Static vs Dynamic Bonus (defensive duelist vs +AC) - Downloaded from the Wizards Community, all coding removed by Solauren

Post/Author/DateTime	Post
#1 mellored Nov 18, 2014 7:12:36	TLDR: Against 4 attacks per turn, Defensive Duelist is worth... +2 = +1.7AC +3 = +2.4AC +4 = +3,0AC +5 = +3.4AC +6 = +3.8AC War cleric, 4 attacks per short rest... +10 = +4.7 to-hit. Against less attacks (like a Duel), DD is more favorable. Against more attacks it's worse. Assumptions: 1: Open rolls. I assume you don't waste use the feature to gain +4 AC when you need +8. If your DM hides your numbers, these lose alot of their value. 2: Bounded accuracy. If you are only hit on a 18+, and gain +6 AC, you've effecivly only gained +2. So compair it as a +2. Notes: Competing actions/resources. Keep in mind competing resources like a bard granting you oppertunity attacks, or a rogue's uncanny dodge. Likewise, turn undead reduces the war clerics channel divinity. Similar features. These numbers can apply to similar features, such as a wizard shield spell vs mage armor. Todo: +Dice: Still working on how much guidance, bless, and bardic insperation (i.e. +1d4) is worth. math and more detail Defensive Dualist = 1-(1-(bonus0.05))^number of attacks = 1-chance to not use it = chance to use it. +AC = (bonus0.05)number of attacks. Breakpoint number of attacks. +2 vs +1 = 16.475 +2 vs +2 = 1 *Sanity check. +2 bonus all the time should be eqaul to +2 some of the time, when your attacked once. +3 vs +1 = 19.103 +3 vs +2 = 6.552 +4 vs +1 = 19.757 +4 vs +2 = 8.499 +4 vs +3 = 3.831 (magic initiate -> shield spell) +5 vs +1 = 19.931 +5 vs +2 = 9.374 +5 vs +3 = 5.153 +5 vs +4 = 2.701 +6 vs +1 = 19.984 +6 vs +2 = 9.684 +6 vs +3 = 5.832 +6 vs +4 = 3.63 +6 vs +5 = 2.126 (war cleric, per short rest) +10 vs +1 = 20 +10 vs +2 = 9.99 +10 vs +3 = 6.598 +10 vs +4 = 4.823 +10 vs +5 = 3.69 +10 vs +6 = 2.88 +10 vs +7 = 2.261
#2 mellored Nov 18, 2014 7:12:55	To-Do: Figure out +1d4 / d6 / d8... (bardic insperation, guidance, ect...)
#3 Coredump00 Nov 18, 2014 9:05:52	Hey MR, I like the idea of what you are doing... but I really can't grasp what you are trying to represent with the equations. mellored wrote:
#4 mellored Nov 18, 2014 9:51:28	Coredump00 wrote:
#5 FrogReaver Nov 18, 2014 10:04:51	This is an interesting problem. I'ma look into it. A couple of questions. 1. There will be some rounds where it will never be beneficial to use defensive duelist. How is that factored in? 2. Can you really make a comparison without looking at a monsters chance to hit you or average chance to hit you?
#6 mellored Nov 18, 2014 10:16:24	FrogReaver wrote:
(Reply to #6) FrogReaver	mellored wrote:
#8 mellored Nov 18, 2014 10:45:57	FrogReaver wrote:
#9 FrogReaver Nov 18, 2014 11:05:56	Starting off: defensive duelist is worthless against a monster that can only hit you on a crit. This means defensive duelist is worthless when monsters have 5% chance to hit. On a monster that can hit you 10% of the time the calculation will be a little more involved. First we will need to know the chance we will be hit with an attack that defensive duelist can turn into a miss. Since 5% of the time we will be crit that leaves 5% of the time we will be hit with an attack that defensive duelist can turn into a miss. So assuming a single attack each round defensive duelist will: 5% chacne to hit: no effect 10% chance to hit: equal to +1 AC 15% chacne to hit: equal to +2 AC 20% chance to hit: equal to +3 AC 25% chance to hit equal to +4 AC 30% chance to hit equal to +5 AC 35% chance to hit equal to +6 AC 40% chance to hit equal to +6 AC ....the rest are equal to +6 AC (unless the monsters chacne to hit me goes over 95%, in which case defensive duelist bonus will drop to near worthless) However the real comparison is how much does defensive duelist help on multiple attacks against the various to hit chances. Those calculations will come later.
#10 mellored Nov 18, 2014 11:35:22	FrogReaver wrote:
(Reply to #10) FrogReaver	mellored wrote:
