Stats
For your hero, Stats are very important. Each level gives you 1 point to place in either Politics, Attack, or Intelligence. Loyalty is Also very important.
Politics
Politics plays a key role when the hero is Mayor. For each point of politics on your hero, you get 1% increased production. That doesn't sound like a lot at first, but when you have a hero with 100 Politics then that effectively DOUBLES production rate. Politics also reduces Construction times as well. An ideal Mayor also has high Stats for Attack and Intelligence. For example, when more troops are required during an all-out attack and all Heroes are committed, having a low Attack Stat mayor slows re-enforcements to a crawl.
Attack
Attack plays a role in both Attack and Mayor. When Mayor, Attack reduces troop recruitment time... For Example:
In order to build a catapult with no mayor, it takes:
Attack 0 Time 1hr 40min 00sec
Attack 18 Time 1hr 31min 22sec (8.633% decrease)
Attack 19 Time 1hr 30min 54sec (9.1% decrease)
Attack 20 Time 1hr 30min 27sec (9.55% decrease)
Attack 21 Time 1hr 30min 00sec (10% decrease)
--DemaFrost 13:52, 7 May 2009 (UTC)
So as you can expect, there is quite a bit of reduction already and it only gets better; however, there is not a set percent each additionally point decreases it by. Take note that each point you add will start taking less of a percentage the more points you get into it at a diminishing value.
Higher attack also increases the Attack when trying to conquer a valley or town. Higher Attack means Better Success.
Intelligence
Intelligence Stat of the Mayor lowers the time it takes you to research something in the Academy.
Loyalty
If you capture an opponent's hero in a battle, giving that hero gold will persuade him/her to join your forces.
See Loyalty. Giving the Hero medals and more gold will increase loyalty after they have been persuaded. Initially
the new Hero will join your forces with 0 loyalty. See Reward Button section in the Feasting Hall.
Hero Formulae
These following formulae are useful for working out what your hero will do:
Production: Base production x Mayor Politics / 100
Construction: Base time x 0.9 ^ Construction level (from accademy) x 0.995 ^ Mayor Politics
Unit Training: Time after improvements x 0.995 ^ Mayor Attack
Research: Base time x 0.995 ^ Mayor Intelligence
The last three show diminishing returns, suggesting that a mayor is better to have a good mix than being particularly strong in one aspect.
Related Information
You can see more about how different things affect production times here: