Yakk
2019-06-06, 12:17 PM
This is me playing with 4e math, partly inspired by some analysis of 5e math.
Can we make the 4e power curve "flat" with strategic changes?
The idea is to remove the +1 per level scaling of the game.
At the same time, I like attribute scaling, so I'm keeping that; we just don't apply attributes to d20 rolls for the most part. And damage scales as usual in 4e.
A pass at the rules changes needed:
(A) All attack rolls are d20+4 +Proficiency vs Defence. You can add a max of +1 enhancement and +1 feat bonus to this. Attributes never add to attack rolls.
(B) Magic armor grants a +1 to your AC, never more. Enhancement bonus grants resist all. Standard MW armor is replaced with Superior armor (which no longer requires a feat); superior armor is worth x2 normal armor (after enchantment).
(C) Light armor is worth +1 AC compared to baseline. When in light or no armor, you may dodge a number of times equal to the greater of your dexterity or intelligence bonus between short rests (if you have a feature that lets you add other-stat to light armor AC, it can be used as your dodge counter). A dodge gives you +4 AC, and can be done in response to being hit and knowing if the dodge will make the attack miss.
When you take your second wind, your dodge usages also reset.
(D) Non-AC defences are equal to the lower of the two stats in question, or 10+ the bonus of the higher, whichever is better. Enhancement bonuses are limited to +1, and feat bonuses to +2. (So a level 20 character can have two NADs that are 20, or one that is 30; I'm ok with that.)
(E) You don't add half your level to your skill checks, Attacks, AC, initiative or NADs (or anything really).
(F) Item bonuses to skill rolls are capped at +2, and to defences are capped at +1. Power bonuses to skill rolls, attacks, and defences are halved (round up).
(G) Being trained in a skill gives you a +10 modifier, but halves your stat bonus (round down).
Stat Untrained Trained
8 -1 +9
10 +0 +10
12 +1 +10
14 +2 +11
16 +3 +11
18 +4 +12
20 +5 +12
22 +6 +13
24 +7 +13
26 +8 +14
28 +9 +14
30 +10 +15
That should permit a slightly saner skill challenge system.
---
In this system, power scales linearly roughly with Level+3 (aka, your HP).
So your "power" doubles at these levels:
1 -> 5
6 -> 15
16 -> 35
We'll rename the tiers:
Heroic: 1-5
Paragon: 6-15
Epic: 16-35 (well 30)
Monsterous: 36-75
Godlike: 76+
Using the formula (Level+3)*5, average player HP is then:
Heroic: 30 (20-40)
Paragon: 67.5 (45-90)
Epic: 142 (95-190 (well, 130 avg 165 with cap of 30))
Monsterous: 277.5 (195-390)
Godlike: 577.5 (395-790)
In a 4e like model, monsters have 1.5x the HP of PCs and lack healing and have lower damage output. A typical blow might deal 1/4 of a PC's HP; about a healing surge's worth.
T0: 15 HP, 4 damage
T1: 45 HP, 8 damage
T2: 100 HP, 16 damage
T3: 200 HP, 32 damage
T4: 400 HP, 64 damage
T5: 800 HP, 128 damage
Now, a T3 monster vs a T1 PC runs into the "problem" that the T3 monster one-shots the T1 player character.
One approach for this is to rotate those higher level monster difficulties from damage to HP.
T0: 15 HP, 5 damage
T1: 45 HP, 8 damage (30 HP players)
T2: 125 HP, 13 damage (70 HP players)
T3: 300 HP, 21 damage (130 HP players)
T4: 700 HP, 32 damage
T5: 1500 HP, 52 damage
I don't like this because it causes higher level combat to take longer; and if we boost higher level PC damage to compensate, we end up with monsters that don't threaten. If we scale back monster HP and damage back up a tad:
T0: 15 HP, 5 damage
T1: 45 HP, 8 damage (30 HP players)
T2: 100 HP, 14 damage (70 HP players)
T3: 200 HP, 23 damage (130 HP players)
T4: 400 HP, 40 damage
T5: 800 HP, 70 damage
now higher level monsters *aren't as threatening* as lower level monsters are against similar level PCs; each tier, instead of x2 damage they do x1.7. This, however, can be handled in the encounter building guidelines. We boost the expected number of monsters by ~25% per tier, in addition to the doubling inherit to the tier change.
