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Inspired by the closed question: DnD Next Hitpoint Inflation,

There have been claims of HP inflation in dnd-next, and there certainly were increased in the absolute value of HP in 4e. In order to objectively assess these claims, we must look at the mechanical-theoretical model of damage across all editions of D&D.

Therefore, at level 1, all things being equal, how many rounds does it take a goblin to drop a Fighter, a thief, and a Magic-User?

In order to ask this question: we must assume conservative builds on all sides, the average hitpoints of each of these classes, and the average damage (including to-hit adjustment) of the goblin in every edition.

If there is significant deviation in 4e, this might provide me with the necessary data to house-rule 4e into a "gritter" experience for purposes of a Break & Enter game.

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While I'm slightly interested in the subjective experience here, this is mainly a math question. Please show your work. –  Brian Ballsun-Stanton Jun 19 '12 at 16:23
    
I think there's an important aspect to survivability that gets left out of "average rounds to kill", which is the variance of that number. In 4e, it takes 10-11 rounds for a goblin to kill a fighter, but you're guaranteed several rounds before you die as your hitpoints are gradually reduced, during which you can run away, get healed, etc. An OD&D fighter could have very few hit points, and their 11 rounds can easily boil down to a 1-in-11 chance of going from full hp to dead each round, with no chance to react. For this reason, I'd say later versions are still more survivable. –  MartianInvader Jun 20 '12 at 22:53
    
@MartianInvader well, perhaps you could provide us with a graph showing the data you find important? So long as you document the methodology, it will contribute to this answer and may show that the present methodology is lacking. –  Brian Ballsun-Stanton Jun 20 '12 at 23:24
    
Rather than error bars, you'd want distributions of time-to-live. Of course, constructing that requires a lot more data than finding the average... –  Sohum Jun 21 '12 at 7:22
    
@MartianInvader added minimum rounds (Really hits here) survived for 4e and Next –  wax eagle Jun 23 '12 at 1:57
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6 Answers 6

up vote 34 down vote accepted

Compiled Results

DnD Next numbers include calculations from both the 1st and 2nd playtests.

          Fighter    Rogue    Wizard  Sturdy Wizard
   OD&D     11         3        2          -
   AD&D     14         6        2          -
    3.5     11         6        3          4
4e(MM1)     13        10        7          9
4e(MM3)     11         8        6          7
Next test1  10         8        6          -
Next test2  12         4        3          -

enter image description here

Summary

AD&D: improved fighter & rogue survivability

3.5: slightly improved wizard survivability, and pulled fighter survivability down considerably (trend towards narrower range begins)

4e: improved everyone's survivability, though mostly rogue & wizard, further narrowing the spread

4e's MM3: reduced all survivability and tightened the spread again

DnD Next (playtest 1): slight reduction in fighter survivability to tighten the spread even more

DnD Next (playtest 2): major reversal of the reduced spread trend

Thoughts

From 3.5 on, every edition change (including the switch inside 4e from MM1 damage expressions to MM3 damage expressions) has essentially worked to reduce the survivability gap between the toughest and weakest PCs, primarily by bringing the fighter down but in 4e's case by bringing the wizard up. We're down to fighters lasting about twice as long as wizards, rather than the 5-7 times longer from OD&D and AD&D. Rogues have moved from being only marginally more durable than wizards to being about halfway between wizards and fighters. Base wizard survivability has approximately tripled since OD&D/AD&D, and later editions have given them more options for improving it further.

A Note on HP Inflation

As of playtest 1, worries about hit point inflation in D&D Next over 4e appear unfounded: D&D Next PCs last about as long as 4e PCs do when using the new 4e monster damage values, and only slightly less than 4e PCs do when using the original 4e monster damage values.

As of playtest 2, DnD Next hit points are back to pre-3rd standards.

