One thing to note is that your stats appear different for you than they do for other players who do a battle against you. Basically the system is always supposed to be skewed in your favor. You benefit from bonuses that your opponents do not get.

Endurance is the baseline for health, and other players will see that number as your health bar. Ego is... inflated based on your alpha's stats, I think? And ego is what you see as your health bar when you battle.

I've noticed that enhancing your character's primary stat will add to your endurance (mine is charm, so the charm stat gives me extra endurance) while enhancing your other two stats (hardcore and know-how in my case) will give a slight boost to your crit chance.

I don't even remember ever seeing a luck stat mentioned so I'll take the other responses' word for it that it was changed to crit.

I assume that excitation is a measure of how quickly the girl will advance the excitement meter to 100% with each turn of combat, but I've never really noticed the difference. But getting that meter to 100% adds the next girl to the fight and I think it also does extra damage.

You also have three stats that only appear in battle, an attack stat which is always matched to your character's type and two defense values matched to the other two types. These three values are a range starting with stats based on only your alpha and ending with stats based on having all three girls involved. (Which calls back to reaching 100% excitement. After that happens your attack and defense both get stronger because of the next girl joining in.) Other players will see your attack and defense stats at a significantly reduced value compared to what you see on yourself. (Tower of Fame doesn't seem to be working at the moment but normally you can verify this on there. Click on your own name and it will show you the profile that other players fight against. You'll see the reduced battle stats there.)

In any given battle only 1-2 of your 3 stats will ever be relevant. Charm vs charm is pure offense against pure offense. No defense is considered at all. Charm vs hardcore is the charm player's attack vs the hardcore player's defense against charm, and it's also the hardcore player's attack vs the charm player's defense against hardcore. Neither side cares one bit about each other's know-how stat.