Well I've been exploring new combat mechanisms these last few months and although I have the combat mechanics well set I'm still fiddling with the hit roll. I'm looking into non linear probability distributions as a way to determine a hit or a miss.
Why this? Excitement. If the probability of certain numbers is greater the action will concentrate on those values rather than spread all over the place. I started out with 2d10 that has a mode of 11. Rolls will tend to fall around 11 unlike 1d20 which can fall anywhere. A one can happen as frequently as a 10, or a 14.
My combat rules say anything above a 10 is a hit. So there are high odds of hitting your target. Although to be honest there is about the same chance of hitting as if you just rolled 1d20. Let us take a look at the curve on the graph below. The black line is the 1d20 and the blue line is 2d10. As you can see the cross just about the middle. Around 10 or 11. So what's the difference. Well the slope. Notice how the blue line becomes steeper as it approaches 9 and begins to level of at 14. Six numbers 9, 10, 11, 12, 13 and 14 tend to occur 50% of the time. Almost as often as the remaining 14. It's quite probable to get a value near 10 of above it. What does this do for the game?
This creates excitement in the battle as there is hit after hit. Now that doesn't mean damage. Under my rules the opposing party can parry or dodge and does so with 2d10 too. That means the defenders roll is prone to land near the attackers roll. Which is what I look for in using 2d10. Not an 18 by the attacker and a 2 by the defender. I mean what the heck happened there? Defenders's cell phone rang? Not likely. So those cases when it seems the defender was not paying any attention to this life threatening fight are gone. Surely a low roll will happen. People mess up, slip or whatever. But not usually, rarely.
Using 2d10 gives value to experience and training. It's less probable to get low values below 7. A +3 bonus takes you to 10 and you score a hit. Just barely maybe and the defender can still parry and succeed in preventing damage. But this is more akin to real life. A well trained fighter gives an unskilled one his run for the money. The unskilled fighter has to try its best while a trained one hits with a somewhat poor hit roll of 7. The curve also makes becoming uber good very hard. Toward the edges the curves slopes decrease and that means that every plus to hit means less. If our fighter rolls a 3 on the 1d20 he gets an effective 6 after his +3. The graph shows us that 75% of the rolls are above 6 for a 1d20, but 85% of the rolls on a 2d10 are above 6. So parrying is easier for the defender when the attacker fumbles bad. So training won't save the attacker so easily from a big mistake. The mistakes are rarer, but when they happen they are hard to hand wave away.
So if 2d10 is so nice, why 2d20. Well let's change the rules a bit so the hit roll is 2d20 (added for a 2 to 40 range). Any value rolled equal or greater to 20 represents a hit. On the graph below the 2d20 curve is shown in orange. Notice how the 2d10 (blue) curve is way steeper than the 2d20. Every plus on the to hit roll is too much of an advantage if you want to allow a lot of training skills and magic. The 2d20 roll provides a more gradual slope that is similar to the 1d20 in the 25 to 75 percentile range. But also has longer tails to each side. A +3 gives you a 75% probability of hitting your target on the 2d20 while being 80 to 85% certain on the 2d10. If you get a lucky shot of 35 it will be hard for a +3 fighter to reach you as he'll more often than not land between 16 and 27.
This makes overspecialization very hard and expensive to the point of being unviable. For a fighter to stop even the most luckiest of shots would mean getting a +10 or +15. How much would that cost him in experience and training. If you add the suggested rules for a self regulating game the player would soon realize that the points spent in reaching these extreme benefits would be best invested in other fields which create a lesser XP burden on the character's progression.
So 2d20 rolls gives a good distribution with a nice set of common values. The slope is lower than for the 2d10, so each extra plus gives less benefit to the character. So it allows the game to have more bonus levels, magic, spells and items that grant pluses to hit while not allowing the creation of super characters. The tails at both ends make it harder to secure a hit or parry in the game with a 100% certainty. A character with a +8 (not very hard to get) can guarantee a hit on a 1d20 and 2d10 system. But hes a long shot from perfect on the 2d20. He's damn good, but not flawless.