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Agility - Increases Accuracy, Critical Hit, and Critical Defense
Luck - Increases Guard, Critical Hit, and Critical Defense
Though I haven't pinned down the exact rate at which they influence those stats.
In the character menu while in camp or through management during deployment you can press B to flip back and forth between Basic Stats and Combat Stats. Hovering over the stats gives a tool tip on what they do.
Dexterity - increases Guard, Accuracy and Crit defense
Agility - increases Accuracy, Crit and Crit defense
Luck - increases Guard, Crit and Crit defense
From my experiments it seems that:
CRIT=(AGI+LUCK*2)/5+15 rounded up.
GUARD=(LUCK+DEX*2)/5+15 rounded up
ACCURACY - that one doesn't seem to be exactly like the other two. What I can say is that DEX contributes less than 20%, while Agi contributes something like 35%
CRIT DEFENSE=(AGI+LUCK+DEX)/7+15 rounded up (low confidence, but works for my roster).
When I looked at his stats, he is substantially weaker on agility and luck than others - enough so that I decided to make robere an aide asap and choose people with a much higher combo of DAL (dex,agi,luck) stats to be my vanguards and templars.