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Yakk
2008-06-17, 03:55 PM
[4e] Do you eat the Elites and Solos Last?

Warning: this is a reasonably long essay, and full of mathematics.

Suppose you have a fight with 6 normal monsters.

You are smart, so you kill them one at a time. For the sake of simplicity, let's assume each takes about the same amount of time to kill.

You end up taking (6+5+4+3+2+1) = 21 times the damage you would take if you where fighting and killing a single monster, plus or minus situational modifiers.

Now, imagine you are fighting 3 elites. You'd think that this should do about the same amount of damage as killing 6 normal monsters.

While killing 3 elites, you will take about (3+2+1)=6 times the damage you'd take while killing a single elite.

Now, in 4e, 3 elites should be about the same challenge as 6 normal monsters. In this case, we'll talk about the damage you take...

So we want (damage while killing a single elite)*6 = (damage while killing a single normal monster)*21.

Or (damage while killing a single elite) =~ 3.5*(damage while killing a single normal monster)

At this stage, we are going to approximate things. So we'll assume that killing an Elite takes twice as long as a normal monster. Then, each Elite should do about 1.75 times as much damage as a similar normal monster, per round of combat.

...

Except this result in some interesting problems. First, Elites have both twice the HP, and higher defenses, than normal monsters. Which slows down the rate you kill Elites, which means they need to deal less damage than I said above.

Second, it means the (incoming damage reduced) per (HP damaging power thrown at the bad guys) ratio is worse on Elites compared to Normal monsters.

Ie, if you have 1 Elite and 4 Normal Monsters, you will reduce the incoming damage you are taking fastest by killing the Normal Monsters first. This isn't just a special case -- it is a general rule.

What is worse is that the DMG (and the MM contains the implementation of) recommends that you make Elite monsters do extra damage when bloodied. This _discourages_ you even more from damaging the Elite!

So now we have the PCs highly encouraged to kill the Elite first, possibly just spending a bit of effort to prevent the Elite from causing as much damage (more on that later).

...

Solo monsters have the same kind of effect, but even larger.

5 normal monsters deal ~15 times the damage you'd take from killing a single normal monster.

This means that a Solo monster should deal about 3 times the damage of a Normal monster per round, if it takes 5 times as long to kill them.

As noted by some, this means that the "start of the battle" incoming-damage spike isn't there when you fight Solo monsters nearly as much. The fight feels more .. flat, and less stressful, as the "start of the battle" overwealming assault by bad guys is one of the harder parts of 4e combat.

In a standard multi-monster encounter, there is an initial wave of incoming damage that the party has to weather, killing off sources of incoming damage, in order to make it to the back end of the encounter. During the back-end, there are fewer monsters left, but the Party has mostly used up their per-encounter powers and has taken damage, so some threat still remains.

With a solo, damage is more consistent. There might be a spike at the start (from per-encounter powers being used), a spike at bloodied (bloodied specials kick in), and some stun locking...

...

Minions end up working the same way, with them being a better target to kill generally than burning 4 hits killing a normal critter.

...

Which brings us to stun locking. Elites and Solos tend to have slightly higher defenses than normal creatures, and instead of saving 55% of the time, they save 65% or 80% of the time.

They have +2ish/+4ish defenses -- which means instead of debuffs landing 50% of the time, they land 40% or 30% of the time.

An "until the next round" debuff is thus 25% harder to land on an Elite and 67% harder on a Solo: but you are soaking up about 75%/200% more damage by doing it.

An "until save ends" debuff lasts 1.81 rounds on a normal, 1.54 on an Elite, and 1.25 rounds on a Solo. 15% shorter on an Elite, 31% shorter on a Solo. Still, compared to the damage they do, well worth it.

...

The goal of the fight is typically to reduce all enemy HP before you run out of your HP. :)

"Stun lock" abilities are thus best applied first to Elites, second to Solos. That reduces the incoming damage by the most per "stun lock" ability used.

All things being equal, it is best first to burn damage actions killing Minions, then Normals, then Elites, then Solos, as in terms of "attacks per incoming HP damage reduced", the order is quite strong.

...

