Author Topic: d20 vs 2d10 and it's effect on defense  (Read 9828 times)

Offline Mooncrow

  • DnD Handbook Writer
  • ***
  • Posts: 983
  • The man who will be Pirate King
    • View Profile
d20 vs 2d10 and it's effect on defense
« on: December 08, 2011, 05:13:27 PM »
In order to not clutter up a thread with off topic chatter, I'm moving this here.

Bell curves wouldn't really work. It got lost in the flamefest, but at one point someone suggested 2d10 instead of 1d20 for the RNG. The result of that would be that enemy actions succeed more often, and player actions would either succeed more or less often depending on the encounter.

Low level is completely unplayable because the entire game is a simple D20 check. If the Orc rolls at least a 10, you die, and there is nothing you can do about it. Beyond that though it tends to only become a luck fest with weak characters. The strong ones avoid that. They also go off the RNG, but then if they weren't, there'd be no way to survive campaigns. Even with those other things, there'd be too many failed saves. It isn't just save or loses. Simple attacks 1-2 round people just the same.

It's slightly more complex than that though - what it does, is even out the the cost per effect curve a bit.  With the d20 - costs to increase a defense scale upward, at least when talking about items rather than spells, while the benefit remains the same: 5% per point, basically.  (at least when talking about a single effect; calculating multiple effects has it's own probability curve, but it's still more linear than not)  With 2d10 (or 3d6 or whatever other variant you want to name) however, the benefit curves upward, making the marginal cost of the next point of a given defense less.  So it ends up rewarding (or punishing less, depending on how you want to look at it) those that put in the effort and cost to optimize their defense.

No, it doesn't. It means you get more benefit as you approach the mid point, and then less as you move past it. It does not make it so that each point is better than the one before it.

Slight problem though. Physical defense is always going to be well to the left side of that line. You just can't get enough AC to make a difference past the low levels, especially if you want to be able to hurt things as well unless you're a CoDzilla or something. Magical defense is always going to be well to the right side of that line, if you know what you're doing that is.

So all you've really done is make physical attacks hit you 99% of the time instead of 95%, save or loses not land quite as often on the enemy and slightly less often on you, and that's it. All of that amounts to enemies destroy you more and not less, as defenses mean less against them.


I'm actually glad to pick this topic up with a more civil tone.  I realize that when you're eyeballing it, it does look that way, but if you look at the probability curve, that's not how it works.  It's probably easiest to think of it like this: you're not looking at the overall percentage, you're looking at the marginal benefit of adding +1 to the defense, and the benefit is calculated as the area under the curve that you're getting rid of, the percent of the percent, as it were.  So, when you go from hitting on a 16 (15% chance) to hitting on a 17 (10% chance), you're increasing the value of your defense by 33% percent.  Or from hitting on an 18 (6% chance) to hitting on a 19 (3% chance) - well, you see how it works.  And no, probability isn't intuitive. 

Granted, there are several other assumptions I make in my games, which is why I brought it up originally as something that works for me - I assume T1 - T3 in my games and that the players are all working to optimize their defenses.  "Melee" without several levels of cleric or something similar are pretty non-existent, or in the one case of the one pure mundane that I do have, he has Leadership for an Archivist cohort :p 

Offline Basket Burner

  • Legendary Member
  • ****
  • Posts: 1072
  • I break Basket Weavers.
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #1 on: December 08, 2011, 05:32:17 PM »
Except that going from a 94% chance to dodge to a 97% chance to dodge is a 3% difference, less than the 5% you get from a linear system. And that's the problem with it. The greater benefits per point are towards the middle of the range. But physical defense will be far to the left no matter what, and special defense will be far to the right if you know what you're doing, so the default assumptions of the meta do not change. What does change is the results - you get hit even more often by physical attacks, and a significant number of enemies are less prone to being taken out, giving them more chances to take you out. Saying you get hit half as often going from 18 to 19 on 2d10 is the same as saying you get hit half as often going from 19 to 20 on 1d20. Technically true, but what matters is how many attacks are successful. The benefit on a point by point basis is secondary.

I tried to leave my games out of it as much as possible and instead focused on the game. If I were to apply those same principles to my game, then what'd happen is that Koth would have been 99% invulnerable instead of 95%. So instead of the party of optimized, mostly 1-2 classes finishing the fight with most of the party in single digits or worse and very few spells left, he would have used his fourth Wings of Flurry, then just attacked whoever was left for the sweep. Looking at things from the PC side those that cared about AC had 28 points of it at level 6, with conditional bonuses on top of that. Mooks hit on a 12-14 or so, so it wouldn't make any real difference. The main threats hit on a 2 or 3. That would help them.

