There are five levels of proficiency:
Untrained - Level -2
Trained - Level
Expert - Level +1
Master - Level +2
Legend - Level +3
There's a few problems I have with this. Mostly its the introduction of more terminology you don't need. It would be as if every +1 you had in an ability score had a different name. You just don't need it and it causes you to have to convert things in your head from words to mechanics every time you make a roll, which slows things down.
All we'd need is a core mechanic that works like this and you'd have no more problems: d20 roll + Level + Ability + Skill. Then you could just label the bubbles +0,+1,+2,+3,+4.
Though this brings me to another issue that bugs me. Untrained skills start at a -1 rather than 0. You're basically spending your first point of proficiency to just not take a penalty, just to get back up to zero. Ugh. Would it kill the math to just have everything shift up one?
Untrained - +0
Trained - +1
Expert - +2
Master - +3
Legend - +4
Here's another gripe about the names here. A person who's what, five percent, better at a skill (whatever a +1 equates to) than someone else is now an expert? And another five percent better is a master? And five more and now they're a legend? So basically a legend in martial arts (say Bruce Lee) going up against a white belt is going to have a difference in skill of 3 on a d20? I don't like that. If you want skills to represent expert, master and legend levels the jump in value needs to be a big one. You'd want the idea that in a competition between two people at a skill check that the person who's trained would need to roll amazingly to have a chance against and expert and would have no chance against a master or legend. I like the idea of 3-5 point jumps maybe?
Untrained - +0
Trained - +3
Expert - +6
Master - +9
Legend - +12
That way legends feel like legends and trained people feel trained.
Though really I'd much rather do away with the per level titles entirely and just have the bonuses expressed in numerical +'s.
In the new math, +3 per step is too strong. HOWEVER, I agree in principle. After reading everything and doing some quick tests, I think there is room in the math for +2 per step, which would make the steps feel much more meaningful. I also agree that Untrained should be 0, so it would go Trained +2, Expert +4, Master +6, Legendary +8.
(This would also help address that you really only have a 50-60% chance of success in the game as written on a level appropriate attack roll or skill check even when fairly optimized, which is too low to me.)
In the new math, +3 per step is too strong.
It depends what your intent is. On one hand, yeah I really do get it that +3 jumps are a little crazy. On the other hand you're trying to model the difference between a person who's trained in a skill and someone who's a master. That seems to deserve a little omph.
What would you say to the increase only kicking in once you pass into Master and Legendary ratings?
Untrained - 0
Trained - +2
Expert - +4
Master - +7
Legendary - +10
That strike you any better?
Bear in mind that +2 now represents not only +10% more chance of success, but +10% more critical successes and -10% less critical failures. I think that is pretty significant and worthwhile.
It'd be even better though if Assurance was built into Expert+ levels of skill, since as written the feat is worthless, but if included in skill advancement would help the higher proficiencies feel more worthwhile despite the current lack of high level skill feats.
The proficiency level labels are used all over the place in the rules. You can't remove them without increasing word count significantly (e.g. "requirement: +2 or better proficiency in Athletics" instead of: "requirement: master in Athletics".
Regarding math: a +1 in PF2 is roughly equal to a +2 in PF1. So, increasing the steps to +3 would clearly be too much. +2 is debatable imo.
Eh. "Requirement: +2 Athletics". Literally just a number and the skill name is all you'd need. Seems fine to me.
Regarding the math, I think it's largely what you want the math to model, but the Pathfinder crowd seems to be very averse to power of any kind outside the fairly rigid curve whereas I like a little more oxygen let in, so understandably YMMV.
Eh. "Requirement: +2 Athletics". Literally just a number and the skill name is all you'd need. Seems fine to me.
Regarding the math, I think it's largely what you want the math to model, but the Pathfinder crowd seems to be very averse to power of any kind outside the fairly rigid curve whereas I like a little more oxygen let in, so understandably YMMV.
The real trick here is that your bonuses would go much farther in some areas than others.
The fighter gets expert at level 1, master at level 3 and legendary weapons by 13.
More than half the classes are lucky to get to expert at all, and if they do, it is usually around level 13 at the earliest. Even by your more narrow scale that means fighters (and NPC fighters) might be running around getting critical hits 50%+ more frequently than other characters of the same level. That will be lights out for a lot of PCs.
Having a swingier scale is certainly a possible direction the game could have gone it, but it probably requires giving up the 4 tiers of success, and radically changing the entire structure of the game.