I developed the 4 hour increment based on many of the marching and soldiering literature, both in historical and modern.
I apply that 4 hour increment in mental activities. Divide the day into the 4 hour increments, minus the 8 hours of sleep. You have 4 slots of noticeably optimal and decreased mental alertness and energy levels. At the last slot, my self control is noticably weakened. I would say a GURPS -1 to -3 to will rolls depending on how much psychological beating I had that day (which can be something of a morale stat).
Some of the slow risers out there, the optimal productivity hours come 4 hours after the zenith of sleep. Depending at what point one reaches this full mental defrag....
I leave it to people who want to min/max mental performance to read up more on sleep and cognition...
More to the point. What is interesting is that in the BPO industry, there is a rule of thumb that comes from average performance of agents of 6 hours. After 6 hours most agents do not have the mental stamina to close a call. (this is in outbound). Talking with the objective to persuade should be counted as a challenging mental task that requires a lot of concentration.
What is remarkable of this rule is that it follows also some of my observations about the 4 hours slots. if I were to assign these slots 1st to 4th. Then the 2nd slot is the most productive, followed by the slot before it and the slot after it. the 1st or the 3rd slot is not necessarily half as productive as the 2nd, but closer inspection at where these episodes of productivity clusters should be observable in the reports provided by the call manager.
So it is Evidence, but not well documented evidence of the performance curve of mental endurance of the day.
In a game, I would use the 1st to four slots as a way to gauge the morale of the NPCs and ideally the way PCs should view challenges (easy when their full of energy, insurmountable when tired).
Damage from Fatigue. What is interesting at looking at all these performance, also watching and experiencing Burn-outs is the RPG abstraction of Damage vs Fatigue. An interesting differences is that Damage is like Burn-outs, it is much harder to climb out off.
When managing our selves and those of our team, Burn-out is Damage. Burn-out is a line which, once crossed your stuck with much diminished capabilities and have to dedicate resources (time) nursing back to health/mental health.
Its not a penalty that will go away in a nights rest, it is something that will take a few days, weeks, months or a lifetime. Psychological wounds doesn't have to come from drama, it can come from incredibly frustrating work... (my opinion about my work).
Play it like a Game. Given the amount of responsibility and the fire-fighting at work, managing one's self is a game which has a lot at stake. Games teach us to weigh risks, plan and maneuver our assets quickly, Unlike PCs, the mind (or ones' sanity), is an entity that is more challenging to preserve since resources are not so clearly written. All one really has are a ton of personal notes and time to reflect on limitations and mistakes. (a PC without a character sheet)