Said party has since leveled up, and gotten a fair bit of loot for their efforts. These numbers have improved and are liable to improve more. 30s are starting to show themselves. And that's without conditional bonuses.  Enemies still have little difficulty hitting, of course. The point of all of that being that in optimized games, offensive abilities improve substantially. Defensive abilities, not as much on the physical side but much better on the special side. Everyone has at least a 75% chance of passing almost any save thrown at them.

Offline JohnnyMayHymn

  • Hero Member
  • ***
  • Posts: 762
  • Former Lord of the Kitchen Sink
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #2 on: December 08, 2011, 05:54:28 PM »
When you switch to a bell curve rolling system (3d6 is most likely to result in 10 or 11) it raises the minimum roll and skews the result toward the center (2d6 is more likely to result in a 7 than any other sum of the two results).

One pro is that in low levels, mooks are far less likely to one hit crit a party member.
Also crit range increases become much better.

One adjustment I would make is to change the base AC to match the most likely roll, (14 for a 4d6 system).
« Last Edit: December 08, 2011, 06:07:32 PM by JohnnyMayHymn »
The Emperor
Can you find the Wumpus?

Offline Mooncrow

  • DnD Handbook Writer
  • ***
  • Posts: 983
  • The man who will be Pirate King
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #3 on: December 08, 2011, 05:56:57 PM »
I don't bring my games up very often either - for the same reason, but in this case I did originally, so I'm explaining why it works under a slightly different set of assumptions.  My list of house rules is extensive though, so we'll leave them out, unless you're actually interested.

But you're still not looking at the math quite right - it's a lot easier to see on a probability graph, but I'm not sure how to insert one, so words will have to do =/ 

It's easier to see the farther to the edge you go, so let's try this: the difference between 95% and 99% doesn't sound like a lot, but in practice, it means that a given effect will land once every 20 times vs an effect landing once every 100 times.  So, effectively, the 2d10 method makes that last point of defense 5x more valuable than it would be under the d20 system.  Does that help the visualization?

Offline Basket Burner

  • Legendary Member
  • ****
  • Posts: 1072
  • I break Basket Weavers.
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #4 on: December 08, 2011, 06:22:29 PM »
This thread really should not have been put here. I keep forgetting about it as I normally don't check this subforum.

When you switch to a bell curve rolling system (3d6 is most likely to result in 10 or 11) it raises the minimum roll and skews the result toward the center (2d6 is more likely to result in a 7 than any other sum of the two results).

One pro is that in low levels, mooks are far less likely to one hit crit a party member.
Also crit range increases become much better.

One adjustment I would make is to change the base AC to match the most likely roll, (14 for a 4d6 system).

At low levels they might be less likely to one hit crit but they are more likely to hit in the first place. Orc goes from threatening a crit 15% of the time to 10% of the time... but as a 10 or better most likely hits, and that went from being 55% likely to 64% likely, and the normal hits still OHKO or 2HKO people...

Moon: I've already seen what happens when you use a set of houserules to attempt to fix the system and then throw powerful characters at it. It works better than the default, and you can potentially get enough AC to make a difference, but a 2d10 RNG still reduces the value of defenses. I also understand the distribution just fine, that is why I say that their values are reduced. The main point though is that your physical defense is already going to be too low because you can't help it and your special defense is already going to be too high because you'd be stupid not to help it. So basically, everyone is Blissey. Watch those Close Combats, now.

Offline Mooncrow

  • DnD Handbook Writer
  • ***
  • Posts: 983
  • The man who will be Pirate King
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #5 on: December 08, 2011, 06:49:03 PM »
Well, I thought I would give it a shot - I'm no good at describing math in words though, it's almost an entirely visual thing for me.  It's funny, I was just on the phone with one of my players, and as he put it: "you're trying to describe how a probability derivative works, in words, over the internet?  What the fuck is wrong with you?" :p 

Sorry for the thread placement though, I just wanted to move it out of the original thread so it wouldn't clutter another subject.  This seemed like the best fit. 