Encounter budgets:
Monsters
Encounter T0 T1 T2 T3 T4 T5
T0.0 4
T0.0 2
T0.0 1
T1.0
T1.0 8
T1.0 4
T1.0 2
T1.0 1
T2.0 20
T2.0 10
T2.0 5
T2.0 1 2
T2.0 1 1
T3.0 24
T3.0 12
T3.0 6
T3.0 3
T3.0 1 1
for parties of 4. Encounters can vary from 1/2 the above to 2x and be "in tier"; note that the hardest T1 encounter is easier than the standard T2 encounter. A party just reaching T2 will find "standard" encounters reasonably hard.
Substituting 1 monster for 2 of a lower tier, or 2 lower tier monsters for 1 of a higher tier, is the same budget. The "max number of monsters of a tier" table is used above. T0 is included, as an encounter below T0 probably shouldn't be used.
So apply this pseudo-MM3 on a business card to 4e monsters. I'd have to come up with limited/standard damage expressions rules; the above might be for limited, with standard being 4/5 of that.
In this flat system, Elites/Solos are just higher tier monsters. So a heroic tier foe that is an elite is a T2 monster, a heroic tier solo is modeled as a T3 monster.
To convert a monster, look at its tier (not its level). Convert level 1-10 standard monsters to T1, 11-20 to T2, 21-30 to T3, 31+ to T4.
Minions are modeled as 1 or 2 tier lower creatures. I think they'll be moderately tougher in this system (they have HP; no 1 HP and no damage on a miss here).
Use collective Mook HP rules for minions to keep tracking simple; add up their HP. They have a damage cap (per hit) of their nominal HP. Every nominal HP that dies a Mook drops.
So: If they are elite, add another tier. If they are solo, add 2 tiers. If they are minions, subtract 1 or 2 tiers (min T0 however).
So 8 epic minions can be modeled as 8 T1 mooks. They have a collective HP pool of 400 (50 per mook) and deal 10 damage per hit.
The math seems to work, next I need to do some simulation to see if it is junk before doing playtesting.
---
Monster Business card stats:
AC: 14+Tier
NAD: 12+Tier
ATK: 5+Tier
ROLE HP
Mook Pooled
Skirmish Standard
Controller Standard
Soldier Standard, +2 AC
Brute *4/3, -3 AC
Artillery *3/4, -2 AC
Lurker *3/4
Business card tables:
AC: 14+Tier
NAD: 12+Tier
ATK: 5+Tier, +2 vs AC
ROLE HP
Mook Pooled
Skirmish Medium
Controller Medium
Soldier Medium, +2 AC
Brute High, -3 AC
Artillery Low, -2 AC
Lurker Low
/---- HP ----\ /--------------- Damage -----------------\
Low Med High AOE Standard Limited Mook
T0 15 20 25 1d6 1d6+2 1d8+2 5
T1 35 50 65 1d8+2 1d8+4 3d6 10
T2 75 100 130 3d6 2d8+5 3d10 15
T3 150 200 260 3d10 3d12+4 1d4x10 +5 25 *
T4 300 400 530 1d4x10 +5 1d4x10+15 2d4x10 40 *
T5 600 800 1100 2d4x10 1d10x10+15 2d6x10+20 70 *
T6 1200 1600 2200 2d6*10+20 3d6x10+10 2d12x10+10 115 *
I tweaked T1 and T0 HP to make minion math easier. Notice Limited T1 is AOE T2; 4/3 * 5/4 is about the damage ratio between tiers.
