Let's look at things from the monster's point of view. We'll calculate the average number of hits "N" to kill a player character (of the same level) and see how it scales when the level goes to infinity.
For this analysis, we'll ignore healing surges and stat increases to CON.
For the player characters, the hit points H scale approximately as:
H = *constant* + CON + CLASS*level
where *constant* is a number between 6 to 10 (depending on class) and:
CLASS = 4 --> wizard, invoker
CLASS = 5 --> cleric, druid, ranger, rogue, bard, sorcerer, warlock, warlord, shaman
CLASS = 6 --> fighter, paladin, barbarian, avenger
CLASS = 7 --> warden.
For the monster damage, the average damage from the "normal damage expression" table on page 185 of the 4E DMG1, follows approximately:
low damage: 6 + level*5/12
medium damage: 8 + level*7/15
high damage: 10 + level*3/5.
(These were found by doing a simple linear fit to the average values).
Calculating "N" for the monster attacking players and scaling the level to infinity, we get:
low damage: N -> 12*CLASS/5 = 2.4*CLASS
medium damage: N -> 15*CLASS/7 = 2.14*CLASS
high damage: N -> 5*CLASS/3 = 1.67*CLASS
For the new monster damage table from the 4E DMG1 errata for page 185, the average damage follow approximately:
single target: 8 + level
two or more targets: 6 + level*3/4.
Calculating "N" for the monster attacking players and scaling the the level to infinity, we get:
single target: N -> CLASS
two or more targets: N -> 4*CLASS/3 = 1.33*CLASS.
Compare the old damage scheme to the errata update one. For the average number of hits "N" of a monster killing a player character, it is suggestive the errata updated monster damage is a lot more formidable.
Using the new errata monster damage, for example a monster fighting a typical defender player character, it takes around 6 to 8 hits to kill the defender without any healing surges. Using the old monster damage table from page 185 of the 4E DMG1, it would take the same monster around 12 hits to kill the defender (without any healing surges).
In contrast from previous posts which calculated the scaling for non-striker and striker player characters, we calculated that a non-striker player character would take around 8 to 10 hits to kill a skirmisher monster using weapons with damage dice d8, d10 or d12. A striker player character would take around 6 to 8 hits to kill a skirmisher monster using weapons with damage dice d6, d8 or d10.
Indeed, the old 4E monsters using the old damage scheme from page 185 of the 4E DMG1, don't appear to be as much of a threat to the players (even without any healing surges). A reverse "always fighting orcs" where the "orcs" are consistently losing to the player characters.
In contrast with the new damage scheme from the 4E DMG1 errata, the "orcs" can actually win sometimes against the players.
Showing posts with label monsters. Show all posts
Showing posts with label monsters. Show all posts
Wednesday, August 25, 2010
Friday, February 26, 2010
Hit points of 4E monsters (part 2).
Let's look at the hit points of low level 4E monsters again.
From a previous post, the hit points of some favorite generic low level monsters are:
Kobold: 24, 27, 36 (level 1-2)
Goblin: 25, 29, 31 (level 1-2)
Let's assume a level 1 player with an at-will power using a weapon which does d8 damage, and the player's primary combat stat has a mod of +4. Hence the damage the player does with each hit is d8+4. The minimum damage per hit is 5 and the maximum damage per hit is 12. The low and upper limits for total damage done by more than one hit is:
1 hit: 5 -> 12
2 hits: 10 -> 24
3 hits: 15 -> 36
4 hits: 20 -> 48
5 hits: 25 -> 60
6 hits: 30 -> 72
The generic kobold or goblin is dead at minimum after 2 or 3 hits, and definitely dead after more than 5 or 6 hits.
To make things more precise, one can examine the probability of the total damage killing a monster after a number of hits. Let's look at the goblin with 29 hit points, using an online dice calculator. The results are:
3 hits: prob(total damage >= 29) = 23.44%
4 hits: prob(total damage >= 29) = 88.01%
5 hits: prob(total damage >= 29) = 99.83%
At a slightly higher level, the hit points of some generic monsters are:
Orc: 46 (level 3)
Hobgoblin: 39, 47 (level 3)
Skeleton: 45 (level 3)
Lycanthrope: 48 (level 3)
Doppelganger: 45 (level 3)
For our player now at level 3 with the same at-will power with a weapon doing d8 damage, the primary combat stat mod is +4 and maybe the weapon is now magic with a +1 bonus to damage. The damage per hit is d8+5. The lower and upper limits for total damage for more than one hit are:
1 hit: 6 -> 13
2 hits: 12 -> 26
3 hits: 18 -> 39
4 hits: 24 -> 52
5 hits: 30 -> 65
6 hits: 36 -> 78
7 hits: 42 -> 91
8 hits: 48 -> 104
It requires a minimum of 3 or 4 hits to kill a generic level 3 or 4 monster, while they're definitely dead after 8 or more hits.