#12 Coredump00 Nov 18, 2014 12:28:47	I take it you are assuming the player will know if DD will be effective? So the player will know that he has AC 16, and the monster got a total of 18 (or whatever)?
#13 mellored Nov 18, 2014 12:32:58	FrogReaver wrote:
#14 mellored Nov 18, 2014 12:37:10	Coredump00 wrote:
#15 FrogReaver Nov 18, 2014 19:54:07	Not factoring in criticals// I have calculated that at 50 percent chance to be hit per attack a +6 one time reaction bonus from defensive duelist is equivalent to +5.1 ac when facing 2 attacks. Thats actually much better than I expected
#16 Clutchbone Nov 18, 2014 14:55:08	I'm not literate in math, so could you all say what the equivalent AC is per proficiency level? That way people can know it's value during every tier of play.
#17 mellored Nov 18, 2014 18:29:06	how many attacks are you taking per round?
(Reply to #17) FrogReaver	mellored wrote:
#19 FrogReaver Nov 18, 2014 20:01:22	At 50 percent hit and 3 attacks defensive duelist at +6 This is equivalent to +4.58 ac
#20 FrogReaver Nov 18, 2014 20:02:24	I think I've made a mistake. I'm rechecking my work Mistake found. I hadn't factored in all the hits in my probabilities that contained multiple hits Numbers fixed
#21 mellored Nov 19, 2014 5:34:47	Clutchbone wrote:
(Reply to #21) FrogReaver	mellored wrote:
#23 mellored Nov 19, 2014 11:52:43	FrogReaver wrote:
#24 mellored Nov 19, 2014 11:58:48	Here we go. Setting the number of attacks to 4 per turn.... Defensive Dualist = flat bonus. +2 = 1.72 +3 = 2.39 +4 = 2.95 +5 = 3.42 +6 = 3.8
(Reply to #23) FrogReaver	nvm I figured out why what I thought was a problem wasn't one mellored wrote:
#26 Rhenny Nov 19, 2014 15:56:59	Not sure about math, but a PC I'm playing in Horde of the Dragon Queen has DD because it fits with his character concept. We've played 7 sessions (about 20 hours). He is 3rd level. Not once has the dang feat deflected a single attack. I must be the most unlucky player on the planet. Granted his AC is 18 and he gets only +2 from the feat. I'm sure it will feel a little better when he has +3 or +4.
#27 Lawolf Nov 19, 2014 17:53:18	Rhenny wrote:
#28 FrogReaver Nov 19, 2014 19:43:35	I have some numbers. I'll post some charts later. The effectiveness will depend on a monsters chance to hit you. My results are vastly different than mellored's. Ill discuss my methodology for now. My method does not factor in crits though it seems possible to add them. With that said I used two formulas. The first one is simple: #attacks * (chance to hit after static ac bonus is factored in) If this was multiplied by avg hit dmg then it would be the #attacks * dpr. THis formula and its derivation are very simple. The other formula took some thinking. So I'm going to take baby steps as I lead up to its derivation. Part 1 (Chance a monster hits me with the ac after the dynamic bonus is factored in)^(#attacks) This tells me the chance that I will never get to use defensive duelist to negate an attack. Keep this in mind because it's important.
#29 FrogReaver Nov 19, 2014 19:52:20	Part 2 of the other formula was: (#attacks - 1)*(chance to be hit without any modifiers) This times the average damage would get me the dpr for the #number - 1 attacks that are never affected by defensive duelist. Part 3 combine these 2 formulas (add them together) Part 4 run some numbers on excel
#30 FrogReaver Nov 20, 2014 3:21:56	I really should do math when im at home and have ample time. To make the story short mellrod was right. For now till I can clean them up ignore all my numbers and statements about calculating it differently.
#31 mellored Nov 20, 2014 5:03:18	FrogReaver wrote:
#32 mellored Nov 20, 2014 6:12:25	Rhenny wrote:
#33 Timborama Nov 20, 2014 6:43:08	Also, while you're editing, Mello, it's "Duel" when you want to go mano-y-mano or whatever. And "dual" means two. So duel-wielding is for when you are holding a pistol and march 10 paces before turning and firing, but dual-wielding is for when you have two swords
#34 mellored Nov 20, 2014 7:56:58	Timborama wrote:

Post/Author/DateTime

Post

mellored

Nov 18, 2014 7:12:36

TLDR: Against 4 attacks per turn, Defensive Duelist is worth...