Mook is average standard damage; Mooks should be as scary as a same-tier monsters, as we have replaced the minion mechanics with the ability to include lower-tier monsters. Mook mechanics are supposed to ease *DM bookkeeping*, not make the monsters fundamentally *easier*.
The "*" is saying "you probably shouldn't use mook rules for T3 monsters". OTOH you could; imagine a battle with 30 T3s on each side as "fluff" around the PCs fighting a T5 or T6(!) boss. You mass roll d20s, every 8 hits drops a T3 "mook" on the other side.
T6 monsters are intended for the "A god that is a level 35 solo" bit. They are beefy. A critical on a normal attack can almost drop a full-HP level 30 defender to 0 HP (190 damage), or kill them if they are even a bit past bloodied.
---
As the table is a bit awkward, we can use an XP based balancing system.
T0 monsters are worth 2 XP.
T1 monsters are worth 4 XP.
T2 monsters are worth 8 XP
T3 monsters are worth 16 XP.
T4 monsters are worth 32 XP
T5 monsters are worth 64 XP.
T6 monsters are worth 128 XP.
A T1 hero has a budget of 4 XP (x1/2 to x2)
A T2 hero has a budget of 10 XP (x1/2 to x2)
A T3 hero has a budget of 25 XP (x1/2 to x2)
Let us try this out:
An encounter with a Kobold Elite (T2 Brute), 2 Guards (T1 Soldiers) and 6 Grunts (T0 mooks).
Kobold Elite Brute (T2): 8 XP
AC 14+2-3 = 13.
ATK: 5+2 = 7 (9 vs AC)
NAD: 12+2 = 15 Fort, 15 Reflex, 12 Will
HP: 130
Damage: 2d8+5, 3d10 on limited use
2 Kobold Soldier (T1 soldier): 4 XP x2 = 8 XP
AC: 14+1+2 = 17
ATK: 5+1 = 6 (8 vs AC)
NAD: 12+1 = 13 Fort, 15 Reflex, 11 Will
HP: 50
Damage: 1d8+4, 3d6 on limited use.
6 Kobold Grunts (T0 mooks): 2 XP x6 = 12 XP
AC: 14
ATK: 5 (7 vs AC)
NAD: 12 = 10 Fort, 15 Reflex, 11 Will
HP: 120 HP pooled (20 per Mook)
Damage: 5
Total : 28 XP.
A party of 4 T1 PCs has a budget of 16 XP (8-32).
A party of 4 T2 PCs has a budget of 40 XP (20-80).
A party of 4 T3 PCs has a budget of 100 XP (50-200).
So on the harder end for a T1 encounter, on the easier end for a T2 encounter.
For advancement, we can use the 10 typical encounters rule.
A T1 hero ~ 40 XP / level (1-5, avg level 3)
A T2 hero ~ 100 XP / level (6-15, avg level 10.5)
A T3 hero ~ 250 XP / level (16-30, avg level 23)
How about "It requires level*10 XP to gain up to a level. When you reach the next level, pay the cost to gain the level out of your XP pool."
So:
Level 1 to 2: 20 XP
Level 2 to 3: 30 XP
Level 3 to 4: 40 XP
Level 4 to 5: 50 XP
Level 5 to 6: 60 XP
Average heroic: 40 XP/level (10.0 encounters of average difficulty)
Paragon: 6-16 is 1150 XP, average of 115/level (11.5 encounters of average difficulty)
Epic: 16-30, ~3290 XP, average of 235/level (9.4 encounters of average difficulty)
Epic seems a bit low; part of this is that you never hit the mathematical end of epic (level 35). In Heroic and Paragon, at the end of the tier you'll be able to blast through harder in-tier encounters. The math says you'll not reach that in epic (of course, the math can lie; as everyone who has played 4e knows, optimization can make epic characters silly; at the same time, I suspect that converting L 30 solos to T5s in this system will give them a power bump; and you can always use T6s.)
