There are two common ways to do ability checks. One is the old school “roll d20 less than or equal to” method that I will call “roll under” or RU in this post. In this method, rolling lower is better. The other is the new school “roll d20 add modifier and hit target number” method that I will call DC (for “difficulty class”) in this post. In the 3E DC method, higher is always better.
The two methods have math that is slightly different. Using the 3E DC method has a slight dampening effect, as all that matters is the modifier (for example, a score of 14 and 15 have the same modifier, and so characters with strength scores of both 14 and 15 have the exact same chances of succeeding on any strength check). It is worth noting beforehand that ability score modifiers are different in 3E than they are in traditional D&D. The Moldvay progression looks like this:
0 0 0 0 1 1 1 2 2 3
0 0 1 1 2 2 3 3 4 4
Both RU and DC style checks can be used with either style of modifier progression. The table I have included below uses the Moldvay progression, but I don’t think the results are much changed if the linear 3E progression is substituted (you get an extra 5% tier on each end, because of the -4 and +4).
A flat RU check with no bonus or penalty is approximately equal to a DC 10 check. Modifying the difficulty of an RU check is usually done by rolling with a bonus or penalty. To compare the two methods, I have calculated percentages DC 5, 10, 15, and 20 3E checks and corresponding RU +5, +0, -5, and -10 checks. Thus, the columns should be compared pairwise:
- Easy: RU +5, DC 5
- Average: RU, DC 10
- Moderate: RU -5, DC 15
- Difficult: RU -10, DC 20
| Score | Mod | RU +5 | DC 5 | RU | DC 10 | RU -5 | DC 15 | RU -10 | DC 20 |
|---|---|---|---|---|---|---|---|---|---|
| 3 | -3 | 40% | 65% | 15% | 40% | 5% | 15% | 5% | 5% |
| 4 | -2 | 45% | 70% | 20% | 45% | 5% | 20% | 5% | 5% |
| 5 | -2 | 50% | 70% | 25% | 45% | 5% | 20% | 5% | 5% |
| 6 | -1 | 55% | 75% | 30% | 50% | 5% | 25% | 5% | 5% |
| 7 | -1 | 60% | 75% | 35% | 50% | 5% | 25% | 5% | 5% |
| 8 | -1 | 65% | 75% | 40% | 50% | 10% | 25% | 5% | 5% |
| 9 | 70% | 80% | 45% | 55% | 15% | 30% | 5% | 5% | |
| 10 | 75% | 80% | 50% | 55% | 20% | 30% | 5% | 5% | |
| 11 | 80% | 80% | 55% | 55% | 25% | 30% | 5% | 5% | |
| 12 | 85% | 80% | 60% | 55% | 30% | 30% | 5% | 5% | |
| 13 | +1 | 90% | 85% | 65% | 60% | 35% | 35% | 10% | 10% |
| 14 | +1 | 95% | 85% | 70% | 60% | 40% | 35% | 15% | 10% |
| 15 | +1 | 95% | 85% | 75% | 60% | 45% | 35% | 20% | 10% |
| 16 | +2 | 95% | 90% | 80% | 65% | 50% | 40% | 25% | 15% |
| 17 | +2 | 95% | 90% | 85% | 65% | 55% | 40% | 30% | 15% |
| 18 | +3 | 95% | 95% | 90% | 70% | 60% | 45% | 35% | 20% |
This table should be read as follows:
- RU +5 = add 5 to the score and then roll less than or equal to it on a d20
- RU -10 = subtract 10 from the score, roll less than or equal to it on a d20
- DC 15 = roll d20, add the modifier, and roll equal to or greater than
So what does this mean? The takeaway here is that DC checks have much less variance, and are thus less interesting in practice. They tend to be almost binary. That is, a DC 15 check is within the same 25% success bracket for all but the bottom 3 ability scores (that is what all that blue in the DC 15 column means). Compare to RU -5, which ranges from 5% to 60%, depending on character competency.
One last note. The Moldvay system assumes bounded ability scores, describing a population that observes the standard bell curve distribution (and races don’t modify ability scores). This says something about the nature of the characters so modeled, and I think this feeds into the general power curve analysis I did before.
