The Sleep Formula

Running low on sleep turns up the suck on everything, especially
intelligence and mood. Sleep deprivation sucks in any job, but is
especially disastrous in a self-motivated, creative-type job like being a
grad student. I can easily lose a whole day of sciencing if I screw up
that night's sleep. What's confusing though is the sense that the night
*before* last night plays a big part too. So how can I predict for how I'm
going to feel on a given day? (the non-geek may wish to skip
to the punchline at this point.) As a simple model, I will call the lack
of sleep deprivation, or the amount of well-restedness, my "sleep charge",
and it will be a function of the last n nights' hours of sleep. Let's make
it a linear function then at time t it's x(1)*s(t) + x(2)*s(t-1) + ... +
x(n)s(1+t-n). So what are the x's and the n? How far back do I look at my
sleep pattern, and what weightings do I give them?

This will differ for different people. But for myself I've decided and
tested the model of going back only 2 nights. And they will be equally
weighted. (so this is a 2-point simple moving average) The formula I now
use, and which has been remarkably successful in predicting how much I get
done and how I feel about it is this then:

Sleep charge = number of hours slept last night * 0.5 + number of hours
slept the night before * 0.5

As an example, 6.5 hours one night and 8 hours the next, equals a sleep
charge of 7.25. Now all I need is interpretation. Using intuition, for me
I think it goes something like this:

Sleep charge < 7: Zombie like.
Sleep charge 7-7.5: Ok
Sleep charge >= 7.5: Shiny and full of pep, cleverness and creativity.

This rule has been astoundingly accurate at predicting my days over the
last week and a half. Just as the formula predicts, one bad night affected
two days and then I was fine. And knowing that showed how it's useful: by
knowing I was going to havee a zombie day, I could stop panicking about
being too scattered and slothful, take it easy on myself, and plan for
what I *can* do - there are always a few zombie jobs around that I've been
putting off. And it becomes ultra-clear what the benefit of getting that
extra bit of sleep is, and when to plan to exploit that burst of willpower
and inspiration (like I had sunday).

What have you figured out about how your sleep works?