There are a bunch of simple abstractions in the above, that a real fight would contain changes to. But the effects I outlined are real (and people have reported them from actual play).

I'm curious -- are there transformations that would change this?

Finding out the solution to that question requires math. Lots of math. Be warned!

Letting Players choose: killing an elite first shouldn't be suicide

First, Solos are intended to be "a fight all by themselves". So it seems acceptable that they don't "mesh" well with other creatures. Elites, however, are supposed to be part of a greater encounter. So the "meshing" of Elites with standard monsters needs more care.

Ideally, some Elites should be "kill the Elite first", and other Elites should be "kill the allies first". Even better, it should be optimal to use anti-mook powers on the Allies, while using your "big guns" on the Elite. Ie: who you should attack should be _situational_.

For this to be true, the "baseline" needs to be closer, for stun-locking, and for picking who to kill first, and we want the "1 Elite can replace 2 Normal monsters" to remain true as well.

To avoid the "stun lock the elite" effect, Elites need to be good at avoiding stun lock. It should not be a no-brainer to stun-lock the Elite instead of an ally (which you choose should be situational). We could get fancy and give Elites status-defenses: but if we just boost Elite defenses instead, we can get a result that is similar.

Let's say that we want Elites to be better targets for "Until Next Round", but worse for "Until Save Ends" (there are mathematical reasons for this, but they are boring).

The average length, in rounds, of a "Hit, then Save Ends" in rounds is (Hit%)*(1/Save%).
(Ie, 50% hit chance, 50% chance to save:
50% chance of 0 rounds
50% chance of 1+ rounds
25% chance of 2+ rounds
...
= average of 1 round of debuff per attack attempt.)

The average length, in rounds, of a "Hit, for one round" debuff is (Hit%). That's pretty easy to work out. :)

We want:
A one-round stun is better on an elite:
(1-EliteDefense%)*Elite_DPR > (1-NormalDefense%)*Normal_DPR
A (save ends) is better on a normal:
(1-EliteDefense%)(1/EliteSave%)*Elite_DPR < (1-NormalDefense%)(1/NormalSave%)*Normal_DPR

(DPR means Damage Per Round).

Now, NormalSave% is 55%, and NormalDefense% is ~50%.
Define E := Elite_DPR/Normal_DPR (the elite damage factor).

Then we get:

EliteSave%*.91 > (1-EliteDefense%)*E > 0.5

The above is the stun lock formula for Elite mobs. We'll use this later.

---

Next, we are going to look at the "3 elites should do the same damage to a group of players as 6 normal creatures do in a fight".

(HP)/(DamagePerHit*Hit%) is the rough amount of time, in rounds, it takes to kill a single creature.

If we assume DamagePerHit doesn't vary with which target, we get that the number of rounds to kill a creature varis with HP/Hit% = HP/(1-Defense%)

The "PC Damage from killing 3 elites = damage from killing 6 normal" equation is:

(Normal_DPR)*21*(Normal_HP)/(100%-NormalDefense%) =~ (Elite_DPR)*6*(Elite_HP)/(100%-EliteDefense%)

Define H = Elite_HP / Normal_HP (the Elite HP Ratio).

Then this reduces to:
E*H =~ 3.5*(1-EliteDefense%)/(1-NormalDefense%)

Next, the kill equation. We want killing an Elite first to be not-dumb.

Damage Per Round / # of Rounds it takes to take out the critter is the "should I kill that first" approximation.

We want it to be a toss-up between an Elite and a Normal monster, leaving situational things to decide between them.

Elite_DPR/[Elite_HP/(1-EliteDefense%)] =~ Normal_DPR/[Normal_HP/(1-NormalDefense%)]
which reduces to:
H/E =~ (1-EliteDefense%)/(1-NormalDefense%)

Interesting. This is similar to the "3 elites need to be as tough as 6 normals", but it is slightly different!