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Line graph ftw. –  oldrobotsneverrust Jun 20 '12 at 13:28
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Advanced D&D 1st edition: Hit points and AC ranges for "typical" 1st level PCs

Fighter: 1-14 HP (1d10, max +4 for CON) AC 4 to -1 (Splinted Mail+Shield, 6-18 DEX)
Thief: 1-8 HP (1d6, max +2 for CON), AC 8 to 4 (Leather, 9-18 DEX)
Magic-User: 1-6 HP (1d4, max +2 for CON), AC 11 to 6 (No armor, 6-18 DEX)

Then there's the Goblin: 1-7 HP, AC 6, damage 1d6

Picking the middle-of-the-road for the PCs, you get something like:

Fighter: 7.5 HP, AC 2
Thief:  4.5 HP, AC 4
Magic-User: 2.5 HP, AC 9

For the one-on-one combat results:

Fighter: The Goblin needs 2.14 average hits to down the fighter, and 
it needs to roll an 18(!) to hit AC2, so it'll take 
14 rounds to kill the fighter.

Thief: He needs 1.28 hits to kill the Thief, and needs to roll 16 to hit
5.12 rounds.

Magic User: Killed with 0.72 average hits, needs a 11 to hit
1.44 rounds

Wow. That's quite a range, even with "average" characters. If the Fighter had 18 DEX, he's essentially untouchable by the Goblin (needs a 20 to hit).


These calculations don't take into account the (much-maligned) Armor Class adjustment by weapon type rule/table. It's not clear if that adjustment is even supposed to apply to monsters, because it's only found in the Player's Handbook. On the other hand, the Goblin is probably using a short sword, which is listed on the table...

If we add that adjustment in, it helps the Goblin vs. the Magic User and Thief, and makes the fighter even harder to hit.

Fighter: 20 to hit = 42.8 rounds
Thief: 15 to hit = 4.27 rounds
Magic-User: 10 to hit = 1.3 rounds
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I'm going to cover 4e and Next in this answer. 4e first:

Assumptions: For ease I will use Essentials classes.

  • Mage HP: 23, AC: 14 (CON 13, INT 18) Surge value: 5 (28 HP)
  • Knight HP: 31 AC: 20 (CON 16, Plate, Heavy Shield) Surge Value: 7 (38 HP)
  • Thief HP: 25 AC: 16 (CON 13, DEX 18, Leather) Surge Value 6 (31 HP)

Goblins and Kobolds (No L1 non-minion Goblins are present in MM3 or later, so I'm going to use a kobold for this role):

  • Grunt (Skirmisher, Minion): +6 vs AC, 4 damage
  • Cutthroat (Skirmisher): +6 vs AC, 1d6+5 (8.5, 11) damage
  • Sniper (Artillery, Minion): +8 vs AC , 4 damage
  • Slinger (Artillery): +8, 1d6+5 (8.5, 11) damage

Ok, let's calculate this for each one vs the Mage:

 Grunt: 13/20 * 4 = 2.6 DPR -> 12.7 RtK (7 rounds min)
 Cutthroat: 12/20 * 8.5 + 1/20 * 11 = 5.65 DPR -> 5.0 RtK (3 rounds min)
 Sniper: 15/20 * 4 = 3 DPR -> 9.3 RtK (7 rounds min)
 Slinger: 14/20 * 8.5 + 1/20 * 11 = 6.5 DPR -> 4.3 RtK (3 rounds min)

Now the Thief:

 Grunt: 11/20 * 4 = 2.2 DPR -> 11.9 RtK (8 rounds min)
 Cutthroat 10/20 * 8.5 + 1/20 * 11 = 5.2 DPR -> 6.0 RtK (3 rounds min)
 Sniper 13/20 * 4 = 2.6 DPR -> 11.9 RtK (8 rounds min)
 Slinger: 12/20 * 8.5 + 1/20 * 11 = 5.65 DPR -> 5.5 RtK (3 rounds min)

Finally the Knight:

 Grunt: 7/20 * 4 = 1.4 DPR -> 27.1 RtK (10 rounds min)
 Cutthroat 6/20 * 8.5 + 1/20 * 11 = 3.1 DPR -> 12.3  RtK (4 rounds min)
 Sniper 9/20 * 4 = 1.8 DPR -> 21.1 RtK (10 rounds min)
 Slinger: 8/20 * 8.5 + 1/20 * 11 = 4.0 DPR -> 9.5 RtK (4 rounds min)

