D&D's bow breaks the fighter

Weapon design should be taken seriously even if D&D is only a game. I'm going to show how the current bow model in D&D negatively affects the fighter. Some may say that overly realistic weapon models may slow down game, that this is the way it's always been, that it's only a game and so many other reasons to maintain the status quo. The truth is the current bow model works against the fighter and in effect leads to its nerfing.

I'll begin by stating the rules I'll be using here. Strength bonus can be applied to a composite bow's damage roll and dexterity bonuses are applied to all bow's to hit roll (range weapon to hit bonus). I'm assuming that given a high score a fighter would most commonly use it in strength and a rogue would use it in dexterity. I will then show that the +1 from DEX works better for the rogue than the fighter's +1 from STR when both are using a composite bow.

A +1 added to damage will make an average arrow (1d8) go from 1-8 hp to 2-9 hp of damage. A +1 added to the to hit roll will increase the odds of hitting.

The average damage done by an arrow without the +1 is 4.5 hp as the 1d8 has a flat distribution, and 5.5 hp if the +1 is added. This damage only counts if the character hits. So against an AC of 10 the character has a 55% probability of hitting (10 or greater on a d20). Multiplying 55% vs 4.5 hp we get 2.48 hp/roll. Doing the same with 5.5 we get 3.03 hp/roll. The net benefit of the +1 STR is 0.55 hp or 22% improvement.

If we look at the rogue we see that the damage does not increase, but the odds of actually hitting are better. So while the hp damage does not increase the hp/roll does. A rogue with a +1 to hit has 60% of hitting an AC 10 target. Doing the math we get 2.48 hp/roll without the modifier and 2.7 hp/roll with the modifier. That's a 9% increase. Which so far is lower than the fighter's, and all would seem well.

But let's do the same process for all rolls leading up to 20. The tables below shows the data for the fighter and the rogue. As the AC improves and the required roll gets higher the hp/roll ratio remains the same for the fighter, but increases for the rogue. The fighter keeps getting that 22% benefit, but the rogue begins to get better beyond a roll of 16. Against a target that requires an 18 or better the rogue has 33% improvement when having the dexterity bonus than without it, while the fighter still has only 22%. A roll requiring a 19 or better requires an 18 or better when fired by the rogue. This creates a 50% hp/roll bonus.

Fighter Bonus Table

To Hit	Odds to hit	hp/roll at +0	hp/roll at +1 STR	Benefit hp/roll	% increase
10	55.00%	2.48	3.03	0.55	22.22%
11	50.00%	2.25	2.75	0.50	22.22%
12	45.00%	2.03	2.48	0.45	22.22%
13	40.00%	1.80	2.20	0.40	22.22%
14	35.00%	1.58	1.93	0.35	22.22%
15	30.00%	1.35	1.65	0.30	22.22%
16	25.00%	1.13	1.38	0.25	22.22%
17	20.00%	0.90	1.10	0.20	22.22%
18	15.00%	0.68	0.83	0.15	22.22%
19	10.00%	0.45	0.55	0.10	22.22%
20	5.00%	0.23	0.28	0.05	22.22%
				Average benefit	22.22%

Rogue Bonus Table

To Hit	Odds to hit	hp/roll at +0	hp/roll at +1 DEX	Benefit hp/roll	% increase
10	60.00%	2.48	2.70	0.23	9.09%
11	55.00%	2.25	2.48	0.23	10.00%
12	50.00%	2.03	2.25	0.23	11.11%
13	45.00%	1.80	2.03	0.23	12.50%
14	40.00%	1.58	1.80	0.23	14.29%
15	35.00%	1.35	1.58	0.23	16.67%
16	30.00%	1.13	1.35	0.23	20.00%
17	25.00%	0.90	1.13	0.23	25.00%
18	20.00%	0.68	0.90	0.23	33.33%
19	15.00%	0.45	0.68	0.23	50.00%
20	10.00%	0.23	0.45	0.23	100.00%
				Average benefit	27.45%

I can conclude that the +1 from dexterity benefits the rogue more than the +1 from strength benefits the fighter. The fighter gets a benefit against unarmored peasants, leather armored magic users, and studded leather on rogues. Whereas the rogue gets a great bonus against plate mail, banded mail, full plate and other highly armored targets. The table below shows the average benefit difference between the impact of STR and DEX as the bonuses increase.

Bonus	STR	DEX
+1	22.00%	27.00%
+2	44.00%	54.00%
+3	66.00%	82.00%

Now as some may say: it’s a game, it’s not meant to be real, but how can it be fun when the guy that’s supposed to be the lead fighter simply sucks against the hardened  opponents on the battlefield?