1. HH
2. Game Mechanics

This is the game mechanics as currently suspected, gathered from data analysis. If you see errors, wrong values, or know something that's missing, please help out.

Battle Team
Your Battle team is comprised of your hero and 3 Haremettes, an Alpha, a Beta, and a Gamma. Only your Alpha currently contributes to the battle stats at the start of the battle, but there is speculation that giving your Alpha an orgasm will allow other team members to contribute as well.

Basics of Battle Mechanics
In Harem Heroes, "Attack" is analogous to "Damage Dealt" and "Ego" is analogous to "HP".
When engaging in combat, every round starts with you dealing damage to the enemy's Ego usually equal to your team's "Attack Power". After their Ego is reduced by this damage, if they have 0 remaining Ego, you have won. If they have more than 0 Ego remaining, they will reduce your Ego by an amount usually equal to their Attack Power.
Sometimes, an attack will be a critical. It will deal more damage (unknown exactly how much more). The "Critical Damage" stat may determine the damage boost when a critical occurs, or it may determine the chance of a critical. This is not known for certain.

When a Haremette's excitation reaches 100%, the next round they will have an orgasm and do bonus damage. It is unknown if this damage is a function of the "Critical Damage" stat.

Battle Stats and Where They Come From
[Team Battle Attack Power] = [Hero's Hardcore stat] + 3 × [Alpha's Hardcore stat]
[Team Battle Ego] = [Hero's Endurance stat] + [Alpha's Hardcore stat] × [Alpha-Specific Ego Boost Multiplier]
[Team Battle Excitation] = 28 × ( [Alpha's Hardcore stat] + [Alpha's Charm stat] + [Alpha's Know-how stat] )

The choice of Battle Harem members has an effect on Charm Defense and Know-how Defense, but this effect(s) is unknown.

Haremette Stats
Members of the harem have 4 main (currently-known) stats from which their contributions are derived. Three of these stats are shown (Hardcore, Charm, and Know-how), one must be calculated (Ego Boost Multiplier).
Hardcore, Charm, and Know-how are a linear function of Haremette level and a linear function of Affection level.
The amount Hardcore, Charm, and Know-how changes is easily determined by observing the Haremette's stats when first acquired, at level 1 with 0 Affection. Henceforth, these will be referred to as BaseHardcoreRate, BaseCharmRate, and BaseKnowhowRate.

A Harmette's stats are determined thus:
[Stat] = [BaseStatRate] × [Haremette's Level] × ( 1 + 0.3 × [Haremette's Affection] )
A Haremette's stats will be the same at any given level and Affection regardless of the order in which they leveled and raised affection.

For example, if at Level 1 Affection 0 Haremette Bob has Hardcore X, Charm Y, and Know-how Z, their stats will always be:
Hardcore = X × ( Level ) × ( 1 + 0.3 × Affection )
Charm = Y × ( Level ) × ( 1 + 0.3 × Affection )
Know-how = Z × ( Level ) × ( 1 + 0.3 × Affection )

The experience required for a Haremette to level is:
Rounded up to the nearest integer: 10×1.0075^([Current level] - 2).
For the total experience value needed to reach a target level L, it gets a bit difficult because of the rounding, but roughly it is: 10×(1.0075^L-1)/0.0075 + rounding error.

Hero Leveling
This might not be entirely true because of the rebalance made during the August 2017 and not taking player's class into account.
Every level, your hero gains +9 Hardcore, +5 Charm, +7 Know-how, +67.5 Endurance, and +0.105% Critical Damage.
The experience required for a hero to level is:
Rounded to the nearest multiple of 10: 12 × [Hero Level] ^ 2 + 10 × [Hero Level] + C, where C must be >=17 and <23

Battle Experience
This is definitely oboslete since August 2017.
Experience granted for winning against another player in battle seems to be random at the start of the game, but eventually remains static for each level.
Confirmed only on levels 11 through 25, the XP/Battle seems to follow either a polynomial or power function:
0.123787976729151 × [Level] ^ 2 - 0.0563671622494653 × [Level] + 1.92992889463452
or
0.1621124 × [Level] ^ 1.9162682

Players with data on the XP generated from each victory as a function of level are encouraged to share this data to assist with determining the formula which governs this.