When I run Old School I prefer to do the checks with 2d6 against a target number (TN) of 9+ or 12+ depending on difficulty of the task and other factors and then add the stat bonus (or penalty) to the roll.
This method is just the Reaction Table made large and seems to work well.
I’ve recently been playing around with a 2d6 general resolution system and it has a lot to recommend it, though perhaps it is just reinventing Traveller mechanics.
What is it about maths that makes my brain temporarily shut down? I mean, percentages aren’t that difficult but put a bunch of them into several columns and my mind bucks away like a Lovecraftian hero trying not to comprehend the shoggoth.
I have always hated arbitrary difficulty levels and preferred rolled under, using d20 for things the character knows expertly and d100 for things they don’t, with various mods. Thanks for reinforcing confidence in my decision!
There’s yet another way to do ability checks and I feel it is the best way, so this is how I handle it in my Cyclopedia campaign:
Roll xd6 and get under the ability.
X is 2 for a tricky task.
x is 3 for a very difficult task.
x is 4 for an almost impossible task.
Using 2 gives a range from 2-12 with a weighting strongly towards 7.
Using 3 gives a normal stat roll from 3-18 and averaging 10.
Using 4 gives a range of 4-24 and will average 14, so it is something that even the most powerful/wisest/genius like characters will struggle with.
I like this method too, especially for a game run with only six sided dice. I plan on doing a follow up post with the percentages for this method. However, I don’t think I agree with your labels. 2d6 is probably an easy task, as it will yield success most of the time, even if the ability score is below average. 3d6 would probably correspond to what I have labeled as average, 4d6 is moderate, and 5d6 is difficult.
Well, considering that in my campaign, not one of my players has a 13 or more in a single attribute (3d6 for character generation will sometimes do that), testing with 2d6 brings some tension to the table, believe me.
Also, consider: if a task is easy, why are you asking for people to roll for it? Just assume it was done. I only ask the players to roll for tasks that are not so easy.
I’ve been trying to take the idea of Moldvay’s bounded ability score to the next level and treat them as relative values. So an elf with a Dex of 15 is more agile than a dwarf with a Dex of 15. Likewise a hobbit with weaker than an Ogre with the same Str score. With Strength and Con doing so is easy. A hobbit is using a d6 damage weapon and gets +1 whereas an Ogre is using a d10 weapon (due to his natural strength) and gets an additional +1. Likewise larger and tougher monsters have more Hit Dice so a bonus for Con does more. With dex you might give an elf a +1 AC that his Dex score adds to.
This is one of the reason I like the vs-DC method of testing abilities since I can give certain races bonuses with certain tasks (like Ogres bending bars) which is much easier with a roll and add compared to a roll under. Also, when testing between two characters, you can use a d6+mod vs d6+mod to test things directly related to the ability (like wrestling or parkour) or use a d20+mod when the ability might provide a less noticeable effect. Or any die in between.
However, my main reason for liking ability mods instead of scores is that, IMHO, it discourages stat inflation. Have a +2 strength is cool when there isn’t a higher number to compare yourself unfavorably to. Also, using only the modifiers where 0 is the default of all races (since ability scores are relative) means you can add or subtract abilities much easier. I can remove Wisdom (since I don’t use clerics) but still give some NPCs a +1 Willpower without having to go back and add that score to all the PCs character sheets. Similarly, I can have a magic item give a PC a +1 Luck and have it used just like any other ability. Finally, it allows me to give NPCs ability score bonuses without needing to roll all 6 scores.
TL;DR …
@Hedgehobbit
I’m not sure I understand your last paragraph. Can’t +2 be unfavorably compared with +3 just as 18 can be unfavorably compared to 19? The primary benefit to using 3 – 18 is that you can determine abilities with 3d6 (and thus have a population distribution). If you are using a point buy or choice system, and a DC style of ability checks, that no longer holds, and the 3 – 18 range is just a legacy affectation.
