Help me houserule NADs

[Damon_Tor]

So let's say my table really misses the 4e innovation of replacing saves with Non-Armor Defenses. (No edition warring please. Some people like NADs, some people don't. This thread assumes we do.)

Is it as simple as generating a "Passive Str/Con/Dex/Int/Wis/Ch save" for each creature based on "12+mods" then having the spellcaster roll "1d20+mods" to determine success? Saves taken on a creature's turn would be taken normally, using "1d20+mods" vs a "save DC" of "8+mods".

Mathematically, it should be the same, yes? It just changes who is rolling the dice and whether high=good or low=good.

[Leith]

Why 12+mod? Why not 10? Or 8? If you do the math on save DCs they all assume that a character with a good stat and proficiency should only need to roll an 8, so shouldn't the inverse be the same? Or shouldn't it start at 10 like 4e did and AC does?
I like this method of doing things, 4e did most mechanical stuff very well but I don't want to confuse my players. For others I suggest giving it a try.

[Zalabim]

If you want to invert who rolls and keep the results the same, then it's 14+mods for the defender's score. You also need to change a few things with who and how you get and assign advantage and disadvantage to keep them the same. It's generally easier to get advantage on an attack roll than to give disadvantage on a saving throw. As long as you keep the differences straight, it shouldn't change any results.

[OldTrees1]

Why 12+mod? Why not 10? Or 8? If you do the math on save DCs they all assume that a character with a good stat and proficiency should only need to roll an 8, so shouldn't the inverse be the same? Or shouldn't it start at 10 like 4e did and AC does?
I like this method of doing things, 4e did most mechanical stuff very well but I don't want to confuse my players. For others I suggest giving it a try.

8->10.5 (1d20) is +2.5
(1d20) 10.5->13 is +2.5
Then +1 for changing who wins ties.
So 8+Attacker => 14+Defender (with roller winning ties)
Ninja'd but at least here is the math

Math: Step by Boring Step
1d20+Defender vs 8+Attacker with Defender wins ties
1d20+Defender vs 7+Attacker with Attacker wins ties
1d20+Defender-7 vs Attacker with Attacker wins ties
1To20+Defender-7 vs Attacker with Attacker wins ties
Defender-7 vs Attacker - 1To20 with Attacker wins ties
Defender-7 vs Attacker + -1To-20 with Attacker wins ties
Defender-7 vs Attacker + -20To-1 with Attacker wins ties
Defender-7+21 vs Attacker + -20To-1 + 21 with Attacker wins ties
Defender+14 vs Attacker + -20To-1 + 21 with Attacker wins ties
14+Defender vs Attacker + -20To-1 + 21 with Attacker wins ties
14+Defender vs Attacker + (21-20)To(21-1) with Attacker wins ties
14+Defender vs Attacker + 1To20 with Attacker wins ties
14+Defender vs 1d20+Attacker with Attacker wins ties

Math 2: Math Harder
1d20+Defender vs 8+Attacker with Defender wins ties
1d20+Defender vs 7+Attacker with Attacker wins ties
10.5+Defender vs 7+Attacker with Attacker wins ties
10.5+10.5-7+Defender vs 7+10.5-7+Attacker with Attacker wins ties
21-7+Defender vs 10.5+Attacker with Attacker wins ties
14+Defender vs 1d20+Attacker with Attacker wins ties

Math 3: The Sequel Nobody Asked For
1d20+Defender vs 8+Attacker with Defender wins ties
1d20+Defender vs 7+Attacker with Attacker wins ties
2d20+Defender vs 1d20+7+Attacker with Attacker wins ties
21+Defender vs 1d20+7+Attacker with Attacker wins ties
21-7+Defender vs 1d20+7-7+Attacker with Attacker wins ties
14+Defender vs 1d20+Attacker with Attacker wins ties

[Tanarii]

Mathematically, it should be the same, yes?
Mathematically, closest is 14+SaveMod.

[RedMage125]

Okay, something about all this math is not adding up to me. I'm not trying to be contentious, I genuinely don't get the 12 or 14 plus mods thing.

Basic 5e is:
Spell DC = 8+proficiency+stat mod
Saving throws = d20+stat+proficiency (if proficient)
Defender wins ties.