+2 = +1.7AC

+3 = +2.4AC

+4 = +3,0AC

+5 = +3.4AC

+6 = +3.8AC

War cleric, 4 attacks per short rest...

+10 = +4.7 to-hit.

Against less attacks (like a Duel), DD is more favorable.

Against more attacks it's worse.

Assumptions:

1: Open rolls. I assume you don't waste use the feature to gain +4 AC when you need +8. If your DM hides your numbers, these lose alot of their value.

2: Bounded accuracy. If you are only hit on a 18+, and gain +6 AC, you've effecivly only gained +2. So compair it as a +2.

Notes:

Competing actions/resources. Keep in mind competing resources like a bard granting you oppertunity attacks, or a rogue's uncanny dodge. Likewise, turn undead reduces the war clerics channel divinity.

Similar features. These numbers can apply to similar features, such as a wizard shield spell vs mage armor.

Todo:

+Dice: Still working on how much guidance, bless, and bardic insperation (i.e. +1d4) is worth.

math and more detail

Defensive Dualist = 1-(1-(bonus*0.05))^number of attacks = 1-chance to not use it = chance to use it.

+AC = (bonus*0.05)*number of attacks.

Breakpoint number of attacks.

+2 vs +1 = 16.475

+2 vs +2 = 1*

*Sanity check. +2 bonus all the time should be eqaul to +2 some of the time, when your attacked once.

+3 vs +1 = 19.103

+3 vs +2 = 6.552

+4 vs +1 = 19.757

+4 vs +2 = 8.499

+4 vs +3 = 3.831

(magic initiate -> shield spell)

+5 vs +1 = 19.931

+5 vs +2 = 9.374

+5 vs +3 = 5.153

+5 vs +4 = 2.701

+6 vs +1 = 19.984

+6 vs +2 = 9.684

+6 vs +3 = 5.832

+6 vs +4 = 3.63

+6 vs +5 = 2.126

(war cleric, per short rest)

+10 vs +1 = 20

+10 vs +2 = 9.99

+10 vs +3 = 6.598

+10 vs +4 = 4.823

+10 vs +5 = 3.69

+10 vs +6 = 2.88

+10 vs +7 = 2.261

mellored

Nov 18, 2014 7:12:55

To-Do: Figure out +1d4 / d6 / d8... (bardic insperation, guidance, ect...)

Coredump00

Nov 18, 2014 9:05:52

Hey MR, I like the idea of what you are doing... but I really can't grasp what you are trying to represent with the equations.

mellored wrote:

mellored

Nov 18, 2014 9:51:28

Coredump00 wrote:

FrogReaver

Nov 18, 2014 10:04:51

This is an interesting problem. I'ma look into it.

A couple of questions.

1. There will be some rounds where it will never be beneficial to use defensive duelist. How is that factored in?

2. Can you really make a comparison without looking at a monsters chance to hit you or average chance to hit you?

mellored

Nov 18, 2014 10:16:24

FrogReaver wrote:

(Reply to #6)

FrogReaver

mellored wrote:

mellored

Nov 18, 2014 10:45:57

FrogReaver wrote:

FrogReaver

Nov 18, 2014 11:05:56

Starting off: defensive duelist is worthless against a monster that can only hit you on a crit. This means defensive duelist is worthless when monsters have 5% chance to hit.

On a monster that can hit you 10% of the time the calculation will be a little more involved. First we will need to know the chance we will be hit with an attack that defensive duelist can turn into a miss. Since 5% of the time we will be crit that leaves 5% of the time we will be hit with an attack that defensive duelist can turn into a miss.

So assuming a single attack each round defensive duelist will:

5% chacne to hit: no effect

10% chance to hit: equal to +1 AC

15% chacne to hit: equal to +2 AC

20% chance to hit: equal to +3 AC

25% chance to hit equal to +4 AC

30% chance to hit equal to +5 AC

35% chance to hit equal to +6 AC

40% chance to hit equal to +6 AC

....the rest are equal to +6 AC (unless the monsters chacne to hit me goes over 95%, in which case defensive duelist bonus will drop to near worthless)

However the real comparison is how much does defensive duelist help on multiple attacks against the various to hit chances. Those calculations will come later.

