[3.5] Bell Curve variant rules

[Myou]

My player told me today that he hates rolling d20 for everything, because the result is highly randomised, and at lower levels the result of a d20 roll is often all that really matters, making character skill less noticable.

We talked it over and agreed that we would both like to change to the bell curve variant rules in Unearthed Arcana, replacing all d20 rolls with 3d6 to create more realistic results that favour skill over luck (more often).

Before I make it official, are there any known issues I need to account for, or any problems with the system you can think of?

[pasko77]

My player told me today that he hates rolling d20 for everything, because the result is highly randomised, and at lower levels the result of a d20 roll is often all that really matters, making character skill less noticable.

We talked it over and agreed that we would both like to change to the bell curve variant rules in Unearthed Arcana, replacing all d20 rolls with 3d6 to create more realistic results that favour skill over luck (more often).

Before I make it official, are there any known issues I need to account for, or any problems with the system you can think of?

You must be more careful when designing encounters. If you hit, say, on 15+ a monster, it can still be viable with a d20, you will hit 1/4 of the times. With 3d6 you will never hit.

So be careful not to throw too strong opponents.
Also, remenber that magic +1s are much stronger. You should tone down every spell that gives +X to any test (mage armor and shield).
Moreover, with the rules of 3.5 for save or dies, remember that a high difficulty save will never succeed, making even more effective SoD spells from an optimized caster.

[ericgrau]

It's not really true that low level encounters have any more to do with luck than high level ones. Whether you're adding a d20 to 3 to try to hit 13 or adding a d20 to 13 to try to hit 23 it's all the same. And in either case a +1 means 10% more successes (1 more out of 10).

Since the results are weighted towards the average, I can see this variant making a big difference on opposed rolls. Being just a little better will make you hard to beat at all. Even on regular rolls this will hold true to some extent. So be careful about sending the party against anything whose individual CR is too much higher or lower than the party level. ECL calculations will probably have to change. 4 CR 6 creatures are no longer a standard (easy, but resource consuming) fight for a 10th level party; it's a trivial fight. You might need 4 CR 7 or CR 8 creatures for the same difficulty. Play around to figure it out, or do the statistical math to figure out how bad a -4 is on 3d6 vs. 1d20.

[Myou]

You must be more careful when designing encounters. If you hit, say, on 15+ a monster, it can still be viable with a d20, you will hit 1/4 of the times. With 3d6 you will never hit.

So be careful not to throw too strong opponents.
Also, remenber that magic +1s are much stronger. You should tone down every spell that gives +X to any test (mage armor and shield).
Moreover, with the rules of 3.5 for save or dies, remember that a high difficulty save will never succeed, making even more effective SoD spells from an optimized caster.

Good point you'd only roll a 15 or better on 9% of rolls rather than 25%.

Are magic +1 actually a lot stronger? You're getting results with less variantion, but the mean result is the same.

Saves that require high rolls did come to mind, yeah, I don't really know the numbers on saves too well, but I would think normally it's enemies that have higher save DCs, so I'd just need to make sure not to overoptimise DCs, and there are a lot of ways to boost saves, so classes with weak saves might not have trouble as long as they actually pay attention to those methods. Or am I deluding myelf there? XD

[Myou]

It's not really true that low level encounters have any more to do with luck than high level ones. Whether you're adding a d20 to 3 to try to hit 13 or adding a d20 to 13 to try to hit 23 it's all the same. And in either case a +1 means 10% more successes (1 more out of 10).

Since the results are weighted towards the average, I can see this variant making a big difference on opposed rolls. Being just a little better will make you hard to beat at all. Even on regular rolls this will hold true to some extent. So be careful about sending the party against anything whose individual CR is too much higher or lower than the party level. ECL calculations will probably have to change. 4 CR 6 creatures are no longer a standard (easy, but resource consuming) fight for a 10th level party; it's a trivial fight. You might need 4 CR 7 or CR 8 creatures for the same difficulty. Play around to figure it out, or do the statistical math to figure out how bad a -4 is on 3d6 vs. 1d20.

I was speaking proportionally though, 1d20 is a far bigger proportion of your ability when you only have a +4 than when you have a +24. But at all levels really, the d20 is too random for us. It just feels more pronuonced early on.

Normally the PCs are the one a little better, but in a hard battle I suppose it could be the opposite. I'll need to be careful not to create foes too much stroger, as you say.
Luckily I only use CR as a very rough guide anyway, and mostly just 'eyeball' things, so I'll just need to slightly reassess my balls.

Good thing I'm doing statistics in school. Just yesterday I was working out the variance of 2d6. xD


Thanks to you both for taking the time to help!

