What is the expected hit chance?

Question

(inspired by this answer)

A cursory look thru the Bestiary has shown values ranging from 12 to 19 (plus level).

Did anyone collect the data, or has seen any guidelines from the creators?

Answer 1

58.75% for Martial characters, 46.25% for spellcasters

The Gamemastery Guide has tables that GMs can use to quickly build a custom monster based on average stats for each level. The tables are also conveniently combined on the Advanced GM Screen. We can use these to estimate the average chance to hit an equal-leveled creature at each level.

Attack bonus is determined by proficiency (including level), ability modifier, and item bonus. For the purpose of this question, I'm going to assume all possible ability boosts are applied to the relevant score, and relevant items including Apex items are acquired one level later than their item level (per the Character Wealth table). Additionally I'm just looking at the first attack, and only considering whether or not the attack hits, not the chance of critical hit or critical failure. Features such as agile weapons, backswing, Exacting Strike, and Flurry Hunter's Edge can greatly affect the chance to hit after the first attack. I've included the tables I used at the bottom of this answer.

For martial characters (excluding fighter) the average to-hit chance for the first attack is 55-60% (58.75%) for most levels. The chance is 65% at levels 5 and 13, which are the levels when proficiency increases. Fighter has an additional 10% chance to hit in all instances.

Spellcasting characters do not get item bonuses to their modifiers or DCs at the time of writing. Their proficiency also increases two levels later than martial characters, however they eventually reach legendary proficiency while most martial characters do not.

The average to-hit chance for attack spells is 45-55% (49.75%). Level 1 is 60%, on par with martial characters, and level 14 is 40%, which is one level before the proficiency increase.

I also analyzed average saves using the moderate save from the Creature Numbers table. The average chance for an enemy to fail their save is 40-45% (42.75%). There are exceptions at levels 6 and 14, one level before a proficiency increase, and levels 19 and 20, after the spellcaster reaches legendary proficiency.

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Tables

Martial Characters

Level	Monster AC	Ability	Proficiency	Item	Hit Chance
1	16	4	2	0	60%
2	18	4	2	0	55%
3	19	4	2	1	60%
4	21	4	2	1	55%
5	22	4	4	1	65%
6	24	4	4	1	60%
7	25	4	4	1	60%
8	27	4	4	1	55%
9	28	4	4	1	55%
10	30	5	4	1	55%
11	31	5	4	2	60%
12	33	5	4	2	55%
13	34	5	6	2	65%
14	36	5	6	2	60%
15	37	5	6	2	60%
16	39	5	6	2	55%
17	40	5	6	3	60%
18	42	6	6	3	60%
19	43	6	6	3	60%
20	45	7	6	3	60%

Spellcasters (Attack)

Level	Monster AC	Ability	Proficiency	Hit Chance
1	16	4	2	60%
2	18	4	2	55%
3	19	4	2	55%
4	21	4	2	50%
5	22	4	2	50%
6	24	4	2	45%
7	25	4	4	55%
8	27	4	4	50%
9	28	4	4	50%
10	30	5	4	50%
11	31	5	4	50%
12	33	5	4	45%
13	34	5	4	45%
14	36	5	4	40%
15	37	5	6	50%
16	39	5	6	45%
17	40	5	6	45%
18	42	6	6	45%
19	43	6	8	55%
20	45	7	8	55%

Spellcasters (Save)

Level	Monster Save	Ability	Proficiency	Failure Chance
1	7	4	2	45%
2	8	4	2	45%
3	9	4	2	45%
4	11	4	2	40%
5	12	4	2	40%
6	14	4	2	35%
7	15	4	4	45%
8	16	4	4	45%
9	18	4	4	40%
10	19	5	4	45%
11	21	5	4	40%
12	22	5	4	40%
13	23	5	4	40%
14	25	5	4	35%
15	26	5	6	45%
16	28	5	6	40%
17	29	5	6	40%
18	30	6	6	45%
19	32	6	8	50%
20	33	7	8	55%