Actually, I think it works like this (5 years experience and multiple explanations boiled down - hope this is more right than wrong).
Every skill has a percentage chance of working in a given situation.
If your chance of success is 100%, you cannot gain skill at that point, on a non-scrolled action. With any action with less than 100% chance, there is a chance of a skill gain. The chance of the skill gain for most skills is based on a ratio of your chance to succeed, versus the level of 100% success, with the chance of a gain getting smaller as you get closer to that 100% success chance (and success/failure also seem to play a part - you seem to gain better from successes before the midpoint of the learning curve, better from failures past it).
The math above is why one should not wear normal skill level boost talismans while trying to gain in crafting skills, or equipment that adds to such skills, unless that bonus is needed to attempt the item being trained.
Now, where power scrolls come in.
While your chance for a gain doing a particular training regimen normally stops at 100% success for that item/action/spell, a power scroll replaces that 100% cap with its level.
To use a crafting skill as an example, most crafting skills advance the rate of success 0.2% for every 0.1 skill gained. As a result, a smith-created item that starts at 50.1 skill, with a 40.0% chance to make, would be 100% success at 80 skill. Normally, one could not gain after 80 when making that item. But, if one uses a power scroll, things change.
Using a 105 Power scroll, the chance of success one would gain at caps at 105% (though is still displayed as 100% for the item)
For the 110 PS, this is 110%, and so on.
So, for this hypothetical item, someone could gain on making the item up to the point where they would be 105%, 110%, 115% or 120% successful with the item, depending on the scroll used.
So, on this item (corresponds to a chain hatsuburi on the Stratics shart, but numbers used as a generic case), a person could gain on the item up to
82.5 with a 105 PS (45% chance of exceptional without talisman)
85.0 with a 110 PS (50% chance of exceptional)
87.5 with a 115 PS (55% exceptional)
90.0 with a 120 PS. (60% exceptional)
This is how a dev explained PS effects on gains several years ago in a post. Note that Blacksmithy is one of the most uniform crafting skills. Some of the other crafting skills (mostly the ones that don't have PS) have items that can progress slower or faster than 0.2% per 0.1 skill.
One also has to look for bonuses to "chance for success" that might kick in at GM. If a skill has such a bonus, it can make what looked like a skill that would gain in the low 100s into one that has no gain chance at that level. Smithing has a +15% chance to exceptional chance at GM, which while it doesn't effect the skill gain chance, confused early attempts to put a chart together to quantify the effects of scrolling on skill gain.
(In the smithing, most items start at 40%, and start being exceptional at normal chance -60%. However, there is a +15% bonus to craft exceptional at GM, which turned 100% normal = 40% exceptional into 100% normal = 55% exceptional. See the example below the main post marked * on how the earlier example works for an item that can be gained on, above GM skill)
Now, for spells and spell-like abilities, they follow a similar rule, with a different step value. 0.25% per 0.1, for magery spells below GM, for example. They also tend to start at 0% chance of casting/use (EA's own charts start at 1% for magery).
At the 0.25% per 0.1 rate, that translates to 1% = 0.4 skill, 5% = 2.0 skill
So, using 6th circle/level magery skills as an example (100% chance is 92 skill), a person trying to gain magery would be able to gain on casting 6th circle spells as follows:
105 PS: 94 instead of 92
110 PS: gain up to 96
115 PS: gain up to 98
120 PS: gain up to 100
So, theoretically, a 120 PS can extend the learning curve for 8-10 skill points, depending in the advance rate of the success chance. Numbers for 1/1, 4/1, & 5/1 given for examples, but unclear if any scrollable skills use those rates.
1/1 (0.1% to 0.1 skill): 20 points
2/1 (0.2% to 0.1 skill): 10 points (most crafting, Chivalry)
2.5/1 (0.25% to 0.1 skill): 8 points (magery)
4/1 (0.4% to 0.1 skill) : 5 points
5/1 (0.5% to 0.1 skill): 4 points
******************
* Running the above example for something that hits 100% success at GM (such as the sai, which starts at 50 skill) gets interesting, because you start getting the interplay of the Smithing +15% to exceptional chance from GM and the need for a PS to progress further.
So it would look as follows...
unscrolled: 100% chance of success at 100.0 skill - displayed chance of exceptional would be 55% (40% + 15% GM bonus)
So, on this item, a person could gain on the item up to
102.5 with a 105 PS (60% chance of exceptional without talisman)
105.0 with a 110 PS (65% chance of exceptional)
107.5 with a 115 PS (70% exceptional)
110.0 with a 120 PS. (75% exceptional)