So shouldn't NAD be:
"Attack" (for spells that require saves) = d20+8+proficiency+stat
And NAD = 10+stat+proficiency (if proficient)

?

Maybe boost the NAD by 1 to be 11 instead of 10, to reflect that attacker wins ties?(like how AC attacks work)?

That's what seems to make sense to me. I don't understand what I'm missing in what others post.

[Malifice]

So shouldn't NAD be:
"Attack" (for spells that require saves) = d20+8+proficiency+stat
And NAD = 10+stat+proficiency (if proficient)

Most definitely not!

[Garfunion]

There is a Unearth Arcana that already has the rule you are looking for.
http://media.wizards.com/2015/downloads/dnd/UA5_VariantRules.pdf

Saving Defense
When a character forces an opponent to make a saving throw, that player instead makes a saving throw check. The bonus to the d20 roll for a saving throw check equals the effect’s save DC − 8.
The DC for this check equals 11 + the target’s saving throw modifier. On a successful check, the character overcomes the target’s resistance and treats the target as if it failed its saving throw. On a failed check, the target is treated as if it succeeded on its save.
As with attacks, the saving throw check has advantage if the target would have disadvantage on its saving throw, and vice versa.

So
Ability Defense = 11 + ability mod + proficiency (if proficient)
A caster would use their spell attack modifier to attack the targets ability defense, instead of the target making a saving throw.

[Tanarii]

The DC for this check equals 11 + the target’s saving throw modifier.
Unfortunately, the UA didn't use a mathematically equivalent target number. It was pointed out repeatedly at the time.

------------

Edit:
Moved rebalancing cantrips portion to its own thread:
http://www.giantitp.com/forums/showthread.php?574156-Rebalancing-save-or-nothing-cantrips&p=23515480#post23515480

[Garfunion]

Unfortunately, the UA didn't use a mathematically equivalent target number. It was pointed out repeatedly at the time.

Not sure I understand. The formula seem to be working out for my group.

I’ll have to try and dig up the thread that talked about it.

[Tanarii]

Not sure I understand. The formula seem to be working out for my group.

I’ll have to try and dig up the thread that talked about it.or you can scroll up in this thread to post number four and read Oldtrees1 detailed breakdown of the math.

[Garfunion]

or you can scroll up in this thread to post number four and read Oldtrees1 detailed breakdown of the math.
Sorry but the math being presented is meaningless to me. The current formula I’m using is working. The creatures have an ability defense (like how AC is) and my players roll to attack it. Simple.

[Tanarii]

Sorry but the math being presented is meaningless to me. The current formula I’m using is working. The creatures have an ability defense (like how AC is) and my players roll to attack it. Simple.
We seem to be talking about two different things here. I'm making no comment on whether or not using UA numbers works for your group.

[Garfunion]

We seem to be talking about two different things here. I'm making no comment on whether or not using UA numbers works for your group.
I’m simply using my group as a reference of the formula working. I have yet to encounter a situation where the formula breaks. Which is why I’m searching for past threads that would reference a creature that can not be properly converted to an ability defense.

[OldTrees1]

Some were not understanding the math despite me writing it 3 (technically 4) different ways. Obviously you can use anything you want (see Garfunion 's example where their conversion nerfed saves by 15% and they still had fun) but I want to make this math as clear as possible by repeating it different ways. So it is time for another Sequel

The main reason the math ends up with weird numbers like 8 and 14 is because
1) WotC decided on 8
2) 1d20-8 =/= 8-1d20
3) The roller (rather than always attacker or defender) wins ties
If WotC decided DCs were 10.5+RelevantBonuses, then the NAD would also be 10.5+RelevantBonuses (because 1d20-10.5=10.5-1d20 and there would never be a tie).


Math 4: The Studio has us Captive in the Basement

Normally the Attacker has a DC (8 + Relevant Bonuses), the Defender rolls (1d20 + Relevant Bonuses) against that DC, and if the saving throw equals or exceeds the DC then the Defender wins (they saved against the effect).

We want to change which side gets the 1d20 AND change which side wins ties (so that the roller is the one that wins ties).

