Thanks a lot LoOp but I still don't follow any of this Anyway, I'll just leave it there, and accept I'm not going to get it, I don't want to take up any more of the thread.

Probably my fault. I think my brain is like a bowl of spaghetti with some gold nuggets thrown in there.

This is a graph of H40, Bob, and Q, AVERAGED:


Can you see that since we added more data (averaged 3 members experiences), the difference between the actual amounts consumed and the trendline narrows or is lessened, compared to the other graphs of members individual experiences?

I haven't included the R^2 value (which is the degree of confidence that the trendline can actually predict the amounts consumed) in any other chart here so far. For all three the R^2 value was in the .1-.2 range (where 1 is optimal, meaning the trendline EXACTLY predicts past, present and future amounts consumed). In this averaged graph, by adding 3 members experiences together, the R^2 value jumps from .1-.2 to .665.

We are removing the noise inherent in individual experiences and revealing the fact that TSM works in a pattern, very predictably described as exponential decay

This is wrong.

This is the equation:

8days

you are correct in that there is little point getting too worked up about graphs till you're cured. You are also correct about the light switch moment - however when lots of subjects are graphed together these effects average and the curve becomes exponential (as Loop has elegantly demonstrated).

The little value that the trendlines have is that they sometimes tell us things that aren't immediately obvious to the eye, as well as providing us with hard numbers that 'improve' as we progress through the journey

LoOp - you are correct with the equation you displayed, which in English means that the slope of the curve is proportional to value of the curve - i.e. at high levels you decrease more quickly, and at low levels more slowly.

You can also reduce it to the form I suggested, which I think is intuitively easier for people to understand - that if you take any two successive values and divide them, you'll always get the same number. A little bit of algebra can transform one into the other.

Could you do it and show me? My brain is still floating in a bath of C2H5OH

LoOp -- Isn't the trend line in this case documenting/illustrating rather than predicting, since you are using historical data?

I'm half sorry I posted this because I think all this technical jargon detracts from the eloquence of the graphs

lena, you are correct - it is smoothing/fitting the past rather than prediction in the examples above

LoOp

here you go:

dN/dt = rate of change of N with respect to time

= (change in N)/(change in time)

So for two successive days this becomes

(N2-N1)/(1 day) = N2-N1

So on day two, the rate of consumption decrease is N2-N1

our equation was: dN/dt = -(lambda)(N), which on day 2 becomes = -(lambda)(N2)

So we have:

N2-N1 = - (lambda)(N2)

divide both sides by N2 to give:

1 - N1/N2 = -lambda

or N1/N2 = 1-lambda

lambda is a constant which means the right hand side above, i.e. (1-lambda) is a constant

which says that the ratio of successive days is a constant

Yeah, I suppose. The reason I'm using the word predicting is because that is the supposed function of a trendline, to predict the value at some point in time. I'm not sure about this but I believe when we use the word "predict" in this case there isn't necessarily a tense. The trendline also predicts values in the past. Bob's trendline predicted he would drink 18 drinks in week 15. It was wrong, he actually drank like 38 or so, but it is still a prediction.

Yes, the trending is useful as an analysis of past data and not as useful in prediction of future consumption rates. Lena warned me about doing that when I started "goal setting" a couple of weeks ago. However, the more data you have, the more accurate you can be within certain limits to predicting the next consecutive week. For instance, based on my drinking history under TSM, statistically I can be 68% sure (if I did my calculation right) that I will drink somewhere between 2 and 14 units next week, with the strongest likelihood of 6 units. That's a wide margin, but still there's a 32% chance my consumption will be outside that range. It could be zero. It could be 16. I won't know until next week.

When I am one year into TSM, the range for one week prediction will be smaller, but it still will be a range and it will still only be likely and not a certainty.

Anyway, for us math weenies, it's fun to model the extinction curve mathematically and make nearly useless assumptions based on it.

Bob

Thanks so very much for the patience to explain things everyone, especially LoOp and One-four. The maths itself may still bamboozle me, but I understand about the average exponential now, and it's fascinating that trends are most probably there even when we can't see them at the time.