Lets throw out the minions and just look at the cutthroat:

  Mage: 12/20 * 8.5 + 1/20 * 11 = 5.65 DPR -> 5.0 RtK  (min 3 rounds)
  Thief: 10/20 * 8.5 + 1/20 * 11 = 5.2 DPR -> 6.0 RtK (min 3 rounds)
  Knight 6/20 * 8.5 + 1/20 * 11 = 3.1 DPR -> 12.3  RtK (min 4 rounds)

And the Kobold

 Mage: 14/20 * 8.5 + 1/20 * 11 = 6.5 DPR -> 4.3 RtK (min 3 rounds)
 Thief: 12/20 * 8.5 + 1/20 * 11 = 5.65 DPR -> 5.5 RtK (min 3 rounds)
 Knight: 8/20 * 8.5 + 1/20 * 11 = 4.0 DPR -> 9.5 RtK (min 4 rounds)

DND Next v1

We don't know what character creation looks like in next, so we will use the Prebuilts. It's also worth nothing that there are no monster levels in 5e as of yet.

  • Fighter: AC 15, HP 20
  • Rogue: AC 15, HP 16
  • Wizard: AC 11, HP 16

And here is the average Goblin from the bestiary:

  • Mace +2 1d6
  • bow +3 1d6+1

Lets calculate RtK for each of these:

Fighter

 Mace: 7/20 * 3.5 + 1/20 * 6 = 1.5 -> 13.3 RtK (min 3 rounds)
 Bow: 8/20 * 4.5 + 1/20 * 7 = 2.2 -> 9.1 RtK (min 3 rounds)

Rogue

 Mace: 7/20 * 3.5 + 1/20 * 6 = 1.5 -> 10.7 RtK (min 3 rounds)
 Bow: 8/20 * 4.5 + 1/20 * 7 = 2.2 -> 7.3 RtK (min 3 rounds)

Mage

 Mace: 11/20 * 3.5 + 1/20 * 6 = 2.2 -> 7.3 RtK (min 3 rounds)
 Bow: 12/20 * 4.5 + 1/20 * 7 = 3.1 -> 5.2 RtK (min 3 rounds)

Let's focus on the bow here:

Fighter: 8/20 * 4.5 + 1/20 * 7 = 2.2 -> 9.1 RtK (min 3 rounds)
Rogue: 8/20 * 4.5 + 1/20 * 7 = 2.2 -> 7.3 RtK (min 3 rounds)
Mage: 12/20 * 4.5 + 1/20 * 7 = 3.1 -> 5.2 RtK (min 3 rounds)

DNDNext v2

(Using Pregens for now, I may do some character creation later and revisit)

 Fighter1 17 AC, 14 HP (Going to ignore Parry for now, but may return to examine impact)
 Fighter2 15 AC, 12 HP
 Rogue 14 AC, 7 HP
 Wizard 12 AC, 6 HP

Now let's hear from the Goblin side of things:

 Mace: -1, 1d6-1 damage
 Short Bow: +1, 1d6+1 damage

Now RtK for each of these

Fighter1:

 Mace: 2/20*2.5 + 1/20*5 = .5 dpr -> 28 rtk (min 3 rounds)
 Short Bow: 4/20*4.5 + 1/20*7 = 1.25 dpr -> 11.2 rtk (min 2 rounds)

Fighter2:

 Mace: 4/20*2.5 + 1/20*5 = .75 dpr -> 16 rtk (min 3 rounds)
 Short Bow: 6/20*4.5 + 1/20*7 = 1.7 dpr -> 7.05 rtk (min 2 rounds)

Rogue:

 Mace: 5/20*2.5 + 1/20*5 = .875 dpr -> 8 rtk (min 2 rounds)
 Short Bow: 7/20*4.5 + 1/20*7 = 1.925 dpr -> 3.64 rtk (min 1 round)

Wizard:

 Mace: 7/20*2.5 + 1/20*5 = 1.125 dpr -> 5.33 rtk (min 2 rounds)
 Short Bow: 9/20*4.5 + 1/20*7 = 2.375 dpr -> 2.53 rtk (min 1 round)