Change which side gets the 1d20. We need to keep the average of both sides equal to each other and end with only 1 1d20 in the equation.
Step 1: Add a 1d20 to both sides
Step 2: Convert 2d20 to its average 21
Step 3: Subtract 8 from both sides so that the Attacker only has a die roll + Relevant Bonuses.

0: Attacker (8+RelevantBonuses) vs Defender (1d20+RelevantBonuses) and Defender wins ties
1: Attacker (1d20+8+RelevantBonuses) vs Defender (2d20+RelevantBonuses) and Defender wins ties
2: Attacker (1d20+8+RelevantBonuses) vs Defender (21+RelevantBonuses) and Defender wins ties
3: Attacker (1d20+RelevantBonuses) vs Defender (13+RelevantBonuses) and Defender wins ties

Now we change who wins ties. Currently the defender wins ties. We can change who wins ties do that by buffing the NAD by 1 so the current tie is a clear save and an old fail is the new tie.

Step 4: Add 1 to the Defender and change it to Attacker wins ties
3: Attacker (1d20+RelevantBonuses) vs Defender (13+RelevantBonuses) and Defender wins ties
4: Attacker (1d20+RelevantBonuses) vs Defender (14+RelevantBonuses) and Attacker wins ties


Math 5: The Reboot!
Currently the Attacker gets 8+RelevantBonuses and the Defender rolls 1d20+RelevantBonuses where the Defender wins ties. If the Defender rolls 1 less than a tie then they fail.

If the Attacker and Defender have equal bonuses then we can say that currently:
rolling a 7 is an Attacker win
rolling a 8 is a Defender win
rolling a purely theoretical 7.5 would be a tie
We can split a 1d20 into a region 1-7.5(Attacker) and a region 7.5-20(Defender).
We can invert this region by subtracting each part from 21.
This gives us new regions of 13.5-20(Attacker) and 1-13.5(Defender)
rolling a purely theoretical 13.5 would be a tie
rolling a 13 would be a Defender win
rolling a 14 would be an Attacker win
Therefore the NAD equation would be 14+RelevantBonuses with attacker winning ties when they roll 1d20+RelevantBonuses.

[jas61292]

Rather than try and use math by itself, let me try to illustrate with a gameplay example:

Say you have a fighter and a ranger, each at level 2. The ranger has a wisdom score of 13, and the fighter has a dexterity score of 10.

The ranger casts Hail of Thorns, and the fighter is caught in the area. Under the normal rules, the fighter must make s dexterity save, with a DC of 8+(ranger's proficiency bonus)+(ranger's wisdom modifier), or DC 8+2+1 = DC 11.

The fighter's save is 1d20+(dexterity modifier) as he lacks proficiency, which comes to 1d20+0. To make a DC 11 save, he must have as total of 11, which, of course, requires rolling an 11 or higher. As half the numbers on a d20 are 11 or higher, he has a 50% chance of being successful.

Now let's convert this to a situation where the ranger is rolling and the fighter is using a dexterity defense. The ranger is, of course, attacking with 1d20 + proficiency + wisdom mod, or 1d20+3. The fighter has a defense of dexterity mod + some static base number. As the fighter's dex mod is 0, that base is equal to it's dex defense.

So, for this system to be balanced with the original, the ranger's spell must still have a 50% chance of working. This now means that it must work on a roll of 11+ and fail if the roll is 10 or less. To figure out what the fighter's defense (and thus the base defense value) is, all we have to do is look at the case where the ranger rolls a 10. In this situation, the ranger has rolled as high as he can while still failing. Therefore, the fighters defense must be one point higher than the ranger's total if he rolled a 10. As the ranger's total would be 10+2+1=13, the fighter's defense (and thus the base defense value) must be 14.

[RedMage125]

Oldtrees1, thank you. Your math makes more sense now.

I also looked back and realized I forgot to drop the 8 for the NADs.

So, while I entirely understand where you are coming from now, I still have a slight bone of contention.

So 10.5 is the median of 1-20, right? Because of whatever reason, WotC decided to use 8 instead of 10 for the base for saves. I think it has to do with bonded accuracy, and keeping saving throws in a reasonable range for chance of success or failure. So we drop 2 from the "old" base of 10, and we round DOWN because ties favor the defender, right?

