I’ve ranted a lot already about the gap between characters at things like skills and various ways to try and close that gap. This is sometimes referred to as “flattening the power curve.” One way that I haven’t really talked about is alternate methods to reward training that aren’t straight numerical bonuses. With the limited expressions of the d20, numerical bonuses quickly differentiate characters enough that it is tough to challenge them both simultaneously.
What if training let you roll 2d20 and take the highest instead of giving +5?
This graph shows the chance to meet or exceed the target number (the left most column) on a d20. The first light-grey column shows that probability on a single d20. The progression shouldn’t surprise anyone. The subsequent columns show the probability of a single d20 meeting or exceeding the target on Xd20.
Hit probability by target and number of rolls | |||||
Target | 1 roll | 2 rolls | 3 rolls | 4 rolls | 5 rolls |
2 | 95% | 100% | 100% | 100% | 100% |
3 | 90% | 99% | 100% | 100% | 100% |
4 | 85% | 98% | 100% | 100% | 100% |
5 | 80% | 96% | 99% | 100% | 100% |
6 | 75% | 94% | 98% | 100% | 100% |
7 | 70% | 91% | 97% | 99% | 100% |
8 | 65% | 88% | 96% | 98% | 99% |
9 | 60% | 84% | 94% | 97% | 99% |
10 | 55% | 80% | 91% | 96% | 98% |
11 | 50% | 75% | 88% | 94% | 97% |
12 | 45% | 70% | 83% | 91% | 95% |
13 | 40% | 64% | 78% | 87% | 92% |
14 | 35% | 58% | 73% | 82% | 88% |
15 | 30% | 51% | 66% | 76% | 83% |
16 | 25% | 44% | 58% | 68% | 76% |
17 | 20% | 36% | 49% | 59% | 67% |
18 | 15% | 28% | 39% | 48% | 56% |
19 | 10% | 19% | 27% | 34% | 41% |
20 | 5% | 10% | 14% | 19% | 23% |
I’ll include the 3d20 to 5d20 in the subsequent analysis, but the most part I am really only thinking about the variation that occurs from 1d20 to 2d20.
We can really see two things going on as we progress from one to two dice. The first is that the bonus is a bell curve with +5% at a target of 2 and 20, but a bonus of +25% in the middle. If we were to examine the incremental bonus (as opposed to percentages), it would look like this:
What we see is that a second die roll is basically identical to training (+5) for the most common DCs in the 8 to 14 range. For most of the game, rolling 2d20 would play identically. Where it differs, though, is at the extremes. Under the current rules, an easy task might be automatic for a trained character and present some modest challenge for an untrained character. For instance, if an untrained character “has to roll a 6,” he has a 75% chance to succeed. The trained character would then “have to roll a 1” and auto succeeds. I agree that the trained character should be better, but some amount of tension is always preferred. Under this system, the trained character “has to roll a 6 on one of two dice” and has a 91% chance to succeed. I prefer that small chance to fail that makes the check still matter.
The second thing we see in the jump from one to two dice is the impact of training. That is, if the first things we discussed is “how likely are you to succeed?”, the second thing is “how much more likely is a trained character to succeed than an untrained character?” That question is answered by dividing the gain by the original likelihood of success. It looks like this:
So against a painfully easy task (2+), a trained character isn’t that much more likely to succeed than an untrained character. It is painfully easy for both of them. Against an average difficulty task (the 8-14 range), a trained character is about 50% more likely to succeed. But against something really hard (20), a trained character is almost twice as likely to succeed.
I haven’t finished tinkering with it, but I think there might be room to develop this to streamline DCs so that the only variable is level instead of level and difficulty. As always, input that helps push this along is appreciated.
Very interesting. Could also mean a slight increase in resolution speed (which you talked about before)? I would think comparing two rolls is faster than adding +5 to a single roll?