[magic9mushroom]

Are magic +1 actually a lot stronger? You're getting results with less variantion, but the mean result is the same.

+1 is a lot stronger. +1 normally is +5%. +1 in Bell Curve is more complicated, but is a lot bigger than +5% when near the average.

[Myou]

+1 is a lot stronger. +1 normally is +5%. +1 in Bell Curve is more complicated, but is a lot bigger than +5% when near the average.

Yeah, but the overall result is the same on average.

[magic9mushroom]

Yeah, but the overall result is the same on average.

No, it's not. Instead of being 20 possible rolls, there are 16. The "overall result" is +6.25% instead of +5%.

[theMycon]

It's not really true that low level encounters have any more to do with luck than high level ones. Whether you're adding a d20 to 3 to try to hit 13 or adding a d20 to 13 to try to hit 23 it's all the same.

These numbers are correct, but... At level 1, a character could reasonably have a skill mod from -1 to 8 - Anything any on character could make on a decent roll, everyone could make on a good roll.

At level 10, without any particular focus, a character could have a skill mod from -1 to 20-something, dependant on skill ranks & stat focus. Some characters can now auto-make rolls which other characters cannot make at all.

I think this is the point the OP was trying to make.

(Also, +1 is +5%, for an extra 1 in 20.)

[Myou]

No, it's not. Instead of being 20 possible rolls, there are 16. The "overall result" is +6.25% instead of +5%.

Ah, yes, I see now what you guys are talking about. Sorry, I was thinking about total results rather than percentages.

But is a 1.25% increase on the effective bonus worth making large-scale changes for? It doesn't bother me too much, unless there's some resulting effect I've failed to realise.

[DragoonWraith]

Ah, yes, I see now what you guys are talking about. Sorry, I was thinking about total results rather than percentages.

But is a 1.25% increase on the effective bonus worth making large-scale changes for? It doesn't bother me too much, unless there's some resulting effect I've failed to realise.

I feel like that is the point of doing it this way, to reward people with ranks in something with actually being better at it.

I definitely agree with his players' complaints. "My backstory says I'm a renowned woodsman, but I can't have more than 4 ranks in Knowledge (Nature) and I only have Int 12, and I just rolled a 2 so I can't even tell a deer from a badger. Great, that's fitting. "

[Greenish]

I definitely agree with his players' complaints. "My backstory says I'm a renowned woodsman, but I can't have more than 4 ranks in Knowledge (Nature) and I only have Int 12, and I just rolled a 2 so I can't even tell a deer from a badger. Great, that's fitting. "

You aren't supposed to be a renowned anything at level 1.

[Myou]

I feel like that is the point of doing it this way, to reward people with ranks in something with actually being better at it.

I definitely agree with his players' complaints. "My backstory says I'm a renowned woodsman, but I can't have more than 4 ranks in Knowledge (Nature) and I only have Int 12, and I just rolled a 2 so I can't even tell a deer from a badger. Great, that's fitting. "

Yes, this, a thousand time this!

As long as we're not going to break the game, we really want to dump that silly randomness.

His backstory is that he's a martial arts prodigy, and yet on a bad roll he can't hit a stationary object.


I can see how static bonuses will be better, but we want them to play a more central role - your actual ability shouldn't be eclipsed by random chance on about a third of attempts.

[Yora]

I would also suggest, that a roll of 18 is automatically a critical hit, without making a secondary roll to confirm. The chance to roll an 18 on 3d6 (0,5%) is much lower than rolling a 20 on 1d20 (5%).

Bell curve rolling also makes weapons with larger crit ranges better in comparison to other weapons. The chance for a critical hit is 4 times as big with a crit range of 17-18 and 9 times as big with a crit range of 16-18. (As opposed to 2 times for 18-20 and 3 times for 18-20).

I found this table that compared %-chances for 1d20 and 3d6 rolls, which seems quite useful to set DCs.

Let's assume an average human who gets a +0 bonus to every roll.
A DC of 10 has a chance of success that is 50% for both 1d20 and 3d6.
To get a chance of success of 25% however, the 1d20 DC is 15 and the 3d6 DC is 12.
DC 15 on a 3d6 roll has a chance of 5%, which would be a DC 20 on an 1d20 roll.

I don't know how to best translate this in difficulty rating for DCs, but it's something to keep in mind.

[Myou]

I would also suggest, that a roll of 18 is automatically a critical hit, without making a secondary roll to confirm. The chance to roll an 18 on 3d6 (0,5%) is much lower than rolling a 20 on 1d20 (5%).

