Yakk

2008-06-30, 02:14 PM

This is an attempt to balance 4e encounters via a "damage budget" mechanism.

The theory goes as follows: Given a 6+ round fight in which players use no more than half of their Daily powers, the players will have probably consumed most of their non-at-will damage budget for the fight.

So you can work out, roughly, how much damage a party of 5 characters will do in ~6 rounds. This rate will be slightly higher at the start, and peter out towards the end.

We then work out roughly how long a group of 5 even-level monsters will live under this level of incoming damage, and work out how much damage the party will take, roughly, during those first 6 rounds.

Then, we work out how much longer the fight lasts, factor in at-will powers of the Party, and work out how long the clean-up takes.

This gives us a value: the damage budget of an even-level encounter: how much damage it should do, roughly before being defeated.

Then, we use this to build a solo monster from first principles. :) We can tweak HP and damage output in such a way that we can generate a fight that is about as dangerous to a party as a swarm of even-level minions, normal monsters, or elites.

This doesn't guarantee a fun encounter: but it does mean that we can see if the "solo monsters are not dangerous enough, and are too tough for their danger, for ideal fun".

...

A first-run approximation.

At level 1, each party member deals an average of 9 damage from at-will attacks that hit. Each attack has a 60% chance of hitting per round.

Per-encounter attack powers do an average of 14 damage, with a 65% chance of hitting. 1/4 of the party uses daily powers, which do an average of 19 damage, and hit 70% of the time. (Players are smart, and only use encounter/dailies when they are more likely to hit).

So, over 5 rounds, using half a Daily and an encounter power, each character dishes out (.7 * 19 + 3* 9*.6)/4 + (14*.65) + (9*.6)*3 damage, or about 37.7 damage. After that, they deal about 5.5 damage per round.

5 characters = 188.5 damage over 5 rounds, or ~37.7 damage per round.

Monsters, meanwhile, hit about 50% of the time. At level 1, they deal about 8 damage per hit, or 4 damage per round per monster. Each has a single per-encounter attack that does about 14 damage, hitting 60% of the time.

They have about 30 HP each. So ~1 monster dies per round. I'll assume 1 monster dies before it uses it's per encounter.

The party takes 4*(5+4+3+2+1 - 4) + 14*.6*4 = ~77.6 damage.

Now, let's build a solo monster from this.

We want it to last about 6 rounds. It should do about 80 damage to the party.

Let's assume it has 3 rounds of doing "double damage" via encounter powers. It also does +50% damage once bloodied.

If it has +4 defenses (this is to prevent stun-lock cheese -- misses rarely stun), and half of the players use a daily attack power, player damage output over 6 rounds becomes:

(.5 * 19 + 9*.4)/2 + (14*.45) + (9*.4)*4 = 27.25

or a total of 136.25 HP at level 1.

Supposing it is normal for 3 rounds, and bloodied for 3 rounds. It burns two damage-double encounter powers while normal, and one while bloodied.

If it has a 50% chance of hitting with it's powers, and one action point to burn at full and at bloodied, it ends up with:

(.5*X*2) + (.5*2X) + (.5*1.5*X*3) + (.5*2*X) = 5.25 X total damage.

It's damage budget is 80, giving us X = 15 damage.

So, a level 1 solo monster created based off of this (6 round expected lifespan):

Gibbering Ghost [Medium sized Solo Skirmisher, level 1, 400 XP]

136 HP.

1 Action Point, +5 Saves

Speed: 6 Alignment: Evil

Vunerable: 5 Radiant Resist: 5 Necrotic

18 AC 16 Fort 15 Reflex 18 Will

Str: 12 Con: 14 Dex: 12 Int: 8 Wis: 16 Cha: 18

Attacks:

Blade of Insanity (Basic Melee Attack, At-will): +4 vs Will, 1d8+4 Psychic Damage. Slide the target 1 square, then the target makes a basic attack against any target of the Gibbering Ghosts choice. (This basic attack does not provoke any opportunity attacks)

Mind Shards: (Basic Ranged Attack, At-will, Ranged 10) +4 vs Reflex. 1d6+1 Psychic Damage, and target takes an ongoing 6 Psychic Damage (save ends). Miss: Target is prone.