ReplyDeleteIt might. I imagine there will still be other modifiers (like ability) so it will probably be about the same. You'll roll 2d20, take the highest, and add +3 instead of +8. Maybe negligibly slower although I think people are in general more comfortable handling smaller numbers which this would promote.
ReplyDeleteJust popping in to say once again, enjoying your blog - so please keep it up. :)
ReplyDeleteIn regards to the above, it is something I have also looked at in terms of breaking down the game's core mechanic and looking at what each part represents:
- The Skill Modifier: is meant to mathematically represent how good a character is at something. You expect a master of the sword to have a higher modifier than one merely proficient or familiar in it's use. By what degree is the interesting question and I think a flattened power curve is a suitable thing to aim for.
- The DC: What really guides all of this is the concept of the novice and the master. Let's assume a novice has a modifier of +0. The limit of what a novice can achieve is a DC 20 [A DC of 21 or higher is simply impossible without assistance]. Is it then reasonable to say that by DEFINITION: A master can effortlessly do what a novice would find impossible? If true this would seem to indicate that the master should have a modifier of +20 with anything now over a DC 40 being impossible. If so, that is your scope. That is the range that you want to base everything around.
Even still, this can be compressed further by deciding where one who is "proficient" sits on the modifier ladder. Conceivably you could reasonably push them up to +8 although if you really wished to flatten the power curve, you could push that up a little further and even push the master back down a little.
With this thinking, it takes just a little while to find that perhaps a huge issue is the size of ability modifiers and the enormous range they create (justifiably or no). I'm not suggesting changing anything here in terms of ability modifiers but it might be something to consider at some stage.
- The Roll: What exactly is the roll meant to represent? I suppose at a basic level, it is meant to represent the vagaries of fate. In the spur of the moment, there is a large variability of results from a single action (20 degrees of success as it were). Does it represent skill or training? I'm not too sure it should. It is like directly double dipping your expertise, once for the modifier (which that modifier is supposed to represent) and once again for the roll.
However, I can see your thinking here and can possibly suggest a slightly different way of skinning the same beast - at least this is what I am looking at doing in my own creation. And that is that the roll represents the conditions under which the action is taken - be they neutral, favourable or not.
Under favourable conditions, you can do the double d20 roll. Chances are your character is going to make the best of favourable circumstances and the double roll taking the best result reflects than nicely.
Under neutral conditions, you roll the d20 as per usual.
Under poor conditions, you roll the double d20 and take the lowest result!
However, there is an interesting aspect that you can overlay over the top of this which ties in nicely with your central idea. How skilled your character is (be you unskilled, proficient, expert or master) is reflected by how your character reacts to certain conditions. A highly skilled character is going to be granted favourable conditions more often while an unskilled character will find them taking such actions under unfavourable conditions more often than not and rarely ever under favourable conditions. A highly skilled character is going to find themselves under unfavourable conditions much less often than the novice. By what degree and how often is a question for another time but again one to think about.
I think such an approach respects the nuances of the core mechanic and what I think they are designed to represent, combining them neatly with your ideas of flattening the power curve.
Just some ideas- look forward to your further thoughts.
Best Regards
Herremann the Wise
I like the analysis but I think it might need two more pieces: "What is success?" and "What is failure?" Without these pieces, it is impossible for the skill system to model behavior (which I posit is at least part of the goal of any game system).
ReplyDeleteThey answers to each sort of have opposite implications but it is easiest to see the impact through looking at "What is failure?" For instance, if the consequence of a failure is that your character dies, you care less about the DC and more about the probability of failure.
You give the example of a novice (+0) being able to at most achieve a DC 20. But regardless what the die result *could* achieve, no novice will even attempt a DC 15 jump over a 1,000 foot gorge because there is too great a chance of failure.
If we look at the reverse scenario with great rewards for success and no penalty for failure, then we see that the DC is, again, irrelevant as all characters will in essence take-20.
I'll have to think more on the favorable-normal-unfavorable model. My initial reaction is that my players would be annoyed by "unfavorable" and it would be a hard sell, but mechanically it does some neat things.