So, our Elite Equations:
E*H =~ 3.5*(1-EliteDefense%)/(1-NormalDefense%)
H/E =~ (1-EliteDefense%)/(1-NormalDefense%)
EliteSave%*.91 > (1-EliteDefense%)*E > 0.5

Solving for E:
H =~ 3.5*(1-EliteDefense%)/(1-NormalDefense%)/E
H =~ (1-EliteDefense%)/(1-NormalDefense%)*E

3.5*(1-EliteDefense%)/(1-NormalDefense%)/E =~ (1-EliteDefense%)/(1-NormalDefense%)*E
3.5 =~ E^2
E =~ 1.87
Or, Elite Monsters need 87% more damage per round than normal monsters of the same kind.

Solving for H, we get:
H =~ 1.87*(1-EliteDefense%)/(1-NormalDefense%)

Let's assume NormalDefense% is 50%. This gives us:
H =~ 3.74*(1-EliteDefense%)

So now we have a relationship between the Elite hp ratio, and the Defense% of Elites.

The stunlock equation is next:
EliteSave%*.91 > (1-EliteDefense%)*E > 0.5

EliteSave%*0.49 > (1-EliteDefense%) > 0.27
EliteDefense% < 0.73
or EliteDefense bonus should not exceed +4.

For various bonuses to Defense over "normal" critters (aka, EliteDefense%), we get the following restrictions on EliteSave% and the HP ratio:
+1 Def, 55%: ES% > 92%, H=~1.68 (Save bonus +8)
+2 Def, 60%: ES% > 82%, H=~1.50 (Save bonus +6)
+3 Def, 65%: ES% > 71%, H=~1.31 (Save bonus +4)
+4 Def, 70%: ES% > 61%, H=~1.12 (Save bonus +2)
+5 Def, 75%: ES% > 51%, H=~0.94 (Save bonus +0)

Going with the middle of the road approach of +3 Def and +4 Save Bonus, we end up with:

CONCLUSION:
An Elite creature, balanced to be a replacement to two normal creatures, should have:
87% higher damage per round
+3 higher defenses
31% higher HP
+4 bonus on saving throws against (save ends) effects.

Such a creature will be a worth replacement for two normal monsters. It will be a toss up if the party should attack it first, or go after othe creatures first. Stun-locking this creature won't be a "no brainer".

As it happens, using [Reliable] powers, and powers that do damage on a miss, on this creature might be a good idea.

---

Let's compare and contrast with the existing Elites.

They 2x higher HP, +2 to saving throws, and ~+2 to defenses.
They do about 1.5 to 2.0 times as much damage as a normal monster.

They are ridiculously ideal for both single-round and (save ends) disable abilities.

They are poor choices to attack first, as they are about 100% to 140% harder to kill, and only do 50% to 100% more damage against the party.

---

How to produce "Elites That The Players Aren't Screwed If They Try To Attack -- Also, Not Stun-Lock Bait"(tm).
Take an existing Elite.
Add 1 to all defenses, and 2 to the lowest defense.
Increase their saving throw modifier to +4 (Ie, save on a 6+ instead of a 10+).
Reduce their HP by 35%, or about (Level * 5).
Make sure that their damage-per-round (or annoying-effects-per-round) are about 87% higher than a standard monster of the same level.

Damage spikes at bloodied are acceptable, but in general the creature shouldn't "get better" at bloodied. If that is the case, then the creature is a "let it sit around being sucky" bait -- ie, players who attempt to attack the big-bad screw the group by increasing the average damage the group takes.

Let's try this on Irontooth. Unmentioned stats are unchanged.

He's a level 3 brute. So his base attack chance is level+3 vs AC, doing 10 damage on a hit, pre-elite.

He has a base HP of 53. *1.31 = 69 HP (Bloodied 34).

He should do an average of +6 vs AC for 19 damage per round.

Base Defenses are AC: 15 Fort: 15 Reflex: 15 Will: 15
Base high stats: 14. Irontooth has +2 Will, and +4 Strength compared to this.
So with that, Defense becomes: AC 15, Fort 17, Reflex: 15, Will: 16
Add +3 average to all defenses, 2 to the lower ones: AC 17, Fort 21, Reflex: 17, Will: 20
Small changes, but generally upwards.

Saving throws go up to +4. A (Save end) power lasts 1.33 rounds on average, instead of 1.82 on most critters.