Doing the same exercise using the online dice calculator for a generic orc with 46 hit points, we get:
4 hits: prob(total damage >= 46) = 5.13%
5 hits: prob(total damage >= 46) = 64.77%
6 hits: prob(total damage >= 46) = 98.11%
At a slightly more higher level, the hit points of some generic monsters are:
Beetle: 88 (level 8)
Behemoth: 82 (level 7)
Boar: 85 (level 6)
Troglodyte: 69, 74, 93 (level 6-8)
Zombie: 71, 88 (level 6-8)
Spider: 80 (level 7)
Shadar-Kai: 77, 86 (level 7-8)
Satyr: 80, 86 (level 7-8)
Ogre: 91 (level 8)
Foulspawn: 86, 87 (level 8)
Succubus: 90 (level 9)
For our player now at level 8 with the same at-will power with a weapon doing d8 damage, the primary combat stat mod is +5 (+1 from enough stat increases) and maybe the weapon is now magic with a +2 bonus to damage. The damage per hit is d8+7. The lower and upper limits for total damage for each hit are:
1 hit: 8 -> 15
2 hits: 16 -> 30
3 hits: 24 -> 45
4 hits: 32 -> 60
5 hits: 40 -> 75
6 hits: 48 -> 90
7 hits: 56 -> 105
8 hits: 64 -> 120
9 hits: 72 -> 135
10 hits: 80 -> 150
11 hits: 88 -> 165
12 hits: 96 -> 180
It requires a minimum of 6 or 7 hits to kill a generic level 7 or 8 monster, while they're definitely dead after 12 or more hits.
Doing the same exercise using the online dice calculator for a generic stayr with 80 hit points, we get:
7 hits: prob(total damage >= 80) = 56.41%
8 hits: prob(total damage >= 80) = 97.38%
9 hits: prob(total damage >= 80) = 98.64%
As one can see from these calculations, the number of hits using only at-will powers with d8 damage (with assumptions from magic bonuses and stat increases), goes from 5 hits to kill level 1-2 monsters, to 6 hits to kill level 3-4 monsters, to 8 hits to kill level 7-8 monsters. (The number of hits are from the first greater than 95% probability of total damage killing a monster, from the online dice calculator).
With the players having more daily powers at higher levels, in principle it should reduce the number of hits it takes to kill such higher level monsters. These calculations will be the subject of a future post.
From a previous post, the hit points of some favorite generic low level monsters are:
Kobold: 24, 27, 36 (level 1-2)
Goblin: 25, 29, 31 (level 1-2)
Let's assume a level 1 player with an at-will power using a weapon which does d8 damage, and the player's primary combat stat has a mod of +4. Hence the damage the player does with each hit is d8+4. The minimum damage per hit is 5 and the maximum damage per hit is 12. The low and upper limits for total damage done by more than one hit is:
1 hit: 5 -> 12
2 hits: 10 -> 24
3 hits: 15 -> 36
4 hits: 20 -> 48
5 hits: 25 -> 60
6 hits: 30 -> 72
The generic kobold or goblin is dead at minimum after 2 or 3 hits, and definitely dead after more than 5 or 6 hits.
To make things more precise, one can examine the probability of the total damage killing a monster after a number of hits. Let's look at the goblin with 29 hit points, using an online dice calculator. The results are:
3 hits: prob(total damage >= 29) = 23.44%
4 hits: prob(total damage >= 29) = 88.01%
5 hits: prob(total damage >= 29) = 99.83%
At a slightly higher level, the hit points of some generic monsters are:
Orc: 46 (level 3)
Hobgoblin: 39, 47 (level 3)
Skeleton: 45 (level 3)
Lycanthrope: 48 (level 3)
Doppelganger: 45 (level 3)
For our player now at level 3 with the same at-will power with a weapon doing d8 damage, the primary combat stat mod is +4 and maybe the weapon is now magic with a +1 bonus to damage. The damage per hit is d8+5. The lower and upper limits for total damage for more than one hit are:
1 hit: 6 -> 13
2 hits: 12 -> 26
3 hits: 18 -> 39
4 hits: 24 -> 52
5 hits: 30 -> 65
6 hits: 36 -> 78
7 hits: 42 -> 91
8 hits: 48 -> 104
It requires a minimum of 3 or 4 hits to kill a generic level 3 or 4 monster, while they're definitely dead after 8 or more hits.