Offline RedWarlock

  • Hero Member
  • ***
  • Posts: 628
  • Crimson-colored caster of calamity
    • View Profile
    • Red Blade Studios
Re: d20 vs 2d10 and it's effect on defense
« Reply #6 on: December 08, 2011, 09:08:07 PM »
This thread really should not have been put here. I keep forgetting about it as I normally don't check this subforum.
Sorry for the thread placement though, I just wanted to move it out of the original thread so it wouldn't clutter another subject.  This seemed like the best fit.
Nah, fits better here, as long as you're assuming system-neutral. Aside from a few people dropping in D&D-specific references, the discussion of the dice itself could be applied to any d20-ish style system. I'm finding all this most enlightening, for the simple fact that I AM working outside of the D&D norms, and I can mine a lot of useful balance concepts to build into my system, before I even hit a playtest stage.
WarCraft post-d20: A new take on the World of WarCraft for tabletop. I need your eyes and comments!

Offline veekie

  • Spinner of Fortunes
  • Epic Member
  • ****
  • Posts: 5423
  • Chaos Dice
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #7 on: December 09, 2011, 12:34:04 AM »
Quote
The main point though is that your physical defense is already going to be too low because you can't help it and your special defense is already going to be too high because you'd be stupid not to help it.
That would be assuming D&D-style numbers though, if you're working the dice system to make it more consistent, you would also be narrowing the gap between bonuses and target difficulties.

In general, you want the offense specialist to have even odds when facing off the defense specialist, but to hit more often when pitting a less specialized defense against specialized offense(assuming of course, a melee spec would have high defense AND offense).
Everything is edible. Just that there are things only edible once per lifetime.
It's a god-eat-god world.

Procrastination is the thief of time; Year after year it steals, till all are fled,
And to the mercies of a moment leaves; The vast concerns of an eternal scene.

Offline Mooncrow

  • DnD Handbook Writer
  • ***
  • Posts: 983
  • The man who will be Pirate King
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #8 on: December 09, 2011, 01:04:26 AM »
Great, I hope that you found some of this useful then - I really wish I were better at explaining the math, because probability is so important to almost every RPG, but it's so counter-intuitive.  Even on relatively simple stuff like this, unless you can see the shape of the graph, it's hard to grasp how changing some of the numbers ends up affecting the probable outcome. 

Offline Basket Burner

  • Legendary Member
  • ****
  • Posts: 1072
  • I break Basket Weavers.
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #9 on: December 09, 2011, 08:36:39 AM »
Nah, fits better here, as long as you're assuming system-neutral. Aside from a few people dropping in D&D-specific references, the discussion of the dice itself could be applied to any d20-ish style system. I'm finding all this most enlightening, for the simple fact that I AM working outside of the D&D norms, and I can mine a lot of useful balance concepts to build into my system, before I even hit a playtest stage.

I am not assuming system neutral. This originally came up in a D&D specific discussion, and that is what I was responding to. Non D&D systems aren't something I'm interested in, both because they are even more imbalanced and because I don't use them, in part due to the first reason.

That would be assuming D&D-style numbers though, if you're working the dice system to make it more consistent, you would also be narrowing the gap between bonuses and target difficulties.

In general, you want the offense specialist to have even odds when facing off the defense specialist, but to hit more often when pitting a less specialized defense against specialized offense(assuming of course, a melee spec would have high defense AND offense).

None of that has anything to do with the sort of RNG used, and making it so people aren't far off to one side or the other just means encounters come down to luck, especially in the long term. There's a reason why 90% accuracy is considered shaky.

Mooncrow: It's very simple to understand. 2d10 is distributed like a spike or a pyramid. 1d20 is a straight line. The thing is it makes defenses less valuable as 7-15 results are more likely to occur than anything else and are more likely to occur than on a D20 RNG, not to mention the lowest non auto fail result changes from 2 to 3, which means attack bonuses effectively increase by 1.

Offline Mooncrow

  • DnD Handbook Writer
  • ***
  • Posts: 983
  • The man who will be Pirate King
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #10 on: December 09, 2011, 09:07:03 AM »
Alright, here's pretty much the simplest example of a probability outcome example I know:

Which of the following do you think has a larger impact on the probable outcome of an event: 1. moving from a 1% chance to a 50% chance, or 2. moving from a 98% chance to a 99% chance?

Offline Basket Burner

  • Legendary Member
  • ****
  • Posts: 1072
  • I break Basket Weavers.
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #11 on: December 09, 2011, 01:46:09 PM »
I don't know what this has to do with anything, but the first obviously.

Offline Mooncrow

  • DnD Handbook Writer
  • ***
  • Posts: 983
  • The man who will be Pirate King
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #12 on: December 09, 2011, 02:36:34 PM »
I don't know what this has to do with anything, but the first obviously.

