TLDR: In my game, finesse and ranged weapons don't get a stat damage bonus and Dueling gives the damage bonus to 1- and 2- handed weapons. Is this balanced?
Starting running a game for the first time in several years. Two of the players are new to D&D (a Warlock and a Bard). The other hasn't played since 2nd edition (a Ranger).
During character creation, I gave them incorrect rules about weapon damage which I must have misremembered. I told them that Finesse and Ranged weapons don't get a damage bonus, whereas other weapons get a strength bonus. The correct rule, having checked, is that Finesse and Ranged weapons get a damage bonus from dexterity.
Now, the Ranger player, remembering 2nd edition, gave his character a high dexterity for archery, but chose to have them wield a longsword with no shield. That means has base damage dice is the same as the bard with his rapier - both a d8. However, his bonuses are actually lower. At 1st level, he was a worse fighter than the bard!
After the first session, I took his player over the bonus and dual-weapon rules and checked if he wanted to keep using the longsword and not use a shield, and he did: he just chose to wield it two-handed for the higher damage dice. So I decided to keep my rules error a feature of the game. That way at least the Ranger gets a bonus on his damage dice, and the Bard does not.
I'm not sure why the Ranger wants to keep the longsword, I think he's just got a strong image in his head from his 2nd edition Ranger characters. As a result, I also rejected the obvious compromise of letting the Ranger have a "longsword" that's actually a rapier. I figured that might also cause problems with distributing magic items (is it a rapier? is it a sword?).
At 2nd level, the Ranger chose Duelling and, again, I've let him keep it as +2 damage with his longsword even though, strictly speaking, it's not supposed to be used two-handed. Now the Bard gets +3 to hit and a d8 damage while the Ranger gets +1 to hit and a d10 +3 damage, which at least makes him seem like a bit more of a warrior.
I haven't explained to the players that I've got the rule wrong. Not out of fear of losing face but because it makes the party a little better balanced, and I don't want the Bard claiming his +3 damage, putting him back in front of the Ranger. None of the other players has a rulebook.
I don't believe this is in any way game breaking: it just gives the party a marginally lower damage output. So long as I tailor the encounters accordingly, I don't see it as an issue. But I know D&D 5e is much better "mechanically balanced" that some older editions and I might have missed something going forward when the party gains more levels and meets more powerful foes.
Is my approach here balanced and fair, in particular, have I made the Ranger overpowered and the Bard underpowered in comparison?