I believe there is a link between how tired you are and how bored you are. The other day I found myself extremely bored. Did I have stuff to do? Yes. Lots of stuff. The problem was, I didn't have the gumption to do it (yes, I just used the word gumption). I was doing everything but what I needed to. I was watching hulu, playing computer games, and just wasting my time. I was also bored out of my mind. Here's the kicker: today I feel the same way. I am battling myself to stay on task and wish I could have a perpetual bucket of water poured on my head to wake me up. I have no gumption. Here's the correlation between my boredom episodes: both of these bored times were after fairly late nights. I am going to do some research on myself and see if I can gather data evidence to back up my theory, but I believe that there is a correlation between boredom and tiredness.
The link is fairly easy to see after you think about it for a minute. When you're tired, what happens? Your brain shuts down to the point of wanting to sleep. When I am at work, I can't sleep. At least, I have to look like I'm awake, right? So, the recipe of a shut-down brain and having to stay awake is also the recipe for boredom. The key is the brain is not finding excitement nor fulfillment in anything you are doing. So, it follows that the brain will try to find entertainment in the usual places that are fun and exciting, watching TV, playing a game, and just regular, non-physical forms of entertainment. You've got a mountain of stuff to do, none of which looks appealing and so the brain naturally goes elsewhere to find something fun. You then begin that activity only to realize that this activity is also not fun (because your brain is turned off) and you look for the next thing and the next until you waste your time, go home, and sleep.
What is the solution, you might ask? Obviously get to bed earlier. Sometimes young parents will not get the best sleep because of children and what not, but by and large, getting to bed earlier will be the best option to stave off boredom. So, before staying up, you have to weigh in your mind how productive you want to be tomorrow compared to the benefits of staying up. Is the time you are spending up worth the loss in productivity the next day? Many times, yes. But it is something to think about before taking the leap.