Limiting Results To Represent Experience

    In most games a character's growing experience and skill are presented by an increasing modifier.  So in the 5e SRD I've been looking at there is the "proficiency bonus" that starts at +2 for a beginning level 1 character and goes to +6 for the supreme level 20 character.  In addition the 5e SRD, like many other games, adds a die roll to represent uncertainty and randomness to that modifier.  In this case it's the d20.  This is a pretty common system, though the size of the dice and modifiers varies.
    But I had a thought- what if instead of adding a modifier for experience/ skill we just changed the dice?
    The idea came from another thought.  I believe that one of the key differences between the amateur and the professional is reliability.  An amateur is unpredictable, they may perform wonderfully one day and terribly the next.  By contrast the master is consistent, they regularly perform at a high level.  They may have bad days, like anybody, but they will not swing as wildly as the beginner.  This can be represented easily in dice.  A single d20 is wild, it has the same odds (5%) of rolling a 1 as it does of rolling a 20.  Add in dice however, make it 2d10, and things change.  With 2d10 you lose the lowest result, the 1.  But at the new extremes, 2 and 20, you only have a 1% chance of rolling either.  But in the middle, at 11, you have a 5% chance of rolling that on a d20 but a 10% chance on 2d10.  This can be easily seen at the great website Anydice...

    So by changing from 1d20 to 2d10 for being "skilled" (let's call it) we've changed the odds quite a bit.  Our less skilled character has a 10% chance of rolling a 1 or 2, while the more skilled as a 1% chance of rolling a 2 and can't roll a 1.  So the more skilled has less critical failure than the less skilled.  That works.  On the opposite end, the less skilled has a 10% chance of rolling a 19 or 20, while the more skilled has a 3% chance - whoa, wait a minute, the more skilled has less opportunity for critical success?  That doesn't seem right.  Well, okay, but let's look at overall success.  The less skilled has a 50% chance of rolling an 11+, while the more skilled has a 55% chance.  So while they get fewer critical successes, they also get fewer critical failures and a slightly better overall chance of success.

    Those results are not terrible, but also not great, just changing the dice doesn't really give the kind of results I'd had in mind.  But then something else came to me: what if we changed the dice a lot?  Let's say we had 6 different skill levels: d20, d12+8, d10+10, d8+12, d6+14 and d4+16.  That's a lot, likely more than we'd want to use, but it gives us a good spread to choose from and just uses the typical RPG dice.  Let's compare these rolls to target numbers.  Let's see the odds of success for each against a DC: 10, 15 and 20...

d20:        55%  30%  5%
d12+8:    92%  50%  8%
d10+10:  100%  60%  10%
d8+12:   100%  75%  13%
d6+14:   100%  100%  17%
d4+16 :  100%  100%  25%

    There are a couple of things I like about this system, and a concern.  the biggest concern is working with only a few target numbers, like I did above.  I think for something like this I'd use more and closer target numbers like 12, 14, 16, 18 and 20.  Which would give:

d20:       45%  35%  25%  15%  5%
d12+8:  75%  58%  42%  25%  8%
d10+10:  90%  70%  50%  30%  10%
d8+12:  100%  88%  63%  38%  13%
d6+14:  100%  100%  83%  50%  17%
d4+16:  100%  100%  100%  75%  25%

    The extra granularity would help I believe.  I do like how higher levels of skill remove the possibility of lower results, in a way.  The idea that a master will never fumble or do something requiring a low roll has a good feeling of accomplishment, even though it eliminates some dramatic possibilities.
    Another thing that I think would be good about this system is modifiers.  Since the different dice create different possibilities I don't think you'd need many modifiers, and the ones you used would have a different effect.  With a +1 modifier the numbers would change like this (a partial table for brevity's sake):

unskilled- d20+1:  50%  40%  30%  20%  10%  (+5% to each)
medium skill- d10+11:  100%  80%  60%  40%  20%  (+10% to each)
high skill- d6+15:  100%  100%  100%  67%  33%  (+17% to each)

    So as you can see modifiers become more important at higher levels, which has the right feel to me.  I think the more skilled should have more draws, that every little thing should be more vital.  This also means that the +1 sword you got at first level (when you were unskilled) is literally 3 times more useful at 20th level, so again you can keep the modifiers down and make your equipment more valuable.  That will hopefully encourage players to hang on to their early items and grow with them instead of discarding them for some new shiny.

    I'm not sure if this is a worthwhile at all, but I think it has potential.