So shouldn't the NAD calculation be 10.5 PLUS 2, and then rounded up, because ties now favor the attacker?

Which would give us 13+relevant mods.

I guess what I'm saying is that while I understand HOW you got there, it seems to me that it should be 1 lower. Namely because i already see the base of 8 in default as having already accounted for the increase of 1 to favor the defender. And the step in your math where you take the average of 2d20, already accounts for those fractions being rounded up, especially because you only subtract a whole number, 8.

TL;DR: since the default static reduces average by 2.5, increasing the average by only 2.5 already accounts for the flip of who ties favor.

[jas61292]

Oldtrees1, thank you. Your math makes more sense now.

I also looked back and realized I forgot to drop the 8 for the NADs.

So, while I entirely understand where you are coming from now, I still have a slight bone of contention.

So 10.5 is the median of 1-20, right? Because of whatever reason, WotC decided to use 8 instead of 10 for the base for saves. I think it has to do with bonded accuracy, and keeping saving throws in a reasonable range for chance of success or failure. So we drop 2 from the "old" base of 10, and we round DOWN because ties favor the defender, right?

So shouldn't the NAD calculation be 10.5 PLUS 2, and then rounded up, because ties now favor the attacker?

Which would give us 13+relevant mods.

I guess what I'm saying is that while I understand HOW you got there, it seems to me that it should be 1 lower. Namely because i already see the base of 8 in default as having already accounted for the increase of 1 to favor the defender. And the step in your math where you take the average of 2d20, already accounts for those fractions being rounded up, especially because you only subtract a whole number, 8.

TL;DR: since the default static reduces average by 2.5, increasing the average by only 2.5 already accounts for the flip of who ties favor.

It's because of ties. A roll equal to a DC is a success. Since you are changing who is rolling, you change who wins ties, and unless you add 1 to the DC, you increase the new roller's chance of success by 5%

[RedMage125]

It's because of ties. A roll equal to a DC is a success. Since you are changing who is rolling, you change who wins ties, and unless you add 1 to the DC, you increase the new roller's chance of success by 5%

I understand that. But by my thinking, the "who wins ties" was already accounts tied for in normal save DC when they rounded the .5 DOWN, and gets accounted for in NAD calculations when they round that .5 UP.

By adding and additional 1, you are, in fact, favoring the defender by one extra point, needlessly.

[Garfunion]

Thank you OldTree1 & Jas61292 for better illustrating the math.

But 14 is still to high.
When you start calculating creatures who have proficiency in ability score, the number becomes much greater then any AC value a player can obtain non-magically.
The attack modifiers are not changing so we need to keep the Ability Defense in line with AC values.
Also I thought the 11 is the tiebreaker seeing as how an unarmored value is 10(+).

[jas61292]

Thank you OldTree1 & Jas61292 for better illustrating the math.

But 14 is still to high.
When you start calculating creatures who have proficiency in ability score, the number becomes much greater then any AC value a player can obtain non-magically.
The attack modifiers are not changing so we need to keep the Ability Defense in line with AC values.
Also I thought the 11 is the tiebreaker seeing as how an unarmored value is 10(+).

The numbers may get higher, but the percentage chances stay the same. For example, let's look at a lv 20 barbarian with maxed out Constitution, that gets boosted further by his capstone ability to 24. And lets give him a magic item (cloak of resistance) that adds one more to his Con save. That makes his total save:

1d20 + 6 (proficiency) + 7 (Con mod) + 1 (magic item) = 1d20 + 14.

If we translate that to a static defensive stat, it would make his Con defense be 28 (14+14) which seems stupidly high. But let's see how they compare.

Say an equally high level Paladin with 16 Charisma casts a Destructive Wave towards him. The DC fir the spell would be:

8 + 6 (proficiency) + 3 (Cha mod) = DC 17

To make a DC 17 save, the barbarian with +14 needs only to roll a 3 or more. That's 18/20 possible results being successful, or 90%.

