Empirical Sleep Time

Good and bad sleep accumulate over days. Thus moment by moment measures of productivity are of limited use and any experiment has to compare extended periods of time, a week at the least, probably better a month. The very widely held consensus in the field is that you should go to sleep at the same time every night and wake up without an alarm. This should be the control for any experiment.

I'm thinking that it should be possible to decide when to sleep based on reduced performance.

It certainly is!

Can anyone suggest a tool for that purpose? Perhaps some reaction time testing software?

Double N-back seems to be precisely what you're looking for. It effectively tests how long a sequence of information you can keep in your mind, and how accurate you can be about recalling the sequence. Being tired impacts your DNB performance, and is a marker for the kind of "reduced performance" you're looking to avoid.

Accounting for training effects aside, the way you'd work this is to test yourself on a DNB regime every hour or so. When your results start to drop, you entertain the hypothesis that you're tired; if the next hour is further down still, you decide you're tired to the point of reduced performance and you go to sleep.

(That is a rule of thumb calculation; you can get Bayesian if you want)

Can anyone suggest a tool for that purpose? Perhaps some reaction time testing software?

I used something called a Psychomotor Vigilance Task when I was doing my sleep deprivation experiments. Essentially, you spend ten minutes watching a screen, reacting when it starts counting up. This measures how frequently your attention lapses (since even at high levels of sleep deprivation, it's possible to accomplish complicated tasks, so long as they're short duration). I coded my own in Ruby Shoes, and can send you the code if that'd be helpful.

While it's useful at measuring sleep deprivation, I don't think it's particularly useful at measuring performance around normal levels. What you're interested in there is not so much "how easily do I get bored?" but "how creative am I?", and the PVT is really unfun and boring to do.

If you don't get enough sleep one night, you'll "rebound" and sleep in longer the next time you get a chance to do so to make up your "sleep debt." If you log your sleep every night with a ZEO (or similar tool) you can get a pretty good estimate of how much sleep you need just by looking at how little sleep you can get without a rebound on the weekend.

Performance can be a tricky issue, because short-term sleep deprivation can improve your mood and alertness, whereas short term sleep deprivation does the opposite. You may find that you do better on a test with less sleep, if you had been well rested up until the night with restricted sleep.

In general the effects of something that happens on one day carrying over to the next is a difficult problem to deal with in self experimentation. I would recommend trying to get more or less sleep than usual in about the same amount for at least a week before drawing any inferences about performance at that sleep duration.

Is your problem determining when to go to sleep, or actually making yourself go to sleep when you think you should for optimal effectiveness?

http://www.quantified-mind.com/ gives you mental tests.

This would have been better in an open thread.

I would think there would be too many confounding variables, and the best you could do is find some testable proxy for performance.

You could just buy a Zeo.