Can we make the 4e power curve "flat" with strategic changes?
The idea is to remove the +1 per level scaling of the game.
At the same time, I like attribute scaling, so I'm keeping that; we just don't apply attributes to d20 rolls for the most part. And damage scales as usual in 4e.
A pass at the rules changes needed:
(A) All attack rolls are d20+4 +Proficiency vs Defence. You can add a max of +1 enhancement and +1 feat bonus to this. Attributes never add to attack rolls.
(B) Magic armor grants a +1 to your AC, never more. Enhancement bonus grants resist all. Standard MW armor is replaced with Superior armor (which no longer requires a feat); superior armor is worth x2 normal armor (after enchantment).
(C) Light armor is worth +1 AC compared to baseline. When in light or no armor, you may dodge a number of times equal to the greater of your dexterity or intelligence bonus between short rests (if you have a feature that lets you add other-stat to light armor AC, it can be used as your dodge counter). A dodge gives you +4 AC, and can be done in response to being hit and knowing if the dodge will make the attack miss.
When you take your second wind, your dodge usages also reset.
(D) Non-AC defences are equal to the lower of the two stats in question, or 10+ the bonus of the higher, whichever is better. Enhancement bonuses are limited to +1, and feat bonuses to +2. (So a level 20 character can have two NADs that are 20, or one that is 30; I'm ok with that.)
(E) You don't add half your level to your skill checks, Attacks, AC, initiative or NADs (or anything really).
(F) Item bonuses to skill rolls are capped at +2, and to defences are capped at +1. Power bonuses to skill rolls, attacks, and defences are halved (round up).
(G) Being trained in a skill gives you a +10 modifier, but halves your stat bonus (round down).
Stat Untrained Trained
8 -1 +9
10 +0 +10
12 +1 +10
14 +2 +11
16 +3 +11
18 +4 +12
20 +5 +12
22 +6 +13
24 +7 +13
26 +8 +14
28 +9 +14
30 +10 +15
That should permit a slightly saner skill challenge system.
---
In this system, power scales linearly roughly with Level+3 (aka, your HP).
So your "power" doubles at these levels:
1 -> 5
6 -> 15
16 -> 35
We'll rename the tiers:
Heroic: 1-5
Paragon: 6-15
Epic: 16-35 (well 30)
Monsterous: 36-75
Godlike: 76+
Using the formula (Level+3)*5, average player HP is then:
Heroic: 30 (20-40)
Paragon: 67.5 (45-90)
Epic: 142 (95-190 (well, 130 avg 165 with cap of 30))
Monsterous: 277.5 (195-390)
Godlike: 577.5 (395-790)
In a 4e like model, monsters have 1.5x the HP of PCs and lack healing and have lower damage output. A typical blow might deal 1/4 of a PC's HP; about a healing surge's worth.
T0: 15 HP, 4 damage
T1: 45 HP, 8 damage
T2: 100 HP, 16 damage
T3: 200 HP, 32 damage
T4: 400 HP, 64 damage
T5: 800 HP, 128 damage
Now, a T3 monster vs a T1 PC runs into the "problem" that the T3 monster one-shots the T1 player character.
One approach for this is to rotate those higher level monster difficulties from damage to HP.
T0: 15 HP, 5 damage
T1: 45 HP, 8 damage (30 HP players)
T2: 125 HP, 13 damage (70 HP players)
T3: 300 HP, 21 damage (130 HP players)
T4: 700 HP, 32 damage
T5: 1500 HP, 52 damage
I don't like this because it causes higher level combat to take longer; and if we boost higher level PC damage to compensate, we end up with monsters that don't threaten. If we scale back monster HP and damage back up a tad:
T0: 15 HP, 5 damage
T1: 45 HP, 8 damage (30 HP players)
T2: 100 HP, 14 damage (70 HP players)
T3: 200 HP, 23 damage (130 HP players)
T4: 400 HP, 40 damage
T5: 800 HP, 70 damage
now higher level monsters *aren't as threatening* as lower level monsters are against similar level PCs; each tier, instead of x2 damage they do x1.7. This, however, can be handled in the encounter building guidelines. We boost the expected number of monsters by ~25% per tier, in addition to the doubling inherit to the tier change.