Now let's look at the static defense version. If it is to be equivalent, the Paladin's spell must only beat the barbarian's defense 10% of the time. The paladins spell roll would be:

1d20 + 6 (proficiency) + 3 (Cha mod) = 1d20 + 9

In order to hit a defense of 28, the paladin needs to roll a 19 or 20. Which is exactly the 10% hit chance we are looking for.

Doesn't matter the exact situation, with a base defense of 14, the odds will always be the same as the current save system.

[RedMage125]

The numbers may get higher, but the percentage chances stay the same. For example, let's look at a lv 20 barbarian with maxed out Constitution, that gets boosted further by his capstone ability to 24. And lets give him a magic item (cloak of resistance) that adds one more to his Con save. That makes his total save:

1d20 + 6 (proficiency) + 7 (Con mod) + 1 (magic item) = 1d20 + 14.

If we translate that to a static defensive stat, it would make his Con defense be 28 (14+14) which seems stupidly high. But let's see how they compare.

Say an equally high level Paladin with 16 Charisma casts a Destructive Wave towards him. The DC fir the spell would be:

8 + 6 (proficiency) + 3 (Cha mod) = DC 17

To make a DC 17 save, the barbarian with +14 needs only to roll a 3 or more. That's 18/20 possible results being successful, or 90%.

Now let's look at the static defense version. If it is to be equivalent, the Paladin's spell must only beat the barbarian's defense 10% of the time. The paladins spell roll would be:

1d20 + 6 (proficiency) + 3 (Cha mod) = 1d20 + 9

In order to hit a defense of 28, the paladin needs to roll a 19 or 20. Which is exactly the 10% hit chance we are looking for.

Doesn't matter the exact situation, with a base defense of 14, the odds will always be the same as the current save system.

I am quite convinced, and I withdraw my objection.

[Garfunion]

The numbers may get higher, but the percentage chances stay the same. For example, let's look at a lv 20 barbarian with maxed out Constitution, that gets boosted further by his capstone ability to 24. And lets give him a magic item (cloak of resistance) that adds one more to his Con save. That makes his total save:

1d20 + 6 (proficiency) + 7 (Con mod) + 1 (magic item) = 1d20 + 14.

If we translate that to a static defensive stat, it would make his Con defense be 28 (14+14) which seems stupidly high. But let's see how they compare.

Say an equally high level Paladin with 16 Charisma casts a Destructive Wave towards him. The DC fir the spell would be:

8 + 6 (proficiency) + 3 (Cha mod) = DC 17

To make a DC 17 save, the barbarian with +14 needs only to roll a 3 or more. That's 18/20 possible results being successful, or 90%.

Now let's look at the static defense version. If it is to be equivalent, the Paladin's spell must only beat the barbarian's defense 10% of the time. The paladins spell roll would be:

1d20 + 6 (proficiency) + 3 (Cha mod) = 1d20 + 9

In order to hit a defense of 28, the paladin needs to roll a 19 or 20. Which is exactly the 10% hit chance we are looking for.

Doesn't matter the exact situation, with a base defense of 14, the odds will always be the same as the current save system.

The 5e d&d system does not calculate magic items or special class features into the math of it.
So a level 19 Barbarian could have a CON defense of 22(11+6prof+5con) against an potential attack of 11(6prof+5ability mod)
The Barbarian’s AC can also be up to 20(10+5con+5str) against the same potential attack of 11.
The Ability Defense already comes out on top by 2 points.

I maybe changing my mind. Many spells still have effects that apply to the target if the saves, attacks do not “normally”.

[OldTrees1]

I guess what I'm saying is that while I understand HOW you got there, it seems to me that it should be 1 lower. Namely because i already see the base of 8 in default as having already accounted for the increase of 1 to favor the defender. And the step in your math where you take the average of 2d20, already accounts for those fractions being rounded up, especially because you only subtract a whole number, 8.

TL;DR: since the default static reduces average by 2.5, increasing the average by only 2.5 already accounts for the flip of who ties favor.

Edit: Looks like you were convinced in the meantime. However I am leaving these explanations because your "reduce from average => increase from average" model was very useful in the first explanation for the tie breaking.

