Stats for Heroes

We just had a discussion on hero's stats and which ones are desirable. I was a little confused myself, so I thought I'll write it up to be clear.

Military Hero
This is probably the most important type of hero in this game, so I'll start here.
STR affects Attack, and each stat increase Attack by 3. This is the most important stats for a military hero.
DEX affects Tactics (probably affecting dodge and critical hits), probably the next most important stats for doing Floating Castle.
AGI affects Speed, and when doing events, this might even be more important than STR.
DEF is the least important, since a hero gets a lot of defense from the 5 pieces of armor. Each stat increases that number by a far smaller percentage when compared to the increase in any of the other 3 stats.

Summary ::
Wild monsters : STR, AGI
Floating castle : STR, DEX
Attacking : STR, AGI
Defending : STR, DEX

Contest Hero
For a contest hero, STR again is the most important. DEX comes next.
AGI affects Evade, and gives a chance of winning against stronger heros. This is not so important for Arena. But in Pagoda, and you are trying to beat a level and willing to try multiple times for a win, you may want to bring up your Evade to have a winning chance.

Summary ::
Arena : STR, DEX
Pagoda : STR, AGI

Political Hero
STR affects recruiting speed
AGI affects building speed
DEF affects defense bonus
DEX affects production
Given that a building speed is determined at the time the building is started, you may want to put on AGI items only when starting on a long construction.
STR again is important, since you really want to be recruiting as fast as you can.
DEF is the most important and the only stat that matters when you are defending against an invasion. In times of war, I'll say this is the most important stats.
DEX is the least important. Your resources can come from farming.

Summary ::
Before starting a long construction, put on AGI items.
Peace time : STR, DEX
War time : DEF, STR