The Bard's Eclectic Skill class feat, pp.101-102, says "You add your level to all skill checks in which you are untrained."
The Untrained Improvisation general feat, p.168, says "Your proficiency bonus to untrained skill checks is equal to half your level instead of +0. If you're 7th level or higher, the bonus increases to your full level instead."
Add to that the Clever Improviser human ancestry feat, which also grants Untrained Improvisation and says, "you can attempt skill actions that normally require you to be trained, even if you are untrained," and don't you have a jack-of-all-trades skill monkey that will surpass even someone with Legendary Proficiency?
Proficiency bonus at Level 20:
Eclectic Skill (+20) + Untrained Improvisation (+20) = +40
Key stat (22 for +6) + Level (+20) + Legendary proficiency (+8) = +34
I am new to Pathfinder. What am I missing?
What we're missing, is language that says the Bard's Eclectic Sill shouldn't stack with Untrained Improvisation. Though I think that's the probably the case.
I highly doubt they intended you to have a +40 bonus to skills and to be able to use them as though you we're trained despite being untrained. You would actually be better at your untrained skills, since you wouldn't get the bonuses to them for the others.
I welcome our untrained overlords!
For the best use, you have to take one of the 2+int skill classes, take an 8 int and multiclass into bard to max out the +40 bonus. ;)
Put all your skill trains and upgrades into lore. You are amazing at every job except the few you actually tried to learn to do. You're a legendary barkeep, but even better at selling umbrellas.
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It is not quite official, but the demi-semi-hemi-quasi-pseudo-official word from Mark Seifter on the matter is:
the only positive numbers you can add to a check, ever, are ability modifier (if positive), proficiency modifier (if positive), item bonus, status bonus, circumstance bonus. There is no untyped bonus or mystery additional modifiers to checks in the system, and it's referring to training, albeit a bit more colloquially there. Follow the sidebar that says if one reading of the rule looks wrong, even if you can't think of another reading right away, don't go with the thing that's wrong.
I suppose that makes sense.
If this weren't a fairly unintentional gap in the rules and resulted in a final skill mod that was closer to baseline, even a point or two below, it would be absolutely perfect for making a luck-based character build. Sort of reminds me of that joke from New Vegas, "They asked if I had a degree in theoretical physics. I told them I have a theoretical degree in physics."