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I would simply assign a flat increase to the DC of any associated concentration check required by another circumstance: +2DC if fatigued and +6DC if exhausted to match the associated penalties. This would cut down the clutter of requiring another d20 roll per spellcasting action.
But if you were to add such a roll, I'd suggest using the DC of 10 + spell level as the base for a "generic" distraction caused by a non-leveled spell effect, and then add the +2 or +6 to the DC on top of that depending on the condition.

Evil Lincoln |

Fair enough. But in this case I explicitly want to add a roll, because fatigue and exhaustion are a disproportionate burden on martial characters.
That's a problem, it's not even on-message for fantasy tropes, with fatigue being a frequent counterbalance to magical power in many, many literary sources.
Fatigue/Exhaustion and Negative Levels both need adjustment in my opinion.

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How often do you want spellcasters to fail and lose a spell while fatigued or exhausted? And what are your assumptions about casting stats and availability of mental stat enhancements? Those will play a big part in determining check DCs.
Does this look about right for your group:
Level 1: Casting Stat 17
Level 4: Casting Stat 18
Somewhere between 4th and 8th level, gain a +2 stat item.
Level 8: Casting Stat 21
Somewhere between 8th and 12th level, gain a +4 stat item.
Level 12: Casting Stat 24
Somewhere between 12th and 16th level, gain a +6 stat item.
Level 16: Casting Stat 27
Level 20: Casting Stat 28
If you know (on average) the casting stat and the desired failure frequency, then you can reverse-engineer a DC progression for something like this.

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If your going to hit the casters with this rule frequently, expect them to quickly invest in gloves of elvenkind or combat casting.
In such a game, I would personally pick up both early in the game, rendering most concentration checks trivial. I might also add in Focused Mind as one of my traits, for a +11 on my roll.

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OK, so based on the numbers above for expected caster level and casting stat, you can get a fairly even failure rate across all levels of play by using a DC of 5 + (Spell Level x 3).
But this assumes that you have a baseline idea about how often you (as the house-rule creator) want spells to fail due to fatigue. For this purpose I set the bar low, with a failure rate of around 5-20% for the highest level spell a caster can use. Casting a spell one level lower than your highest reduces the failure rate by 15%.
Characters with only 6 levels of spellcasting see the rate of failure become completely trivial by character level 6, assuming they throw resources into their casting stat. (for purposes of this idea, I am assuming this.) I assume a 4-level spellcaster is even more laughable.
See this google spreadsheet for the math used.
It has a tab each for prepared, spontaneous, and 6-spell-level characters. I have given the stat boosting item at 5th, 10th, and 15th levels.
If this helps you get a better idea of the impact, awesome!

Evil Lincoln |

The real goal is to make casters think twice about casting their highest level spells while fatigued. It makes highest-level spells feel "hard" to cast.
To that end, I might even jack the DCs you give (5+SL*3) another five points (10+SL*3). That more or less ensures that casters hate fatigue, makes healers who can cure fatigue integral to non-barbarians, and achieves my goals.
High level casters can still fall back on their easier spells, and it would be nice if they had to estimate what DC they could actually hit. Yes, it's a little cruel, but that's the point. I love to play casters when I get the chance to be a player, I know they'll still be totally worth it.
Thanks for the math!
EDIT: I like how the half-casters (Bard, Inq, Magus) end up auto-passing after a fashion. I'll be that happens with the martial casters too. Makes sense to me!