Comparison between editions melee (4e Goblin Cutthroat, Next Goblin with Mace):

          4e     Nextv1 Nextv2
Fighter   12.3   13.3   28
Fighter2                11.2
Rogue     6.0    10.7   8
Mage      5.0    7.3    5.33

Comparison Between Editions Ranged (4e Kobold Slinger, Next Goblin with bow):

          4e     Nextv1  Nextv2
Fighter   9.5    9.1     11.2
Fighter2                 7.05    
Rogue     5.5    7.3     3.64
Mage      4.3    5.2     2.53

Comparison Between Editions of Minimum rounds survived:

          4e     Nextv1  Nextv2
Fighter   4      3       3
Rogue     3      3       2 (or 1)
Mage      3      3       2 (or 1)

It looks like the Goblin may not the best example of a melee fighter in Next. But survivability between the Next Goblin and the 4e Kobold are quite similar, with the Rogue and the wizard looking slightly more durable in Next than in 4e (though this was fixed in v2). It takes at minimum 3 hits to drop any character in 4e and the first pass of next. However the latest edition of Next feature a much squishier rogue and wizard in the pregens.

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But if you compare the Next mace with the 4e skirmisher, so that both situations are melee attacks, then all the PCs become more durable in Next than they are in 4e. –  ioanwigmore Jun 19 '12 at 18:49
    
I've looked at this for the v3 playtest that came out last week. I don't feel the need to update as the changes to the basic structure are fairly minimal. chat.stackexchange.com/transcript/message/6817333#6817333 has the details if you're interested. The only big change is that a Goblin can now no longer one shot a rogue or wizard on a crit. –  wax eagle Nov 8 '12 at 16:25
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4e

Con is a useful stat for fighters, and as heavy armor users they can afford to grab a 14. Rogues are all about Dex, so they too can afford to diversify a little bit to get a 12 Con. Wizard1 is a staff-wielder, so he has a 14 Con. Wizard2 is going orbs, so he has a 10 Con. We'll assume each spends 1 healing surge (presumably through 2nd wind, but factoring in the defense bonus would greatly complicate the math).

Fighter: 14 Con => 29 HP (+1 surge = 36 effective HP), scale + heavy shield => 19 AC
Rogue: 12 Con => 24 HP (+1 surge = 30 effective HP), leather + 18 Dex => 16 AC
Wizard1: 14 Con => 24 HP (+1 surge = 30 effective HP), cloth + 18 Int + staff => 15 AC
Wizard2: 10 Con => 20 HP (+1 surge = 25 effective HP), cloth + 18 Int => 14 AC

2 sample critters, since MM3 & later moved monsters to having less HP & more damage

Goblin Warrior, level 1 skirmisher (MM1 pg137) => +6 vs AC, 1d8+2 dmg (6.5 average, 10 crit)

Xivort Slasher, level 1 skirmisher (MM3 pg208) => +6 vs AC, 1d6+5 dmg (8.5 average, 11 crit)

VS Fighter
hit (non-crit): 7/20 chance; crit: 1/20 chance
Goblin effective DPR: (7/20)*6.5 + (1/20)*10 = 2.775
Xivort effective DPR: (7/20)*8.5 + (1/20)*11 = 3.525

VS Rogue
hit (non-crit): 8/20 chance; crit: 1/20 chance
Goblin effective DPR: (8/20)*6.5 + (1/20)*10 = 3.1
Xivort effective DPR: (8/20)*8.5 + (1/20)*11 = 3.95

VS Wizard1
hit (non-crit): 9/20 chance; crit: 1/20 chance
effective DPR: (9/20)*6.5 + (1/20)*10 = 3.425
Xivort effective DPR: (9/20)*8.5 + (1/20)*11 = 4.375

VS Wizard2
hit (non-crit): 10/20 chance; crit: 1/20 chance, 10 damage
Goblin effective DPR: (10/20)*6.5 + (1/20)*10 = 3.75
Xivort effective DPR: (10/20)*8.5 + (1/20)*10 = 4.8

Rounds to Kill

All values rounded up to nearest round.