So, when I say things like "probability isn't intuitive", this is why.  Because the answer is the second one, though they're almost identical in effect.  In both cases, you're eliminating half of the potential other outcomes (or nearly half in the case of the first) - increasing the probable outcome by 50%.

That example is basically the 1+1=2 of probability - I would highly recommend to anyone that's interested in actual game theory to take a class on the subject.  Auditing is usually pretty cheap, and you don't have to put up with the bullshit makework that the class usually comes with, but you should still get a pretty good grasp on how the basics work. 

Offline Vasja

  • Full Member
  • **
  • Posts: 109
  • I always edit posts just after posting.
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #13 on: December 09, 2011, 03:22:15 PM »
You mean the probably of a given event not happening instead?

If an event has a 1% chance to occur, increasing it to 50% is a large increase. If an event has a 98% chance to occur, increasing it to 99% is a small increase. I understand your previous explanations, but if they refer to increasing your defense the event is the attack landing, in which case this specific example doesn't apply (well, the inverse applies).

(Ninja Edit 2: I do understand your previous examples, though. The point of defense that improves the chance of missing from 95% to 99.5%, is, relatively, 5x as effective as the point that gets you from 90% to 95%.)
« Last Edit: December 09, 2011, 03:59:21 PM by Vasja »

Offline Basket Burner

  • Legendary Member
  • ****
  • Posts: 1072
  • I break Basket Weavers.
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #14 on: December 09, 2011, 04:10:15 PM »
I don't know what this has to do with anything, but the first obviously.

So, when I say things like "probability isn't intuitive", this is why.  Because the answer is the second one, though they're almost identical in effect.  In both cases, you're eliminating half of the potential other outcomes (or nearly half in the case of the first) - increasing the probable outcome by 50%.

That example is basically the 1+1=2 of probability - I would highly recommend to anyone that's interested in actual game theory to take a class on the subject.  Auditing is usually pretty cheap, and you don't have to put up with the bullshit makework that the class usually comes with, but you should still get a pretty good grasp on how the basics work.

...That makes no sense at all. Going from 1% to 50% means something goes from almost never happening to happening half the time. Going from 98% to 99% means going from something almost always happens to... something almost always happens, and slightly more often. In the first, it goes from an outlier to a likely possibility. In the second it barely changes the overall outcome at all. You'd have to look at it very weird to make the claim you are, and completely ignore the practical effect.

Offline Mooncrow

  • DnD Handbook Writer
  • ***
  • Posts: 983
  • The man who will be Pirate King
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #15 on: December 09, 2011, 04:14:16 PM »
You mean the probably of a given event not happening? If an event has a 1% chance to occur, increasing it to 50% is a large increase. If an event has a 98% chance to occur, increasing it to 99% is a small increase.

I'm using the only model that's been discussed in this thread so far, and thus, the only one that's relevant. 

edit: but since it sounds like there was somehow still confusion over which model, feel free to reverse the numbers and go from 99% to 50% and 2% to 1%.  It's still the same problem. 
« Last Edit: December 09, 2011, 04:43:26 PM by Mooncrow »

Offline Vasja

  • Full Member
  • **
  • Posts: 109
  • I always edit posts just after posting.
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #16 on: December 09, 2011, 04:55:04 PM »
I'm using the only model that's been discussed in this thread so far, and thus, the only one that's relevant.

Good point - stupid question. :)


I'd say that if you can optimize your defense to the point where you are in the 'hit on a 17 or higher' range, additional points are very effective - it's generally much cheaper to crank your AC from 28 to 29 than to buy a cloak of displacement to get about the same effect. But which defenses can be optimized to go that high? Other than AC at low- to mid-levels, it seems like the way to go about improving a defense is either layering miss chances or simply negating attack completely.

Offline Basket Burner

  • Legendary Member
  • ****
  • Posts: 1072
  • I break Basket Weavers.
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #17 on: December 09, 2011, 05:18:53 PM »
That's the point though. For the difference between 28 and 29 to mean hit on a 17 vs hit on an 18, we're talking level 5 or 6. Most builds won't even touch that number at those levels, especially not while being able to hurt things as well. You can't afford a cloak of blur either, but at the same time this is the level where AC is comparatively better off. Go forward to the levels at which having such a cloak become reasonable, and the numbers you'd have to have for the same assumption to be true are in the high 40s... which isn't even possible, but if it were it'd cost a lot more than the cloak. Which is why I said physical defense is going to be way off to the left, even if you spend a lot of money on it, and you're better off spending that in other ways.

