Min/Max crit as of athenaeum

Accursed 2MB limit. I'll just link.

Just to prove that I do indeed have an S Rank Hayato Card.

Base, no buffs, no Explorer's Critical Ring. Hayato Card and Soul Shooter Expert.

20% base + 15% from Soul Shooter Mastery + 6% from Hayato Card = 41%, makes sense. I have no passive maximum critical damage boosters.

Now, what happens when I wear my Explorer's Critical Ring?

20% base + 15% from Soul Shooter Mastery + 6% from Hayato Card + 10% from Explorer's Critical Ring = 51% minimum... but wait. I only have 50%, and I now have 51% maximum. Huh?

Now let's try with Decent Combat Orders and no Explorer's Critical Ring.

20% base + 16% from Soul Shooter Expert + 6% from Hayato Card = 42%. That's all good and dandy.

Re-equip the Explorer's Critical Ring with Decent Combat Orders active..

20+16+10+6=52, but again, I'm stuck at 50% minimum, and my maximum has gone up to 52%.

Everything goes back to normal once my maximum critical is higher than my minimum critical, though. The math checks out.

More interesting example is my Battle Mage. They don't get any passive maximum critical damage boosts, but they do get Battle Mastery, which gives 20% minimum critical damage and Staff Expert, which gives 15% minimum critical damage. I should have 61% minimum and 50% maximum, but they're reversed...

But, there's also the 150 Hyper, Battle Master, which boosts maximum critical damage by 20%.

Everything's back to normal now that the maximum has exceeded the minimum.

Then there's Battle Rage, which explicitly states that it boosts minimum critical damage by 15%...

 But it goes and does this. P.S. Ignore my IGN. I was young.

Weird. Seems that whenever the minimum is greater than the maximum, the minimum critical damage matches whatever the current maximum critical damage is, and then whatever is left of the minimum critical damage gets added onto the maximum critical damage.