Explanation 1:
You are right that the first step is taking the deviation from 10.5 and flipping its direction. However you want to measure the deviation to the true tie rather than the tiebreaker. 8 is a win for the attacker so 7.5 is the true tie because nobody wins. 7.5 is a deviation of 3 from 10.5. 13.5 is a deviation of 3 from 10.5 in the opposite direction. Then we can give 1-13 to one side (the defender) and 14-20 to the other side (the attacker).

8-20 (attacker wins), means 1-7 (defender wins), means 7.5 is the true tie
7.5 + 3 = 10.5
10.5 + 3 = 13.5
13.5 being the true tie, means 1-13 (defender wins), means 14-20 (attacker wins)


Explanation 2:
When we change the roller we are subtle changing which direction we are rounding.

Let us take jas61292 concrete example to see this difference
The Ranger has a DC of 11 (8+2+1) vs the Fighter's 1d20+0 with the Fighter winning ties. The Ranger wins on 1-10 and the Fighter wins on 11-20. So a 50% Ranger win

If we go with 13+Defender then the Fighter has a NAD of 13 (13+0) vs the Ranger's 1d20+2+1 with the roller (the Ranger winning ties). The Fighter wins on 1-9 and the Ranger wins on 10-20 (Because 13=10+3). So a 55% Ranger win.

So clearly we have not accounted for the tiebreaker flipping yet and need the DC to be 14+Defender.


Thank you OldTree1 & Jas61292 for better illustrating the math.

But 14 is still to high.
When you start calculating creatures who have proficiency in ability score, the number becomes much greater then any AC value a player can obtain non-magically.
The attack modifiers are not changing so we need to keep the Ability Defense in line with AC values.
Also I thought the 11 is the tiebreaker seeing as how an unarmored value is 10(+).

Edit: I appear to be late to the party. Both of you (have/might have) changed your minds while I was writing my response.
While a NAD of 14+Bonus is the mathematical equivalent. Obviously you, Garfunion, had success/fun/etc when playing your way. Fun trumps math even if math can informed initial estimates.

Currently a Save DC is lower than an Attack roll.
Save DC: 8+Bonus-LosesTies
Save DC: 7.5+Bonus
Attack: 1d20+WinsTies+Bonus
Attack: 10.5+WinsTies+Bonus (but there are no ties for 0.5)
Attack: 10.5+Bonus
7.5 < 10.5

So if you converted SavingThrow into a NAD then you would expect the NAD to be higher than an Attack roll.
NAD: 14+Bonus-LosesTies
NAD: 13.5+Bonus
10.5<13.5
10.5 - 7.5 = 13.5 - 10.5
So a NAD of 14+Bonus conserves the current Save DC of 8+Bonus.

Now is the current Save DC too low at 8+Bonus? Should the current Save DC be 11+Bonus like your NAD of 11+Bonus would imply? Well that is up to the DM to decide. It would depend on the desired accuracy difference between Saves vs Attacks and the desired accuracy of Attacks vs AC.

[Cynthaer]

I know it's been written a number of different ways already, but I'll throw my hat in the ring. Maybe this approach will help someone see why the number should be 14.



Defender
Attacker


(The extra 0.5 is the tiebreaker)
1d20 + SaveBonus + 0.5
8 + AttackMod


(Subtract 0.5)
1d20 + SaveBonus
(Subtract 0.5)
7.5 + AttackMod


(Translate 1d20 to the average)
10.5 + SaveBonus
7.5 + AttackMod


(Add 3)
13.5 + SaveBonus
(Add 3)
10.5 + AttackMod


13.5 + SaveBonus
(Translate average into 1d20)
1d20 + AttackMod


(Add 0.5)
14 + SaveBonus
(Add 0.5, the tiebreaker term is back)
1d20 + AttackMod + 0.5



I personally find it easier to track the switch from "defender wins ties" to "attacker wins ties" when it's part of the actual math. Here, we can see how both numbers have to go up in order to turn (8 + AttackMod) into (1d20 + AttackMod), and how the defender base number ends up being 14 after we make sure to leave the attacker with the (+0.5) "tiebreaker" term.

IDK, maybe this works for others, maybe it doesn't.

[OldTrees1]

I like your phrasing Cynthaer. That is a good way to include the tiebreaking switching.