Doing the same exercise using the online dice calculator for a generic orc with 46 hit points, we get:
4 hits: prob(total damage >= 46) = 5.13%
5 hits: prob(total damage >= 46) = 64.77%
6 hits: prob(total damage >= 46) = 98.11%
At a slightly more higher level, the hit points of some generic monsters are:
Beetle: 88 (level 8)
Behemoth: 82 (level 7)
Boar: 85 (level 6)
Troglodyte: 69, 74, 93 (level 6-8)
Zombie: 71, 88 (level 6-8)
Spider: 80 (level 7)
Shadar-Kai: 77, 86 (level 7-8)
Satyr: 80, 86 (level 7-8)
Ogre: 91 (level 8)
Foulspawn: 86, 87 (level 8)
Succubus: 90 (level 9)
For our player now at level 8 with the same at-will power with a weapon doing d8 damage, the primary combat stat mod is +5 (+1 from enough stat increases) and maybe the weapon is now magic with a +2 bonus to damage. The damage per hit is d8+7. The lower and upper limits for total damage for each hit are:
1 hit: 8 -> 15
2 hits: 16 -> 30
3 hits: 24 -> 45
4 hits: 32 -> 60
5 hits: 40 -> 75
6 hits: 48 -> 90
7 hits: 56 -> 105
8 hits: 64 -> 120
9 hits: 72 -> 135
10 hits: 80 -> 150
11 hits: 88 -> 165
12 hits: 96 -> 180
It requires a minimum of 6 or 7 hits to kill a generic level 7 or 8 monster, while they're definitely dead after 12 or more hits.
Doing the same exercise using the online dice calculator for a generic stayr with 80 hit points, we get:
7 hits: prob(total damage >= 80) = 56.41%
8 hits: prob(total damage >= 80) = 97.38%
9 hits: prob(total damage >= 80) = 98.64%
As one can see from these calculations, the number of hits using only at-will powers with d8 damage (with assumptions from magic bonuses and stat increases), goes from 5 hits to kill level 1-2 monsters, to 6 hits to kill level 3-4 monsters, to 8 hits to kill level 7-8 monsters. (The number of hits are from the first greater than 95% probability of total damage killing a monster, from the online dice calculator).
With the players having more daily powers at higher levels, in principle it should reduce the number of hits it takes to kill such higher level monsters. These calculations will be the subject of a future post.
Thursday, February 25, 2010
Hit points of generic 4E monsters. (part 1)
Continuing from the previous post, let's examine the monster hit point formula:
N avg (D)
where N is the number of hits it takes to kill a monster, and avg (D) is the average damage done by a player per attack.
In 4E, a player can max out their primary combat stat such that it has a stat adjustment of +4 or +5 to attacks and damage. The damage dice is anywhere from a d4 (ie. dagger) to a d12 (ie. greataxe) or 2d6 (ie. maul, heavy flail). Many weapons and magic attacks typically have damage dice of d6 or d8 for at-will powers.
Let's take an example of a player with a primary stat adjustment of +4 for combat attacks and damage, along with d6 damage dice. For such a level 1 player attacking a monster, the average damage per attack would be avg(d6 + 4) = 7.5.
If we want a monster to die after being hit a number of times, the hit points should be:
- 6 hits -> 6(7.5) = 45 hit points
- 5 hits -> 5(7.5) = 37 hit points
- 4 hits -> 4(7.5) = 30 hit points
- 3 hits -> 3(7.5) = 22 hit points
In the case of where the player's damage dice is d8, the average damage per attack would be avg(d8 + 4) = 8.5.
If we want a monster to die after being hit a number of times, the hit points should be:
- 6 hits -> 6(8.5) = 51 hit points
- 5 hits -> 5(8.5) = 42 hit points
- 4 hits -> 4(8.5) = 34 hit points
- 3 hits -> 3(8.5) = 25 hit points
Looking through the 4E Monster Manual, various low level generic monsters have hit points:
Kobold: 24, 27, 36, 42 (level 1-4)
Goblin: 25, 29, 31 (level 1-2)
Hobgoblin: 39, 47 (level 3)
Orc: 46, 64 (level 3-5)
Halfling: 22, 34 (level 1-2)
Human: 37, 42, 47 (level 2-4)
Wolf: 38, 67 (level 2-5)
Wraith: 37 (level 5)
Skeleton: 45, 53 (level 3-5)
Lizardfolk: 50, 54 (level 4-5)
Lycanthrope: 48 (level 3)
Rat: 36, 38 (level 1-2)
Zombie: 40, 46, 54 (level 3-4)
Elf: 32, 39 (level 2)
Gnoll: 50 (level 5)
Gnome: 34, 46 (level 2-3)
Doppelganger: 45 (level 3)
Drake: 29, 38, 40, 48, 77 (level 1-5)
A number of monsters at level 1 or 2 fit into the range of 3 or 4 hit kills, by players with weapons which do d6+4 or d8+4 damage for their at-will powers.