On the special side, it is possible to get saves up, and everyone that is smart will. So those are going to be far off to the right.

Now compare 2d10 to 1d20. All of the following are true:

Natural 20s always hit. The lowest number always misses.
Numbers in the range of 7-15 are more likely to occur on 2d10 than on 1d20.
Numbers in the range of 2-5, 17-20 are less likely to occur on 2d10 than on 1d20.
6 and 16 have the same probabilities either way.
With physical defense way off to the left, most physical attacks hit you. By making the middle range of numbers more likely, they hit you even more often.
With special defense way off to the right, most magical attacks miss you. By making the middle range of numbers more likely, they miss you even more often.
Against monsters, the same holds true. The physical side doesn't matter especially much, but the special side does as while some enemies have bad saves, others have rather good ones. Make them shake off the spells even more often, and they get more chances to launch their own attacks, which are more likely to work. End result is that defense does less to stop attacks. This is true at all levels of play, from the Orc going from a 55% to a 64% chance of a OHKO or 2HKO with simple attacks and only losing 3% of its crit OHKO chance in turn to at the higher levels where everything hits 99% of the time instead of 95% and is much harder to stop.
The lowest non auto fail number changes from 2 to 3, effectively boosting attack bonuses by 1.

Offline Mooncrow

  • DnD Handbook Writer
  • ***
  • Posts: 983
  • The man who will be Pirate King
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #18 on: December 09, 2011, 05:34:15 PM »
The thing is, armor is costly to raise, not impossible to raise.  Now, with 2d10, you've made high armor worth 5x as much as it is under d20 - now the marginal benefit of raising your AC increases.  At the same time, the marginal benefit of raising saves drops, making this an more complex picture.  And we're just looking at the value of a single hit so far; when we look at how it changes the graph of the value over an encounter, it changes the scenery even more.

The lowest non auto fail number changes from 2 to 3, effectively boosting attack bonuses by 1.

And this is just flat out wrong on so many levels. 

Offline Basket Burner

  • Legendary Member
  • ****
  • Posts: 1072
  • I break Basket Weavers.
    • View Profile
Re: d20 vs 2d10 and it's effect on defense
« Reply #19 on: December 09, 2011, 05:51:17 PM »
The thing is, armor is costly to raise, not impossible to raise.  Now, with 2d10, you've made high armor worth 5x as much as it is under d20 - now the marginal benefit of raising your AC increases.  At the same time, the marginal benefit of raising saves drops, making this an more complex picture.  And we're just looking at the value of a single hit so far; when we look at how it changes the graph of the value over an encounter, it changes the scenery even more.

It is both costly and impossible. Costly because of the high price involved, impossible because the amounts needed to get anywhere with it are unobtainable. You'd have to have around double wealth, AND devote it all just to physical defense in order to get a physical defense that means anything. And of course that says nothing for special defense, offense, support/utility...

Quote
And this is just flat out wrong on so many levels.

It's exactly right. The lowest possible result that has any chance of success is a 2 on a 1d20 and a 3 on a 2d10. So when fighting something with an attack bonus of x, instead of needing a defense of at least x + 3 to do anything at all, you need a defense of at least x + 4 to do anything at all. Otherwise, all attacks that could hit will. You might as well have defense 0 for all the good it's doing.

And that's the same sort of effect as boosting attack bonuses by 1.

What's more...

Enemies hit on any non auto fail: 95% with 1d20, 99% with 2d10.
Enemies hit on a 3/4: 90% with 1d20, 97% with 2d10.
Enemies hit on a 4/5: 85% with 1d20, 93% with 2d10.
Enemies hit on a 5/6: 80% with 1d20, 90% with 2d10.
Enemies hit on a 6/7: 75% with 1d20, 85% with 2d10.
Enemies hit on a 7/8: 70% with 1d20, 79% with 2d10.
Enemies hit on a 8/9: 65% with 1d20, 72% with 2d10.
Enemies hit on a 9/10: 60% with 1d20, 64% with 2d10.
Enemies hit on a 10/11: 55% either way (the break even point).

So just to even begin getting ahead, you'd have to have defenses of attack +12 or better. Except that that isn't possible for PCs to do for physical defense, so instead they get hit more often and on the special side enemies benefit from that more than the party does.

Someone also pointed out that enemies CAN get high physical defense simply by stacking buffs. Any level 20 enemy could casually throw out a 50-60 AC. For the weak builds at least, that puts them into the same sort of doesn't hit often, now hits even less type situation. Which just means that the party is screwed on both sides.