Illusions of Madness: (Burst 5, Recharge 4/5/6, Minor action) Exchange the places, via teleport, of any creatures in the Burst 5. New locations must be legal positions. This includes the Gibbering Ghost itself.

Winds of Hell: (Encounter, only after the Ghost takes damage, recharged when bloodied) Burst 1, +4 vs Fortitude, 1d10+4 Psychic Damage, target is dazed until the start of the Ghosts next turn.

Cage of Souls: (Move, Encounter, Only right after the Ghost has damaged a target within 1 square, recharge when bloodied). Ghost Teleports into the location of the target it hit. Target creature is pinned but cannot be directly attacked, and all damage to the Ghost is half-dealt to the Target. The target may attempt to break free: Charisma vs Will, hit and the creature escapes the Cage of Souls, miss and both Ghost and Victim take 1d10 psychic damage (this damage is not split). After the Ghost takes 15 damage, the Cage fails, and the Ghost teleports 3 squares.

Shadow Walk: (Move, at-will) Teleport 3 squares.

...

Damage done to party (about the same in bloodied and unbloodied phases)

Pre-bloodied: ~14 basic attack (ranged or melee) @ 50% chance

Scream of Hell: 9.5 burst 1 (2.5 targets) @ 40% chance

Cage of Souls: ~15 damage (pretty much guaranteed)

[14*.5*2.5 + 9.5*2.5*.4 + 15 = 39.5]*2 = 84 damage.

Right on the damage budget.

So the question is, what happens if you try this quick-attempt at a level 1 solo party? How does it compare to a fight against (say) 5 normal level 1 creatures, in actual play? How far off are my damage approximations for PCs/Monsters?

How hard would it be to reduce this to a formula, both on the player-damage-dealing side, and the monster-damage-dealing side?

The theory goes as follows: Given a 6+ round fight in which players use no more than half of their Daily powers, the players will have probably consumed most of their non-at-will damage budget for the fight.

So you can work out, roughly, how much damage a party of 5 characters will do in ~6 rounds. This rate will be slightly higher at the start, and peter out towards the end.

We then work out roughly how long a group of 5 even-level monsters will live under this level of incoming damage, and work out how much damage the party will take, roughly, during those first 6 rounds.

Then, we work out how much longer the fight lasts, factor in at-will powers of the Party, and work out how long the clean-up takes.

This gives us a value: the damage budget of an even-level encounter: how much damage it should do, roughly before being defeated.

Then, we use this to build a solo monster from first principles. :) We can tweak HP and damage output in such a way that we can generate a fight that is about as dangerous to a party as a swarm of even-level minions, normal monsters, or elites.

This doesn't guarantee a fun encounter: but it does mean that we can see if the "solo monsters are not dangerous enough, and are too tough for their danger, for ideal fun".

...

A first-run approximation.

At level 1, each party member deals an average of 9 damage from at-will attacks that hit. Each attack has a 60% chance of hitting per round.

Per-encounter attack powers do an average of 14 damage, with a 65% chance of hitting. 1/4 of the party uses daily powers, which do an average of 19 damage, and hit 70% of the time. (Players are smart, and only use encounter/dailies when they are more likely to hit).

So, over 5 rounds, using half a Daily and an encounter power, each character dishes out (.7 * 19 + 3* 9*.6)/4 + (14*.65) + (9*.6)*3 damage, or about 37.7 damage. After that, they deal about 5.5 damage per round.

5 characters = 188.5 damage over 5 rounds, or ~37.7 damage per round.

Monsters, meanwhile, hit about 50% of the time. At level 1, they deal about 8 damage per hit, or 4 damage per round per monster. Each has a single per-encounter attack that does about 14 damage, hitting 60% of the time.