You could leave the powers alone, or:
Powers:
Basic attack: BattleAxe: Weapon, +6 vs AC, 1d8+4 (reduced to-hit chance compared to standard Irontooth)
Follow-through: Move action, only after missing a target this round. Make a basic attack against a different target.
Frenzied Assault: Move action, only after hitting a target this round. Make a basic attack against the same target. If it succeeds, push the target 1 square. Irontooth may optionally shift into that square.
(Irontooth follows through with a second attack, pushing you back.)
(Together, these are better than Dual Axe. This boosts Irontooth's offense.)
Blood Crazed: When bloodied lose Goblin Tactics and heal 5 HP per round. (weakened compared to the old one.).
(Irontooth spits a glob of blood out of his mouth, and ... smiles. You really don't like that smile.)
Blood Frenzy: Standard action, Recharge 6. Recharges the first time Irontooth bloodied in an encounter. Do a basic attack against all creatures in close burst 1.
(Irontooth's lets loose a cry of pure rage, and strikes out at you and your friends.)

...

And now you have an elite Irontooth that isn't a TPK waiting to happen if the players choose to try killing it first, and isn't "stun-lock bait".

He should be described as almost looking like a cross between a Goblin and a Dwarf -- a solid brick of muscle, weilding two large Battle-Axes, armored only in leather straps. As he fights, his eyes are bloodshot, and bloody drool dribbles down his chin.

---

Annendum:
Miss damage (Further work needed)
Many powers "do damage on a miss". I didn't factor that in: so the Elites I balanced will be good targets for abilities that have miss effects or don't roll to do damage/debuff, and acceptable targets for "only do damage on hit" effects.

Attacks that do damage on miss generally get credit for that. A power that does 2 damage on a hit, and 1 on a miss, is about as good as a power that does 3 on a hit as far as the game is concerned.

These powers will be better on Elite creatures. Let's assume that about 1/3 of attacks are attacks with a miss component.

On a normal creature, they do an average of 1.5 damage per attack (same as all-or-nothing powers).

On an elite, the all-or-nothing does 1.05 damage on average, while the power-with-half-miss does 1.35 -- 29% more damage.

With this happening about 1/3 of the time, that means we should toss another +10% HP at the Elite -- from 1.31x normal HP, up to 1.44x normal HP.

That brings Irontooth up to 76 HP from 69. A minor tweak. :)

So, with this annendum, we have (compared to a normal monster of the same type):
+3 average to defenses
+4 to saves
1.87 times as much damage per round.
1.44 times as much HP.

To convert an existing Elite to this new Elite pattern:
+1 to all defenses (can vary, but +1 on average)
If the creature powers up in the Bloodied phase, reduce this power up, and give it more up-front power.
Increase saves to +4.

...

So, am I crazy? :)

fractal
2008-06-17, 05:22 PM
It seems like a reasonable balancing approach.

On the other hand, maybe it's the game's INTENT to force you to save the Elite monsters for last. That gives them more time to stick around, inspire fear in the players, and show off their (often fancy) abilities. If the Elite monsters are always the last ones left standing, you give them more respect.

After all, how often in fiction do characters kill the boss first, and then take out the retinue? Generally they don't, they work their way up. Revenge of the Sith comes to mind - Palpatine first kills the minion Jedi, then the other Jedi Master, and only focuses on Mace Windu after that.

The extra power when Bloodied plays into this - you've killed the normal monsters, the fight seems a lot easier, you're working on the Elites, and then bam!, the Bloodied powers kick in, and the fight is harder again.

Goober4473
2008-06-17, 07:26 PM
Looks pretty cool.

My personal fix is, when making elite and solo monsters, to make them interesting and central to the fight more than just hp/damage. The link in my signature goes to a boss-fight compendium, which I think makes solo monsters much cooler. Instead of just being a group of monsters on its own, a boss is an entirely differant encounter. I'm still getting better at making this work, but it's pretty cool so far.

As for elites, I would probably try to make them change a lot at bloodied (or some other time during the fight), rather than just get a power-up. They switch tactics, gain differant but equal abilities, etc.

: One thing I notice though, is that the DMG suggests giving elites another use of a power after being bloodied, not to give them a bit power boost. This lets them say, use an encounter power twice in a fight, which makes sense considering they're supposed to be two monsters.