Sometimes I think about game design. Rarely, it even results in a good idea! I have good friends that have worked with me on our own D&D replacement, and it makes me happy. There are a lot of things that it does better than D&D. But because it is our creation, we're constantly tinkering. Instead of just letting my mind wander and then potentially presenting a suggestion, I thought it might be interesting to share my thought processes about what we did; why we did it; and what changes might make sense.
In 3.x, you track individual skill points. Particularly when creating a high level character with multiple class levels, this can be needlessly time-consuming. 3.x also has characters multiple their initial skill allotment by 4 at character creation. This results in differences between otherwise identical characters (ie, a Rogue 1/Fighter 1 has many more skill ranks than a Fighter 1/Rogue 1). Tracking and optimizing for when you take each level to determine whether a skill could be purchased as a class-skill or cross-class skill is best done by advancing a character from 1st level one level at a time. Doing it right is hard; doing it any other way is wrong.
The Current Solution
In our system, characters have three possible options for skills: untrained/trained/expert. An untrained character rolls d20+Attribute+1/2 Level. A trained character receives a +4 bonus; an expert character receives a +6 bonus.
Thoughts Regarding the current Solution
One of the things that we are exploring is replacing the d20 with 2d10 (added together). That has some interesting effects on the probabilities. In both 3.x and our current system, it is possible for an expert to be +8 relative to someone untrained (ie, an untrained person might have a +3 attribute bonus; the expert using a skill that relies on their best attribute might have a +11. Considering these numbers, it is possible that the novice will outperform an expert. If the novice rolls a Natural 20 and the Expert rolls a 1, the novice has a 23 to the Experts 12. Even if the Expert took 10, he would have a 21 compared to the novice's 23. So let's do some math hammering! How likely is it?
We know that if the Novice rolls a 20 (5% of the time), he'll beat the Expert on anything below a 12. The Expert is 55% likely to roll an 11 or lower. This means that 2.75% of all skill contests result in the Novice rolling a 20 and the expert rolling low enough to fail. If the Novice rolls a 19, the Expert loses on an 10 or lower (5% * 50% = 2.50%). Skipping a bit; a roll of 10 is the lowest result that the Novice can still win; his modified 13 beats the Expert only if the Expert rolls a 1 (for a result of 12).
Novice Rolls a: Number of 'Losing Rolls' for the Expert Probability
10 1 0.25%
11 2 0.50%
12 3 0.75%
13 4 1.00%
14 5 1.25%
15 6 1.50%
16 7 1.75%
17 8 2.00%
18 9 2.25%
19 10 2.50%
20 11 2.75%
Adding all those probabilities together gives us: 16.5% of the time. That's basically one out of every six times. In fact, if the party has four members (3 novices and 1 expert), the expert is only likely to beat EVERYONE 58% of the time. That bothers me - I think the expert should be beating the novices most of the time. But what about take 10? Sure, it bothers me that the Expert could lose but if they're just doing their ho-hum average and the novice is REALLY TRYING the odds shift pretty significantly. Taking 10, the Expert always has a 21. The Novice only wins with a 19 or 20. That's a simple 10% of the time. Against his three companions, the Expert is 'winning' about 73% of the time. Definitely enough that people will notice that they're good, but they're definitely sacrificing their ability to get their 'best result'.
In our system, we allow people to 'take 10' after a roll. It costs a resource, so you can't do it all of the time, but it does address this situation. We already calculated that if the expert rolled they'd usually win even if the novice rolled a 19 or 20. 5.25% of results. Even against three companions, the expert is winning 85% of the time. So in a party of four, the expert 'leads' 5 out of 6 times. That's probably enough for it to feel like the expert is consistently performing better than the companions.
All of the above calculations are assuming a d20 with a flat probability curve. Using 2d10 the novice has approximately a 10% chance of winning against the expert. There is only a 1.74% chance of the novice rolling a 19 or 20, so if the Expert can 'take 10' after the roll, that's the odds of winning. That works out to a 95% chance of coming out ahead against three novice companions. I'm definitely liking those numbers better.
One thing I've been wondering about is if it would be better to have 4 levels of skills: untrained/trained/expert/master. We currently use diminishing returns (ie, trained is +4, expert is +6). If we followed that existing logic, Expert would only be an additional +1 for a total of +7. Alternatively, we could make Trained +4; Expert an additional +3; Master would then be a further +2 (+4/+7/+9).
Implementing that would result in an additional +1 compared to my original examples (+12 versus +3). With a 9 point difference the odds of losing to a Novice are 13.75% for d20 and 7% for 2d10.
Now, other than the bonus for the various levels of training, it seems like there should be other benefits. There are various ways to adjust the probabilities. I'm focusing on the 2d10 from here on out since that's what I care about most for my game preferences.
Rolling Additional Dice
One potentially simple way of helping adjust the odds is simply adding additional dice, and letting players take the best 2. Trained could be 3d10; expert could be 4d10; master could be 5d10. Of course, the extra dice could start with expert/master; there's some flexibility.
Treating some number of Dice as a Particular Result
Another way is to allow a level of mastery impact the ability to take 10 (either before or after the roll). For example, someone who is trained could 'take 10' or roll, but couldn't take 10 after the roll. An expert could take 10 after the roll. A master could treat one of the dice as a 10 (ie, they'd roll 10+1d10).
Allow 'take x' after the roll
I already mentioned that above, but allowing someone to treat the roll as higher than it was eliminates bad results. In our current system, we do allow it with a limited resource.
Putting it all Together
Untrained: 2d10+attribute modifiers. Characters cannot 'take 10' on a skill that they're not trained in (announced before rolling). Our system allows them to treat the roll as a 10 if they spend a limited resource.
Trained: 2d10+4+attribute modifiers. Characters can take 10 (announced before rolling). Our system allows them to treat the roll as a 10 if they spend a limited resource. If they know taking 10 will succeed, they should just take 10; they should never need to spend a resource on this roll.
Expert: Best 2 of 3d10+6+attribute modifiers.
Master: I don't need a master rank.
So if I have an unskilled novice (+3 ability modifier only) versus an Expert (+5 ability modifier and +6 expert bonus), the difference is +8 (as considered before). An untrained character will have to roll for success. The trained person could take 10 if that would be sufficient. The only thing I don't like is that the trained person won't know if taking 10 'wins' unless the untrained person goes first. That's not satisfying for me.
In any case, that's what I'm thinking about. I'm interested in feedback. I'll let it stew for a day or two myself and see if my thinking changes. I'm not sure I like an extra die roll (seems fiddly) and I'm concerned about not enough difference between Untrained/Trained - I looked at Untrained versus Expert - obviously with the smaller difference a Trained Character dominates less than an Expert.