They have about 30 HP each. So ~1 monster dies per round. I'll assume 1 monster dies before it uses it's per encounter.

The party takes 4*(5+4+3+2+1 - 4) + 14*.6*4 = ~77.6 damage.

Now, let's build a solo monster from this.

We want it to last about 6 rounds. It should do about 80 damage to the party.

Let's assume it has 3 rounds of doing "double damage" via encounter powers. It also does +50% damage once bloodied.

If it has +4 defenses (this is to prevent stun-lock cheese -- misses rarely stun), and half of the players use a daily attack power, player damage output over 6 rounds becomes:

(.5 * 19 + 9*.4)/2 + (14*.45) + (9*.4)*4 = 27.25

or a total of 136.25 HP at level 1.

Supposing it is normal for 3 rounds, and bloodied for 3 rounds. It burns two damage-double encounter powers while normal, and one while bloodied.

If it has a 50% chance of hitting with it's powers, and one action point to burn at full and at bloodied, it ends up with:

(.5*X*2) + (.5*2X) + (.5*1.5*X*3) + (.5*2*X) = 5.25 X total damage.

It's damage budget is 80, giving us X = 15 damage.

So, a level 1 solo monster created based off of this (6 round expected lifespan):

Gibbering Ghost [Medium sized Solo Skirmisher, level 1, 400 XP]

136 HP.

1 Action Point, +5 Saves

Speed: 6 Alignment: Evil

Vunerable: 5 Radiant Resist: 5 Necrotic

18 AC 16 Fort 15 Reflex 18 Will

Str: 12 Con: 14 Dex: 12 Int: 8 Wis: 16 Cha: 18

Attacks:

Blade of Insanity (Basic Melee Attack, At-will): +4 vs Will, 1d8+4 Psychic Damage. Slide the target 1 square, then the target makes a basic attack against any target of the Gibbering Ghosts choice. (This basic attack does not provoke any opportunity attacks)

Mind Shards: (Basic Ranged Attack, At-will, Ranged 10) +4 vs Reflex. 1d6+1 Psychic Damage, and target takes an ongoing 6 Psychic Damage (save ends). Miss: Target is prone.

Illusions of Madness: (Burst 5, Recharge 4/5/6, Minor action) Exchange the places, via teleport, of any creatures in the Burst 5. New locations must be legal positions. This includes the Gibbering Ghost itself.

Winds of Hell: (Encounter, only after the Ghost takes damage, recharged when bloodied) Burst 1, +4 vs Fortitude, 1d10+4 Psychic Damage, target is dazed until the start of the Ghosts next turn.

Cage of Souls: (Move, Encounter, Only right after the Ghost has damaged a target within 1 square, recharge when bloodied). Ghost Teleports into the location of the target it hit. Target creature is pinned but cannot be directly attacked, and all damage to the Ghost is half-dealt to the Target. The target may attempt to break free: Charisma vs Will, hit and the creature escapes the Cage of Souls, miss and both Ghost and Victim take 1d10 psychic damage (this damage is not split). After the Ghost takes 15 damage, the Cage fails, and the Ghost teleports 3 squares.

Shadow Walk: (Move, at-will) Teleport 3 squares.

...

Damage done to party (about the same in bloodied and unbloodied phases)

Pre-bloodied: ~14 basic attack (ranged or melee) @ 50% chance

Scream of Hell: 9.5 burst 1 (2.5 targets) @ 40% chance

Cage of Souls: ~15 damage (pretty much guaranteed)

[14*.5*2.5 + 9.5*2.5*.4 + 15 = 39.5]*2 = 84 damage.

Right on the damage budget.

So the question is, what happens if you try this quick-attempt at a level 1 solo party? How does it compare to a fight against (say) 5 normal level 1 creatures, in actual play? How far off are my damage approximations for PCs/Monsters?

How hard would it be to reduce this to a formula, both on the player-damage-dealing side, and the monster-damage-dealing side?