Thanks for everybody's input so far! I thought about the matter again and here is what I came up with.
Goal: Allow each PC to use whatever stat he likes for melee attacks, but explain it in the game in a flavorful and believable way.
So here we are:
Combat Styles
At first level, pick a combat style. Your class preselects one combat style by default, but you can switch to a different one if you like. (I believe that "default that you can trade away" will be a common design element in 5E)
Each combat style consists of a stat to use for melee attacks and two other goodies (some of the styles below have more... this is just for design ideas, it would have to be reduced to two). You can spend a feat to gain a second combat style.
Muscle
You swing your weapon with the raw strength of your muscles. You are most effective with a heavy weapon that crushes bones wherever it connects.
* Strength for melee attacks
* +2 to damage when fighting with two-handed weapons
* Push extra square with shield rush
* Knock enemy prone on critical hit
* Default for: Fighter, Barbarian, Paladin
Agile
You're a master of slender, agile weapons, and fancy footwork. With uncanny precision, you strike the enemy where he is most vulnerable.
* Dexterity for melee attacks
* +2 to AC against opportunity attacks
* no attack penalty for fighting prone
* +Dex to damage on critical hit with piercing weapon
* Default for: Rogue
Archer
Your specialty is ranged weapons, but you can draw a blade quickly when enemies come too close.
* Dexterity for melee attacks
* +2 to AC against opportunity attacks provoked by ranged attacks
* switch between melee and ranged weapon as part of attack action
* On a critical hit with a melee action, get a free shift
* Default for: Ranger
Endurance
Blow by blow, you wear your enemy down. When he can't hold his defenses up anymore, you strike him down.
* Constitution for melee attacks
* Use second wind as minor action / gain second second wind
* No ability check penalty / no speed penalty for wearing heavy armor
(Note: details of this one depend on the second wind mechanics and dwarven racial features of 5E)
Tactical
You fight with your smarts. You have studied the old fencing masters from leathery tomes, and know the difference between Giordano's Riposte and the Green Dragon Counter.
* Intelligence for melee attacks
* Give +Int bonus to damage with aid another
* Gain flanking bonus when adjacent to enemy together with ally,
regardless of exact square
* On a critical hit, enemy grants combat advantage to everyone for one turn
* Default for: Warlord
Arcane
Your Wizard training included strict lessons on staff fencing and combat casting.
* Intelligence for melee attacks
* Intelligence save to avoid opportunity attacks when spellcasting
* On a critical hit with a melee attack, use an arcane attack feat on the target as a free action.
* Default for: Wizard
Mystic
Years of training in a monastery have heightened your senses and sharpened your body.
* Wisdom for melee attacks
* Wisdom save against grappling
* Ignore concealment with melee attacks
* On a critical hit, stun the enemy for 1 round
* Default for: Monk
Veteran
You might be new to adventuring, but you've seen battle before. You've fought all your short life, and there is hardly any trick you haven't seen.
* Wisdom for melee attacks
* Does not grant combat advantage to flanking enemies
* Always act in surprise round
* On a critical hit, add your Wisdom modifier to damage
Dashing
You are a swordsman extraordinaire. You know that it's not enough to just be the best, you have to make your enemy feel it. If you can display confidence, your enemy has lost the battle before it started.
* Charisma for melee attacks
* Feint as move action
* Charisma save to defend against feints
* On a critical hit, your enemy takes a penalty on his next attack against you equal to your Charisma bonus
* Default for: Bard
Goal: Allow each PC to use whatever stat he likes for melee attacks, but explain it in the game in a flavorful and believable way.
So here we are:
Combat Styles
At first level, pick a combat style. Your class preselects one combat style by default, but you can switch to a different one if you like. (I believe that "default that you can trade away" will be a common design element in 5E)
Each combat style consists of a stat to use for melee attacks and two other goodies (some of the styles below have more... this is just for design ideas, it would have to be reduced to two). You can spend a feat to gain a second combat style.
Muscle
You swing your weapon with the raw strength of your muscles. You are most effective with a heavy weapon that crushes bones wherever it connects.
* Strength for melee attacks
* +2 to damage when fighting with two-handed weapons
* Push extra square with shield rush
* Knock enemy prone on critical hit
* Default for: Fighter, Barbarian, Paladin
Agile
You're a master of slender, agile weapons, and fancy footwork. With uncanny precision, you strike the enemy where he is most vulnerable.
* Dexterity for melee attacks
* +2 to AC against opportunity attacks
* no attack penalty for fighting prone
* +Dex to damage on critical hit with piercing weapon
* Default for: Rogue
Archer
Your specialty is ranged weapons, but you can draw a blade quickly when enemies come too close.
* Dexterity for melee attacks
* +2 to AC against opportunity attacks provoked by ranged attacks
* switch between melee and ranged weapon as part of attack action
* On a critical hit with a melee action, get a free shift
* Default for: Ranger
Endurance
Blow by blow, you wear your enemy down. When he can't hold his defenses up anymore, you strike him down.
* Constitution for melee attacks
* Use second wind as minor action / gain second second wind
* No ability check penalty / no speed penalty for wearing heavy armor
(Note: details of this one depend on the second wind mechanics and dwarven racial features of 5E)
Tactical
You fight with your smarts. You have studied the old fencing masters from leathery tomes, and know the difference between Giordano's Riposte and the Green Dragon Counter.
* Intelligence for melee attacks
* Give +Int bonus to damage with aid another
* Gain flanking bonus when adjacent to enemy together with ally,
regardless of exact square
* On a critical hit, enemy grants combat advantage to everyone for one turn
* Default for: Warlord
Arcane
Your Wizard training included strict lessons on staff fencing and combat casting.
* Intelligence for melee attacks
* Intelligence save to avoid opportunity attacks when spellcasting
* On a critical hit with a melee attack, use an arcane attack feat on the target as a free action.
* Default for: Wizard
Mystic
Years of training in a monastery have heightened your senses and sharpened your body.
* Wisdom for melee attacks
* Wisdom save against grappling
* Ignore concealment with melee attacks
* On a critical hit, stun the enemy for 1 round
* Default for: Monk
Veteran
You might be new to adventuring, but you've seen battle before. You've fought all your short life, and there is hardly any trick you haven't seen.
* Wisdom for melee attacks
* Does not grant combat advantage to flanking enemies
* Always act in surprise round
* On a critical hit, add your Wisdom modifier to damage
Dashing
You are a swordsman extraordinaire. You know that it's not enough to just be the best, you have to make your enemy feel it. If you can display confidence, your enemy has lost the battle before it started.
* Charisma for melee attacks
* Feint as move action
* Charisma save to defend against feints
* On a critical hit, your enemy takes a penalty on his next attack against you equal to your Charisma bonus
* Default for: Bard
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