Here’s another idea for ability scores: roll 3d6 and discard the high and low rolls. Ability scores are just modifiers, and correspond to the remaining die as follows:
1: -2
2: -1
3: 0
4: 0
5: +1
6: +2
And, if you like choice, you can use the above array as a set of starting scores (or any other set that balances out to net zero, if that makes sense). The rest of the d20 system should function as expected, if you ignore ability score minimums for classes.
Just as a point of order, using a point-buy system doesn’t mean that the population distribution no longer holds, it just means that you’re deliberately choosing a character rather than grabbing one at random. It only breaks down if the whole world is done with point-buy, that is, it’s up to the DM to ensure that the population outside the PCs matches the curve. The 3-18 range for PCs is no more a legacy affectation than IQ scores at NASA are (you’ve changed the population you’re considering, and that population may be entirely outliers).
I disagree with this. Point buy is not random and so does not conform to the probability distribution any more. 1 in 216 characters do not end up with Strength 18 (for example), more like 1 in 4!
My point is that the only utility of the 3 – 18 range is for simulating PCs as drawn randomly from the entire population. If you are not doing that, why not just use the modifiers?
@ Recursion King:
I never said that point-buy was random or that characters made with point-buy conform to the distribution — in fact I said the exact opposite, point-buy is explicit selection and results in outliers.
But that doesn’t mean that the 3-18 range is “just a legacy affectation” as Brenden claims. It describes the range of human ability, whether or not your player group matches the normal distribution of the general populace. If 1 in 4 of your PCs have a STR 18, that doesn’t mean the scores lose their meaning, it means your players chose characters in the top percent.
@Brenden
I disagree that that is the only utility; I think the range is useful for measuring PCs against the entire population, whether or not they were selected randomly. You can just use modifiers regardless of which way you want to do it (randomly chosen or point buy) but the system as it stands allows for both (you note the same can’t be true if we reduce to modifiers, because you lose the ability to accurately draw from the random pool).
That is, even if you aren’t using 3-18 to draw at random it’s still useful to see where in the pool you stand, and resisting the impulse to reduce to just modifiers allows you (notably the GM) to pull randomly when necessary or desired.
Really this comes down to whether you want adventurers to be exceptional individuals or ordinary people in extraordinary circumstances. I would argue that the first approach inherently breaks the population distribution model. Strength 18 will only seem special to the degree that it is rare to players, not characters. Players will only see the part of the campaign world they they are exposed to.
This is probably a larger issue that deserves its own post though. I understand where you’re coming from; it seems like using 3d6 in order for NPCs and point buy for PCs would allow the kind of comparison that you suggest. However, in practice, I don’t think it works out that way, especially once all the “important” NPCs start getting their stats picked, too.
@Brenden
That I’ll definitely agree with, with the exception of attributes only being meaningful if they’re rare to Players. This is more true if the places the PC explore (the part of the campaign world they are exposed to) only includes PCs. The more NPCs are around, the more you can demonstrate that the STR 18 PC is a colossus, the less this is the case.
In the end, I prefer PCs to be regular folks in extraordinary situations, but that’s not necessarily the game (or the roles) my players want. And even then, 3d6-in-order doesn’t guarantee this — someone COULD roll up a Heracles while everyone gets John Doe, and now everything tastes unfair. Point-buy at least puts players on balanced, deliberate footing, and if you don’t want Heracles and Einstein, lower the amount of points you allow (as I tend to).
In old school rulesets, and 18 in every attribute does not in any way guarrantee that the character will live. A +3 to dex and a +3 to hit points in no way shape or form make a character invulnerable; with 4-11 hit points, two lucky strikes from a longsword, or one two handed sword strike from a berserker, can slay the first level character instantly. Something to bear in mind here.
That’s interesting, but I’m not sure why you chose 25-point brackets to group things in. That’s kind of a huge range when you look at it (anything between 1/4 and 1/2 is the same bracket).
I’m not convinced that “more variance” is a virtue in this case, but I’m still chewing on the numbers. I do like the result that 15 vs 14 is meaningful, which 3.X generally fails at (negligible exceptions being in STR and CON).
The 25% blocks are mostly arbitrary and chosen for convenience based on the number of colors I have available. I think thirds, tenths, or most other simplifications would yield a similar picture.