#10

mellored

Nov 18, 2014 11:35:22

FrogReaver wrote:

(Reply to #10)

FrogReaver

mellored wrote:

#12

Coredump00

Nov 18, 2014 12:28:47

I take it you are assuming the player will know if DD will be effective? So the player will know that he has AC 16, and the monster got a total of 18 (or whatever)?

#13

mellored

Nov 18, 2014 12:32:58

FrogReaver wrote:

#14

mellored

Nov 18, 2014 12:37:10

Coredump00 wrote:

#15

FrogReaver

Nov 18, 2014 19:54:07

Not factoring in criticals//

I have calculated that at 50 percent chance to be hit per attack a +6 one time reaction bonus from defensive duelist is equivalent to +5.1 ac when facing 2 attacks.

Thats actually much better than I expected

#16

Clutchbone

Nov 18, 2014 14:55:08

I'm not literate in math, so could you all say what the equivalent AC is per proficiency level? That way people can know it's value during every tier of play.

#17

mellored

Nov 18, 2014 18:29:06

how many attacks are you taking per round?

(Reply to #17)

FrogReaver

mellored wrote:

#19

FrogReaver

Nov 18, 2014 20:01:22

At 50 percent hit and 3 attacks defensive duelist at +6

This is equivalent to +4.58 ac

#20

FrogReaver

Nov 18, 2014 20:02:24

I think I've made a mistake. I'm rechecking my work

Mistake found. I hadn't factored in all the hits in my probabilities that contained multiple hits

Numbers fixed

#21

mellored

Nov 19, 2014 5:34:47

Clutchbone wrote:

(Reply to #21)

FrogReaver

mellored wrote:

#23

mellored

Nov 19, 2014 11:52:43

FrogReaver wrote:

#24

mellored

Nov 19, 2014 11:58:48

Here we go. Setting the number of attacks to 4 per turn....

Defensive Dualist = flat bonus.

+2 = 1.72

+3 = 2.39

+4 = 2.95

+5 = 3.42

+6 = 3.8

(Reply to #23)

FrogReaver

nvm I figured out why what I thought was a problem wasn't one

mellored wrote:

#26

Rhenny

Nov 19, 2014 15:56:59

Not sure about math, but a PC I'm playing in Horde of the Dragon Queen has DD because it fits with his character concept. We've played 7 sessions (about 20 hours). He is 3rd level.

Not once has the dang feat deflected a single attack. I must be the most unlucky player on the planet. Granted his AC is 18 and he gets only +2 from the feat. I'm sure it will feel a little better when he has +3 or +4.

#27

Lawolf

Nov 19, 2014 17:53:18

Rhenny wrote:

#28

FrogReaver

Nov 19, 2014 19:43:35

I have some numbers. I'll post some charts later. The effectiveness will depend on a monsters chance to hit you.

My results are vastly different than mellored's.

Ill discuss my methodology for now.

My method does not factor in crits though it seems possible to add them.

With that said I used two formulas. The first one is simple:

#attacks * (chance to hit after static ac bonus is factored in)

If this was multiplied by avg hit dmg then it would be the #attacks * dpr. THis formula and its derivation are very simple.

The other formula took some thinking. So I'm going to take baby steps as I lead up to its derivation.

Part 1

(Chance a monster hits me with the ac after the dynamic bonus is factored in)^(#attacks)

This tells me the chance that I will never get to use defensive duelist to negate an attack. Keep this in mind because it's important.

#29

FrogReaver

Nov 19, 2014 19:52:20

Part 2 of the other formula was:

(#attacks - 1)*(chance to be hit without any modifiers)

This times the average damage would get me the dpr for the #number - 1 attacks that are never affected by defensive duelist.

Part 3 combine these 2 formulas (add them together)

Part 4 run some numbers on excel

#30

FrogReaver

Nov 20, 2014 3:21:56

I really should do math when im at home and have ample time. To make the story short mellrod was right.

For now till I can clean them up ignore all my numbers and statements about calculating it differently.

#31

mellored

Nov 20, 2014 5:03:18

FrogReaver wrote:

#32

mellored

Nov 20, 2014 6:12:25

Rhenny wrote:

#33

Timborama

Nov 20, 2014 6:43:08

Also, while you're editing, Mello, it's "Duel" when you want to go mano-y-mano or whatever. And "dual" means two. So duel-wielding is for when you are holding a pistol and march 10 paces before turning and firing, but dual-wielding is for when you have two swords

#34

mellored

Nov 20, 2014 7:56:58

Timborama wrote: