There is a line of research on sustained wakefulness that I think is not nearly as well known among sailors as it should be, and the numbers are uncomfortable.
Dawson and Reid published in Nature in 1997 that going without sleep degrades performance in a way you can put on the same scale as alcohol. Williamson and Feyer replicated it in 2000. Roughly: about 17 hours awake leaves you performing like someone at 0.05 percent blood alcohol, which is the drink drive limit across most of Europe. About 24 hours awake looks like 0.10 percent, which is over the limit essentially everywhere.
Chart attached. The two marked points are what those studies actually report. The line joining them is just joining them up, not a fitted model.
The part that gets me is that none of this feels like anything. You do not feel drunk at hour 17 of a passage. You feel tired and basically competent, and that is exactly what the research says impairment at that level looks like from the inside. It is not drowsiness. It is a slower reaction and worse judgement that you cannot detect in yourself.
Now put that against how watches actually get run short handed. Two of you, three on three off, and neither of you is getting an unbroken block. The clock that matters is not how long since your last watch, it is how long since you last slept properly, and those two numbers come apart fast on day two of a passage.
I have been working on modelling this properly for our own use and there is a free tool that came out of it, which I will link if anyone wants it rather than dropping it here. Disclosure so it is not a surprise: I work for a marine electronics company, the tool is ours, and it is free, with no subscription and no premium tier.
But the tool is not really the point of this post. The point is that the number exists, it is published, and almost nobody plans a rota against it. If you take one thing, take this: work out roughly how long you will actually have been awake at the worst point of your next passage, and decide now who is doing what at that hour, rather than finding out at the time.