, an exponential may be written as an infinite series, names exp(x) = 1 + x + x^2/2! + x^3/3! +...; you cut it off after two terms, with x = -1/7, you get exp(-1/7) ~ 1 + (-1/7)