Bell curve rolling also makes weapons with larger crit ranges better in comparison to other weapons. The chance for a critical hit is 4 times as big with a crit range of 17-18 and 9 times as big with a crit range of 16-18. (As opposed to 2 times for 18-20 and 3 times for 18-20).

I found this table that compared %-chances for 1d20 and 3d6 rolls, which seems quite useful to set DCs.

Let's assume an average human who gets a +0 bonus to every roll.
A DC of 10 has a chance of success that is 50% for both 1d20 and 3d6.
To get a chance of success of 25% however, the 1d20 DC is 15 and the 3d6 DC is 12.
DC 15 on a 3d6 roll has a chance of 5%, which would be a DC 20 on an 1d20 roll.

I don't know how to best translate this in difficulty rating for DCs, but it's something to keep in mind.

Well, for premade DCs like the difficulty of identify an animal, etc, it should be fine, but for setting things like AC it's something I'll need to be mindful of.

The boost in power for high crit range weapons is something I'm not entirely happy about, but I'm not sure how to change it. I can live with it.

[DragoonWraith]

Also, some discussion that might be enlightening.

[BenTheJester]

Why not just roll 2d20 and divide the result by 2?

This also creates a bell curve effect

[Myou]

Why not just roll 2d20 and divide the result by 2?

This also creates a bell curve effect

Because this is a nicer bell curve and doesn't require you to divide and round every roll.

[ericgrau]

...
(Also, +1 is +5%, for an extra 1 in 20.)

A common misconception. 5% more attacks hit, but the actual increase in hits is always more than 5%. 10 out of 20 to 11 out of 20 is both 10% more hits and 10% more damage per round than before. 15 out of 20 to 16 out of 20 is 7.5% more hits & damage per round. And when you have 5 different sources of +1's, they add up fast and that d20 doesn't seem so big anymore.

I can see how at low levels 0 BAB and 1 BAB may not be all that much different for hitting. But people rarely make level 1 focused builds and thus the fighter with a high strength will still be ahead of the rogue who can't get weapon finesse yet and the cleric who is MAD. Or even on a level 1 focused build their other attributes are still valuable; a high strength rogue still suffers greatly from lower AC and HP. He must sacrifice a great deal of defense merely to be almost par on offense.

While theoretically you can have a wider variation at higher levels, practically this is not so except with poor players. When everyone is optimizing the classes that are worse at something tend to be only a few points behind on anything worth attempting (wizards will not wield a greatsword, for example, so their poor BAB is a moot point). Mid BAB is at most 5 points behind full BAB, and poor saves are at most 6 points behind good ones. Even then the mid BAB classes that still fight tend to have buffs to close the gap. Those with poor saves actually only gain a -3 compared to good saves over the span of 18 levels, since 2 points of the difference happens at level 1 and the last point doesn't happen until level 20.

[sofawall]

"My backstory says I'm a renowned woodsman, but I can't have more than 4 ranks in Knowledge (Nature) and I only have Int 12, and I just rolled a 2 so I can't even tell a deer from a badger. Great, that's fitting. "

Hey, at least you have a chance to tell them apart. Most people won't know at all.

[2xMachina]

If you port the system to the real world, everyone is dead, cause they're all idiots, even at 120IQ.

[pasko77]

Good point you'd only roll a 15 or better on 9% of rolls rather than 25%.

Are magic +1 actually a lot stronger? You're getting results with less variantion, but the mean result is the same.

I meant if I have a +1 item and you don't, with d20, whatever, with 3d6 i'm seriously gonna kick your ass. :)
So beware of classes that can stock modifiers.

[Pechvarry]

You aren't supposed to be a renowned anything at level 1.

A common farmer in the American Frontier in the days of the Oregon Trail could probably:
-Reasonably forecast today's weather
-Thatch his leaking roof
-Plane some rough beams and use them to fashion a shed
-Go hunting for dinner

This is all in addition to his true, farmerly tasks such as tending animals, keeping them from getting anxious, birthing their young, and all that "growing and harvesting" plants bit.

ALL of that is a level 1 commoner. I'd like to see even a 1st level Ranger accomplishing all of that reliably. Could he waste some skills on craft and profession and then still have some for survival? yes. But he's probably a good 50% likely to fail at any attempt to do the above.

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@ericgrau: I think it's kind of misleading to say "a common misconception". It's more accurate to say a miscommunication.

An increase from +10 to +11 is 5% more success rate. Against DC 21, you go from 50% success rate to 55% success rate.

However, it's a 10% increase from your previous standing. This is because 55% is 10% more than 50%.

---

Why not roll 2d10? This seems like it'd hit the same range as 1d20, have half the bell curve of 3d6 but twice that of 1d20. Natural 20 becomes Natural... 2x10. Which happens like 1% of the time. I must be screwing up my math because an 18 should only turn up on 3d6 once every 216 rolls.