Encounter budgets:
Monsters
Encounter T0 T1 T2 T3 T4 T5
T0.0 4
T0.0 2
T0.0 1
T1.0
T1.0 8
T1.0 4
T1.0 2
T1.0 1
T2.0 20
T2.0 10
T2.0 5
T2.0 1 2
T2.0 1 1
T3.0 24
T3.0 12
T3.0 6
T3.0 3
T3.0 1 1
for parties of 4. Encounters can vary from 1/2 the above to 2x and be "in tier"; note that the hardest T1 encounter is easier than the standard T2 encounter. A party just reaching T2 will find "standard" encounters reasonably hard.
Substituting 1 monster for 2 of a lower tier, or 2 lower tier monsters for 1 of a higher tier, is the same budget. The "max number of monsters of a tier" table is used above. T0 is included, as an encounter below T0 probably shouldn't be used.
So apply this pseudo-MM3 on a business card to 4e monsters. I'd have to come up with limited/standard damage expressions rules; the above might be for limited, with standard being 4/5 of that.
In this flat system, Elites/Solos are just higher tier monsters. So a heroic tier foe that is an elite is a T2 monster, a heroic tier solo is modeled as a T3 monster.
To convert a monster, look at its tier (not its level). Convert level 1-10 standard monsters to T1, 11-20 to T2, 21-30 to T3, 31+ to T4.
Minions are modeled as 1 or 2 tier lower creatures. I think they'll be moderately tougher in this system (they have HP; no 1 HP and no damage on a miss here).
Use collective Mook HP rules for minions to keep tracking simple; add up their HP. They have a damage cap (per hit) of their nominal HP. Every nominal HP that dies a Mook drops.
So: If they are elite, add another tier. If they are solo, add 2 tiers. If they are minions, subtract 1 or 2 tiers (min T0 however).
So 8 epic minions can be modeled as 8 T1 mooks. They have a collective HP pool of 400 (50 per mook) and deal 10 damage per hit.
The math seems to work, next I need to do some simulation to see if it is junk before doing playtesting.
---
Monster Business card stats:
AC: 14+Tier
NAD: 12+Tier
ATK: 5+Tier
ROLE HP
Mook Pooled
Skirmish Standard
Controller Standard
Soldier Standard, +2 AC
Brute *4/3, -3 AC
Artillery *3/4, -2 AC
Lurker *3/4
Business card tables:
AC: 14+Tier
NAD: 12+Tier
ATK: 5+Tier, +2 vs AC
ROLE HP
Mook Pooled
Skirmish Medium
Controller Medium
Soldier Medium, +2 AC
Brute High, -3 AC
Artillery Low, -2 AC
Lurker Low
/---- HP ----\ /--------------- Damage -----------------\
Low Med High AOE Standard Limited Mook
T0 15 20 25 1d6 1d6+2 1d8+2 5
T1 35 50 65 1d8+2 1d8+4 3d6 10
T2 75 100 130 3d6 2d8+5 3d10 15
T3 150 200 260 3d10 3d12+4 1d4x10 +5 25 *
T4 300 400 530 1d4x10 +5 1d4x10+15 2d4x10 40 *
T5 600 800 1100 2d4x10 1d10x10+15 2d6x10+20 70 *
T6 1200 1600 2200 2d6*10+20 3d6x10+10 2d12x10+10 115 *
I tweaked T1 and T0 HP to make minion math easier. Notice Limited T1 is AOE T2; 4/3 * 5/4 is about the damage ratio between tiers.