Goblin
Fighter: 36 effective HP / 2.775 DPR = 13 rounds to kill
Rogue: 30 effective HP / 3.1 DPR = 10 rounds to kill
Wizard1: 30 effective HP / 3.425 DPR = 9 rounds to kill
Wizard2: 25 effective HP / 3.75 DPR = 7 rounds to kill

Xivort
Fighter: 36 effective HP / 3.525 DPR = 11 rounds to kill
Rogue: 30 effective HP / 3.95 DPR = 8 rounds to kill
Wizard1: 30 effective HP / 4.375 = 7 rounds to kill
Wizard2: 25 effective HP / 4.8 DPR = 6 rounds to kill
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3.5

(I'm adding another answer rather than editing my existing one because my existing answer is already pretty darn long).

I'll be assuming the maximum value for the level 1 hit die; this was a common house rule, and I believe was also the official rule in many of the organized play leagues.

Let's give the fighter a +1 Dex mod (he's going for plate), a +2 Con mod, a heavy shield, and scale mail (all he can afford). The rogue probably has a +3 Dex mod, a +1 Con mod, and grabs studded leather. The wizards have a +2 Dex mod (gotta be able to hit with rays) and a +1 Con mod (they can dump strength and charisma, and arguably wisdom). Wizard1 is lucky enough to have Mage Armor up when the goblin arrives, while wizard2 is stuck with non-magical Robes of No AC.

Fighter: 10 base + 2 Con = 12 HP; scale + hvy shield +1 Dex = 17 AC
Rogue: 6 base + 1 Con = 7 HP; studded leather +3 Dex = 16 AC
Wizard1: 4 base + 1 Con = 5 HP; +4 Mage Armor +2 Dex = 16 AC
Wizard2: 4 base + 1 Con = 5 HP; +2 Dex = 12 AC

1st level Goblin Warrior (MM1 pg133): +2 attack, 1d6 damage (3.5 average, 7 crit average)

VS Fighter
hit chance = 5/20; unconfirmed crit chance = 1/20*14/20; confirmed crit chance = 1/20*6/20
effective DPR = (5/20)*3.5 + (1/20)*(14/20)*3.5 + (1/20)*(6/20)*7 = 1.1025

VS Rogue & Wizard1
hit chance = 6/20; unconfirmed crit chance = 1/20*13/20; confirmed crit chance = 1/20*7/20
effective DPR = (6/20)*3.5 + (1/20)*(13/20)*3.5 + (1/20)*(7/20)*7 = 1.28625

VS Wizard2
hit chance = 10/20; unconfirmed crit chance = 1/20*9/20; confirmed crit chance = 1/20*11/20
effective DPR = (10/20)*3.5 + (1/20)*(9/20)*3.5 + (1/20)*(11/20)*7 = 2.02125

Rounds to Kill

All values rounded up to nearest round.

Fighter: 12 HP / 1.1025 DPR = 11 rounds
Rogue: 7 HP / 1.28625 DPR = 6 rounds
Wizard1: 5 HP / 1.28625 DPR = 4 rounds
Wizard2: 5 HP / 2.02125 DPR = 3 rounds
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Basic D&D

Fighter: 7.5 HP (1d8+CON), AC 2 (Plate+shield)
Thief: 2.5 HP(1d4), AC 4 (Leather, -3 DEX bonus)
Magic-User: 2.5 HP(1d4), AC 9 (No armor, no DEX bonus)
Goblin: HD 1-1, avg. dam 3.5

Rounds to kill:

Fighter: 2.14 hits, 17 to hit = 10.7 rounds
Thief: 0.71 hits, 15 to hit = 2.37 rounds
Magic-User: 0.71 hits, 10 to hit = 1.29 rounds
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Looking at this, and the AD&D numbers above, I'm reminded of how we used to roll up at least two characters per player when starting out, and just deus ex machina'd them into the adventure when the first wizard or thief bit the dust. –  Mark Bessey Jun 19 '12 at 21:32
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