N avg (D)
where N is the number of hits it takes to kill a monster, and avg (D) is the average damage done by a player per attack.
In 4E, a player can max out their primary combat stat such that it has a stat adjustment of +4 or +5 to attacks and damage. The damage dice is anywhere from a d4 (ie. dagger) to a d12 (ie. greataxe) or 2d6 (ie. maul, heavy flail). Many weapons and magic attacks typically have damage dice of d6 or d8 for at-will powers.
Let's take an example of a player with a primary stat adjustment of +4 for combat attacks and damage, along with d6 damage dice. For such a level 1 player attacking a monster, the average damage per attack would be avg(d6 + 4) = 7.5.
If we want a monster to die after being hit a number of times, the hit points should be:
- 6 hits -> 6(7.5) = 45 hit points
- 5 hits -> 5(7.5) = 37 hit points
- 4 hits -> 4(7.5) = 30 hit points
- 3 hits -> 3(7.5) = 22 hit points
In the case of where the player's damage dice is d8, the average damage per attack would be avg(d8 + 4) = 8.5.
If we want a monster to die after being hit a number of times, the hit points should be:
- 6 hits -> 6(8.5) = 51 hit points
- 5 hits -> 5(8.5) = 42 hit points
- 4 hits -> 4(8.5) = 34 hit points
- 3 hits -> 3(8.5) = 25 hit points
Looking through the 4E Monster Manual, various low level generic monsters have hit points:
Kobold: 24, 27, 36, 42 (level 1-4)
Goblin: 25, 29, 31 (level 1-2)
Hobgoblin: 39, 47 (level 3)
Orc: 46, 64 (level 3-5)
Halfling: 22, 34 (level 1-2)
Human: 37, 42, 47 (level 2-4)
Wolf: 38, 67 (level 2-5)
Wraith: 37 (level 5)
Skeleton: 45, 53 (level 3-5)
Lizardfolk: 50, 54 (level 4-5)
Lycanthrope: 48 (level 3)
Rat: 36, 38 (level 1-2)
Zombie: 40, 46, 54 (level 3-4)
Elf: 32, 39 (level 2)
Gnoll: 50 (level 5)
Gnome: 34, 46 (level 2-3)
Doppelganger: 45 (level 3)
Drake: 29, 38, 40, 48, 77 (level 1-5)
A number of monsters at level 1 or 2 fit into the range of 3 or 4 hit kills, by players with weapons which do d6+4 or d8+4 damage for their at-will powers.
How many hit points should a monster have?
In an older WotC article by David Noonan, it is suggestive that monsters last around 5 rounds. How exactly this is implemented, the article does not state precisely.
Perhaps this "5 rounds" means the number of times it takes to hit a monster, before it is killed by the players?
To investigate this question, we need to recall a few things.
Recall that the average number of attacks it takes to hit a monster N times is N/p, where p is the probability of hitting a monster.
Also recall that the average amount of damage done by one attack is p avg(D), where D is the damage dice (ie. such as 1d6+2) and p is the probability of hitting a monster. (avg(D) is the expectation value of D).
If a monster dies after being hit N times, it will take on average N/p attacks to kill it. So on average the number of hit points it should have, is the average number of attacks multiplied by the average amount of damage done by each attack. Assuming each attack is done by the same player with the same weapon on the same monster, the number of hit points the monster should have is:
(N/p)(p avg(D)) = N avg(D)
Interesting that the number of monster hit points in this scenario, is independent of the probability to hit the monster. N avg(D) is only dependent on the number of hits a monster will take before dying, and the average damage done by the player.
Perhaps this "5 rounds" means the number of times it takes to hit a monster, before it is killed by the players?
To investigate this question, we need to recall a few things.
Recall that the average number of attacks it takes to hit a monster N times is N/p, where p is the probability of hitting a monster.
Also recall that the average amount of damage done by one attack is p avg(D), where D is the damage dice (ie. such as 1d6+2) and p is the probability of hitting a monster. (avg(D) is the expectation value of D).
If a monster dies after being hit N times, it will take on average N/p attacks to kill it. So on average the number of hit points it should have, is the average number of attacks multiplied by the average amount of damage done by each attack. Assuming each attack is done by the same player with the same weapon on the same monster, the number of hit points the monster should have is:
(N/p)(p avg(D)) = N avg(D)
Interesting that the number of monster hit points in this scenario, is independent of the probability to hit the monster. N avg(D) is only dependent on the number of hits a monster will take before dying, and the average damage done by the player.
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