Pathfinder: % Chance to Hit Based on BAB

So I was working out mechanics for a character class and I came to an impasse when I was assigning it a BAB Progression. I wasn't sure, but it was POSSIBLE I had made a class that was able to be an effective melee combatant with Low* BAB Progression. I started to think... "Well then... I want to give it Medium* BAB Progression... but it might hit to often.... shit. What if I did low? No... I don't think it would EVER hit!"

*Low BAB Progression is that of a Wizard. (Ending in +10)
Medium BAB Progression is that of a Rogue. (Ending in +15)
Full BAB Progression is that of a Fighter. (Ending in +20)


So I set out to find the % chance to hit based on a character's BAB.
First I had to find AC to compare it to. I broke out my bestiary and averaged the AC at levels 1,5,10,15,and 20. It looks something like this:

Level	Highest AC	Avg AC	Lowest AC
1	17	15	13
5	21	18	15
10	27	23	18
15	37	31	28
20	39	37	36

Then I jotted down the BAB progressions at levels 1,5,10,15, and 20.

Level	Full BAB	Med. BAB	Low BAB
1	1	0	0
5	5	3	2
10	10	7	5
15	15	11	7
20	20	15	10

Encounters are balanced with SOME equipment and stats in mind so I decided to assign some bonuses (a LITTLE lowball.) at given levels based on my experience as a GM and Player.

Assuming		Total Bonus
1	+2 In Hit Stat	2
5		2
10	+3 In Hit Stat	3
15	+1 Weapon	4
20	+2 Weapon	5

That meant the following adjustments to my BAB Progression tables:

Level	Full BAB	Med. BAB	Low BAB
1	3	2	2
5	7	5	4
10	13	10	8
15	19	15	11
20	25	20	15

So then I factored in dice rolls. I later used the Highest and Lowest Hits to calculate the percent chances to hit:

		Full BAB
Level	Highest Hit	Avg Hit	Lowest Hit
1	23	13	4
5	27	17	8
10	33	23	14
15	39	29	20
20	45	35	26

		Med BAB
Level	Highest Hit	Avg Hit	Lowest Hit
1	22	12	3
5	25	15	6
10	30	20	11
15	35	25	16
20	40	30	21

		Low BAB
Level	Highest Hit	Avg Hit	Lowest Hit
1	22	12	3
5	24	14	5
10	28	18	9
15	31	21	12
20	35	25	16

Though some math magic, I found the solutions.
(Basically the range of numbers that represented a successful hit over the total data range provided at a given BAB, represented as a percent)

This was the result:

	Chance	To	Hit
Level	Full BAB	Med. BAB	Low BAB
1	47.00%	42.00%	42.00%
5	52.00%	42.00%	36.00%
10	57.00%	42.00%	31.00%
15	47.00%	26.00%	5.00%
20	47.00%	21.00%	--
Avg	50.00%	35.00%	23.00%

Notes:
-Full BAB is really a beast. It pretty much remains at a static 50% chance to hit the entire way to 20. I wouldn't expect to find any variance in the level gaps.

-Medium BAB is really pretty badass starting out... until JUST after level 10- then shit hits the fan. That's an ugly 21% at closing, so if you are GM with a melee Medium BAB character in your group (like a Rogue), remember to give them opportunities to hit things. Try presenting them with targets that play to their strengths so they don't feel left out.

-JEEZ! Even with a +2 weapon and +3 in Strength (or dex if using weapon finesse), a low BAB character CAN NOT (without a natural 20) hit a L20 creature. The lowest AC in the Pathfinder Bestiary is 6 and it's HIGHEST roll possible is a 35)

-I know characters at 15th level and above might have more than a +3 in a stat. I know they might have more than a +2 enchantment bonus from their weapon. Some skills give bonuses. I was just using a baseline for the entire party. A melee character might have a better to hit, but that was just my baseline.



Hope you guys enjoy!
(Credit me if you use this)