It was also pointed out that there is no upper limit to any of the rolls. A "trained" roll can equal a "legendary" roll since, improbable as it may be, the player rolling for "trained" can get a streak of 20 ones and just keep adding to the roll and in that manner inch its way to beating an opposing "legendary" opponent that just happens to roll a low or at best an average "legendary" roll. But how far apart is the average "skilled" roll from an average "legendary" roll? In other words how much do I need in modifiers to (on the average) equal one with the other.
Turns out the modifier bonus required to equal a "skilled" roll to a "legendary" roll is in the order of +23. That's quite a bit! Thinking in D&D combat terms, that's like matching a 1st level fighter with a 20th level fighter!
The chart below shows the difference between the rolls' mean values.
I like to see things graphically rather than laid out on a table, so the next graph shows the information in a radial layout on which each spoke graphs the mean difference between its level and the skill levels above it. Starting with unqualified on top and moving counter-clockwise we see that all points are at zero since unqualified is above no other skill level. The next skill counter-clockwise is trained which is slightly above trained as you can see the blue line begin to spiral downwards. Skilled is above the yellow and blue lines, and so forth. You can clearly see how much faster the lines circle downwards as we approach the master and legendary skill levels. This means these higher levels are distancing themselves faster and faster from the lower levels. In other words you'll need exponentially more and more modifiers in the form of weapon bonuses, magic modifiers, blessings from the gods, etc., just to keep up to the skill's improvement rate.
You can't just buy yourself into master or legendary skill levels, you've got to sweat it out through adventures, learning and training.
So what do I seek to achieve with this?
For starters a simple skill representation with levels that aren't just +1 points away from each other. This makes reaching each a significant milestone, specially for the upper tier. It's something you can be proud of as a player. It's not easy for an NPC or another player to simply stack up modifiers and reach the roll values of a master or legendary. But don't feel 100% safe in your master or legendary skill level! Remember that the Black Swan System allows lower levels to reach higher levels if they keep getting low rolls and adding these to the total (called a black swan roll in the game, an unexpected and highly impacting event). As a high level character you can feel confident, but not 100% safe, in your high skills. A lowly goblin can always happen to roll a black swan and beat your master roll!