I want to offer a rule that recreates that in OD&D or Basic. Towards that end I offer two house rule ideas, one very simple and the other a bit more complex.
Very Simple: Give Fighters and Demi-humans a +1 to-hit and damage at 2nd level. This is over and above their normal to-hit progression and weapon damage. The bonus increases by another +1 every three levels beyond that (4th, 7th, 10th, 13th). Ignore bonuses from magic weapons.See? Simple. However, personally, I find this unsatisfying. You see, one my "problems" with the current status of D&D combat is that your AC and damage are more or less fixed at 1st level (or whenever you buy plate armor), and never improve without magic. Meanwhile your Hit Points and To-Hit improve with level. But you know what's weird about that? If To-hit improves but AC doesn't, your odds of hitting get ridiculously good pretty quickly, to the point where it's hardly worth rolling. Meanwhile your damage per round becomes fairly inconsequential relative to the number of Hit Points your opponents have. It's like "En guarde! I will now nibble you to death!".
The only thing that keeps the above death-nibble phenomena from getting out of hand is the magic item bonus to damage. And while we have provided that with the Very Simple Fix I proposed above, I want to also propose a system where To-hit is fixed relative to AC at 1st level, and Damage output scales with Hit Points and Hit Dice.
Towards that end I threw together this quick spreadsheet computing the number of rounds it would take a fighter of a given level to kill an opponent of the same number of Hit Dice. This is not a fancy spreadsheet, and does not account for damage dealt back to the fighter or any other factors. However, crude as it may be, it allows us to at least ballpark what sort of numbers would be required to keep a damage-scaling Fighter competitive with player expectations formed by the to-hit-and-magic scaling fighter.
Here's the link to the spreadsheet again. Please note there are two sheets, and the important table is on the second one.
For those who don't want to click through, or find the formatting difficult to read for some reason (like you're on mobile) here's the summary of what a damage scaling fighter would look like:
At Level 1 a fighter has +4 to-hit and a damage multiplier of x1 (this multiplies the number of dice of damage his weapon does).
To-hit only increases a small amount - +5 at 5th, +6 at 10th, +7 at 15th. The reason for having a to-hit bonus at all is that I wanted something to set the fighter apart from the non-fighter classes at 1st level.
The damage multiplier increases 1 step every 3 levels. x2 at 4th, x3 at 7th, x4 at 10th, etc. You can interpret this either as a single blow that does 4d8+8 damage, or as four attacks that do 1d8+2 each. Personally I prefer the latter, as it allows a high-level fighter the option of attacking multiple weak opponents.
Magic items give a +1 to-hit and to damage, but that's the best they ever do. It's not the sword, but the arm that wields it. Presumably in this campaign, magic items are wielded for secondary reasons, like the ability to detect the presence of orcs, rather than for flat numerical bonuses.
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