Let's assume you spend 30% of your time sleeping (7.2 hours a day), and your expected lifetime to be T. Then your "useful time" is 0.7T. So you decide to sleep 25% more (9 hours), so you sleep through 37,5% of a day and your life expectancy is now T'=1.25T, so your useful time is 0.625T'=0.625 x 1.25T=0.781T. Your useful time grown around 12%.
Note that if you take your working hours into account and you are only interested in your free time after work, then this free time will hoard up more at the end of your life when you will be retired but you will lose free time before that.
> But that extra time spent sleeping is time spent not being awake to do things. So the overall number of useful hours is the same either way?
Am I the only person that likes sleeping and dreaming? If I were to suddenly find sleep impossible and unnecessary, I would consider that a reduction in my quality of life.
> Also if you sleep well, and live 25% longer, that 25% will be when you're old, senile, and unable to do anything useful.
That's assuming you do become senile and unable to do anything useful. Doesn't necessarily have to happen, and that doesn't mean you shouldn't live a good life.
> Studies about sleep are often just crazy. When did people stop using their common sense? Just have as much sleep as you think works for you.
What's considered "common sense" can vary greatly from person to person, and people aren't always aware of how their habits can have long-term negative consequences on them.