There are two important ramifications from this shift from static bonuses to rerolls (which is effectively what this is, you just roll the reroll at the same time as the original roll). Whether these are good or bad for your game I guess is up to you.
ReplyDelete• The roll of the die is much more important
• The benefit is harder to gauge
The first big benefit is that the roll of the die matters much more. One of the good things about the static bonuses is that when you're incredibly good at something, like a +30 bonus to a skill, even your worst possible roll is still incredible. It's literally impossible for someone with a +30 to Jump to jump worse than a commoner on his best day. And in some ways, that's a good thing, because it models what we see in real life. When you're incredibly good at something, it makes sense that you're ALWAYS better at it than someone without training. Using your reroll mechanic it's entirely possible for someone to flub both of their rolls and botch a roll that they should be great at.
On the other hand, this also means that people have an incentive to try things that they might not otherwise. If you always have a chance of succeeding at something, you're much more likely to take risks and give it a shot, which is much better for the game than having everyone pidgeonholed into their one little specialty. Specialized people are more likely to succeed, but anyone can try anything with a chance of success.
The second big ramification is that the odds of a reroll are much much harder to conceptualize than a flat bonus. This is bad in that people find it really hard to value in comparison to other abilities or bonuses, because the probabilities are hard to figure out. On the other hand, if you've got a problem with players with incredible system mastery this makes it much harder to game the system. Again, whether the benefits outweigh the odds depends on the kind of game you're playing.
From a statistics stand point the roll of the die is not more important, it is just that the average of 2d20 is not 10.5 but much higher. Your reaction and comments *feel* correct at first, but if you go back and look at the math of the table you see that they are a little misplaced.
ReplyDeleteTake two characters attempting a jump check with 10 strength. One is trained in jump and has to pass a DC 15. The other gets to roll 2d20 and has to pass a DC 15. They basically have the same chance to pass. I guess you're right that more of the result is represented on the die, but that is statistically insignificant. They have the same chance to fail so the die roll is no more important.
You are correct that one has a lower minimum result. That minimum result, though, shows up significantly less often than the other character's minimum result. To return to our example above, the minimum result of the +5 guy is 6 (5% of rolls) and 25% of all results are 10 or lower. The roll 2d20 guy has a minimum result of 1 (0% of rolls), has 6% of roll 6 or lower, and has 20% of rolls at 10 or lower. So he is actually *more talented* at the simple stuff, but there is almost always a chance of failure.
If your goal is to mimic things like a professional long jumper always jumping really far, this probably isn't the best system because 1 out of every 400 jumps he fails spectacularly. What this system does do well is introduce a constant potential for success or failure regardless of training. That is a good mechanic for a game and a bad mechanic for real life.
I just found this thread on ENWorld and thought you might find it interesting:
ReplyDeletehttp://www.enworld.org/forum/general-rpg-discussion/307597-comparing-dice-mechanics-how-they-affect-flavor-style-gameplay.html
I casually skimmed that thread and went back at your recommendation to read it in full. The thing I am taking away from all of this is that the more I study D&D, the more I am conflicted. There is a lot of value to making a D&D clone because it is a great system and people are familiar with it. But the more you study RPGs, the more you realize that there is an amazing wealth of mechanics that all have their own merit, their own style, and their own strengths. It makes this whole process damn hard because I want all of the toys of every system, but I also want consistency and elegance. Fortunately, there is a lot of fun mixed in with the challenge.
ReplyDeleteI feel the exact same way. I really like the "+1d6 -1d6" system that was mentioned (at least for skill checks) as it puts a lot more emphasis on the skill of the character, and avoids the problem of the full plate fighter being more stealthy than the sneaky rogue.
ReplyDeleteNot to go on a rant, but I also dislike how a single good/bad roll can ruin group skill checks. For example, if the party is trying to sneak past a group of monsters actively looking for them. Either one character will have a low stealth roll or one monster will have a great perception roll. This makes sneaking very unreliable to attempt.