It's not such an easy question to answer.
Google "Fatigue and accident rates" and you'll get many answers- yet even the best admit that it's difficult to define, let alone measure, fatigue. A very large share of the links look at fatigue in terms of traffic accidents.
It's quite hard to really nail the topic down. Ultimately, it comes back to the old dispute whether "behavioral sciences" are science at all. Yet, there's no denying the anecdotal evidence. There's also no denying that outside factors can alter the feeling of fatigue- at least for awhile.
I've seen far too many suffer from trying to do just ONE more for the Gipper .... and, without a doubt, the bad decisions came from bad judgement ... which leads me to conclude that judgement is the first thing to be affected by fatigue.