Mook is average standard damage; Mooks should be as scary as a same-tier monsters, as we have replaced the minion mechanics with the ability to include lower-tier monsters. Mook mechanics are supposed to ease *DM bookkeeping*, not make the monsters fundamentally *easier*.
The "*" is saying "you probably shouldn't use mook rules for T3 monsters". OTOH you could; imagine a battle with 30 T3s on each side as "fluff" around the PCs fighting a T5 or T6(!) boss. You mass roll d20s, every 8 hits drops a T3 "mook" on the other side.
T6 monsters are intended for the "A god that is a level 35 solo" bit. They are beefy. A critical on a normal attack can almost drop a full-HP level 30 defender to 0 HP (190 damage), or kill them if they are even a bit past bloodied.
---
As the table is a bit awkward, we can use an XP based balancing system.
T0 monsters are worth 2 XP.
T1 monsters are worth 4 XP.
T2 monsters are worth 8 XP
T3 monsters are worth 16 XP.
T4 monsters are worth 32 XP
T5 monsters are worth 64 XP.
T6 monsters are worth 128 XP.
A T1 hero has a budget of 4 XP (x1/2 to x2)
A T2 hero has a budget of 10 XP (x1/2 to x2)
A T3 hero has a budget of 25 XP (x1/2 to x2)
Let us try this out:
An encounter with a Kobold Elite (T2 Brute), 2 Guards (T1 Soldiers) and 6 Grunts (T0 mooks).
Kobold Elite Brute (T2): 8 XP
AC 14+2-3 = 13.
ATK: 5+2 = 7 (9 vs AC)
NAD: 12+2 = 15 Fort, 15 Reflex, 12 Will
HP: 130
Damage: 2d8+5, 3d10 on limited use
2 Kobold Soldier (T1 soldier): 4 XP x2 = 8 XP
AC: 14+1+2 = 17
ATK: 5+1 = 6 (8 vs AC)
NAD: 12+1 = 13 Fort, 15 Reflex, 11 Will
HP: 50
Damage: 1d8+4, 3d6 on limited use.
6 Kobold Grunts (T0 mooks): 2 XP x6 = 12 XP
AC: 14
ATK: 5 (7 vs AC)
NAD: 12 = 10 Fort, 15 Reflex, 11 Will
HP: 120 HP pooled (20 per Mook)
Damage: 5
Total : 28 XP.
A party of 4 T1 PCs has a budget of 16 XP (8-32).
A party of 4 T2 PCs has a budget of 40 XP (20-80).
A party of 4 T3 PCs has a budget of 100 XP (50-200).
So on the harder end for a T1 encounter, on the easier end for a T2 encounter.
For advancement, we can use the 10 typical encounters rule.
A T1 hero ~ 40 XP / level (1-5, avg level 3)
A T2 hero ~ 100 XP / level (6-15, avg level 10.5)
A T3 hero ~ 250 XP / level (16-30, avg level 23)
How about "It requires level*10 XP to gain up to a level. When you reach the next level, pay the cost to gain the level out of your XP pool."
So:
Level 1 to 2: 20 XP
Level 2 to 3: 30 XP
Level 3 to 4: 40 XP
Level 4 to 5: 50 XP
Level 5 to 6: 60 XP
Average heroic: 40 XP/level (10.0 encounters of average difficulty)
Paragon: 6-16 is 1150 XP, average of 115/level (11.5 encounters of average difficulty)
Epic: 16-30, ~3290 XP, average of 235/level (9.4 encounters of average difficulty)
Epic seems a bit low; part of this is that you never hit the mathematical end of epic (level 35). In Heroic and Paragon, at the end of the tier you'll be able to blast through harder in-tier encounters. The math says you'll not reach that in epic (of course, the math can lie; as everyone who has played 4e knows, optimization can make epic characters silly; at the same time, I suspect that converting L 30 solos to T5s in this system will give them a power bump; and you can always use T6s.)