[pasko77]

Why not roll 2d10? This seems like it'd hit the same range as 1d20, have half the bell curve of 3d6 but twice that of 1d20. Natural 20 becomes Natural... 2x10. Which happens like 1% of the time. I must be screwing up my math because an 18 should only turn up on 3d6 once every 216 rolls.

On 3d6, there are different suggested values for critical hits.
For instance, a "nat 20" should be considered a 16+.
A 19+ becomes 15+
etc.

Or you will face a severe decrease in weapon damage (no more critical hits) and of feats that rely on those results.

Bye, Pasko

[Sliver]

Why not roll 2d10? This seems like it'd hit the same range as 1d20, have half the bell curve of 3d6 but twice that of 1d20. Natural 20 becomes Natural... 2x10. Which happens like 1% of the time. I must be screwing up my math because an 18 should only turn up on 3d6 once every 216 rolls.

Not exactly the same range of a d20.. You don't have a 1 with 2d10, and the 2 becomes a 1 in terms of fumbles I guess..

[2xMachina]

And it's slightly higher in average. 1d10 averages at 5.5, thus 11 for 2d10s, while 1d20 averages at 10.5

[BruteSquad01]

Try 1d8 + 1d12 instead. I've never used it, but I knew a DM once who swore by it. This was back in 2ed days.

[ericgrau]

A common farmer in the American Frontier in the days of the Oregon Trail could probably:
-Reasonably forecast today's weather
-Thatch his leaking roof
-Plane some rough beams and use them to fashion a shed
-Go hunting for dinner

This is all in addition to his true, farmerly tasks such as tending animals, keeping them from getting anxious, birthing their young, and all that "growing and harvesting" plants bit.

ALL of that is a level 1 commoner. I'd like to see even a 1st level Ranger accomplishing all of that reliably. Could he waste some skills on craft and profession and then still have some for survival? yes. But he's probably a good 50% likely to fail at any attempt to do the above.

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@ericgrau: I think it's kind of misleading to say "a common misconception". It's more accurate to say a miscommunication.

An increase from +10 to +11 is 5% more success rate. Against DC 21, you go from 50% success rate to 55% success rate.

However, it's a 10% increase from your previous standing. This is because 55% is 10% more than 50%.

Arguably a DC 10 survival check, if you even need a check at all. This could be assumed to be common knowledge. Heck I'll make a decent enough guess as a child. Survival only lists a DC 15 for as far as tomorrow's weather, plus 5 per day. Ditto for the next 2 as common knowledge. Likewise finding food is a DC 10, which you could do untrained by taking a 10. Or even if you don't take a 10 you may have a 45% chance of failure but you also have a decent chance of getting enough food to last you multiple days. This is more of an issue of cruel DMs setting arbitrary DCs when the DC should be low or when you shouldn't even need a check at all. Under a bell curve these arbitrarily high DCs will only be harder to make untrained whenever you can't simply take a 10.

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Yet if you look at anything that matters, like your actual damage output or number of successes, then a 7.5%-10% increase per +1 is more accurate. This is a key point when the complaint is that a d20 provides too much randomness for a +1 to matter. Success rates are typically 50% if you're okay at something and 75% if you're good at it. That's only a 5 point margin before random chance is gone entirely. This is why I poked fun at Pathfinder Alpha for throwing out arbitrary +5 and higher bonuses (in addition to the normal bonuses) as you reached higher levels. It's a horribly broken idea that almost lets you come to games without your d20. Fortunately the later versions toned things back quite a bit.

[Caphi]

You require players to roll knowledge skills for trivial knowledge? Telling a squirrel from a deer should be free with the description of the area, certainly not a skill challenge.

Also, level 1 characters are glorified mooks. He can be "a renowned woodsman" at 4 or 5.

[Quellian-dyrae]

A house rule I was fiddling with recently, which may be helpful here, was really limiting the bonuses that can apply to attack rolls and AC (it's a high-power game, and I wanted to cut down the possibility of one character having an AC of 30 or so and another 50, or something). Basically, both attack rolls an AC bonuses were equal to BAB + appropriate ability score + an enhancement bonus of up to +5. Haste and size bonuses still applied, and I added armor-boosting feats similar to the weapon-boosting feats, and they applied. All other sources of attack roll bonuses (stacking rules allowing) get doubled and added to damage rolls, and all other sources of AC get added to a stat called Resilience, which was basically like DR.

Anyway, it's part of a large list of house rules, so there's a bit more to it than that, but if you do something like that, you won't have to worry as much about a few extra bonuses completely skewing probability.