D&D 4E Forked: "Math and Grind" or "Why Rechan is Right" (From: "4e One-trick ponies")

RyvenCedrylle

First Post
Forked from: 4e One-trick ponies: Why is it the DM's fault about combat grind?

Rechan said:
I simply do not accept the statistical average increase = more damage output. Period.

It also doesn't help grind, which is the point. The increase in chance to hit still is depending on another character attacking with something they would've done on their turn anyway, and if that isn't exciting, then it's still grinding.

There’s a lot of talk on these boards using average damage calculations to determine the speed of a fight. That is, the assumption is made that if your average damage is higher, the fight ends faster. This, as far as I can tell, is not entirely true.

The basic reason for is that damage can be wasted. If I hit a monster that has 3 HP left for 15 HP damage, that 12 HP doesn’t go anywhere else. It simply disappears into the void. In terms of speed of killing multiple monsters, I only did 3 HP worth of elimination, not 15. Why does this matter? It matters because the average damage calculations are exactly that. Averages.

Example:

There are two opponents, A and B. A has 2 HP, B has 20. I hit each one in consecutive rounds for 1d8 damage each. If I hit A for 7 points and B for 2, I have averaged the 4.5 HP assumed by the damage calculations. However, only 4 of it counts towards the total HP pool of the enemy forces. This does not have the same in-game effect as if I hit A for 2 and B for 7. Here, I did the full 9 HP of elimination to the opposing forces AND averaged my 4.5 HP to boot.

In short, if your high damage rolls hit opponents with low remaining HP totals, the fight takes longer to actually perform than the mathematics should indicate. With solo monsters, you don’t have this problem as there is no opportunity for wasted damage. This, I believe, is the reason D&D 3E fights seemed to grind less despite the fact that the same powers were spammed more often. You fought fewer enemies at a time and thus had a lesser chance to throw away your good damage rolls.


What can be done about it? Minions seem to be a key answer intuitively but in fact exacerbate the problem as you continue to ‘waste damage’ or at least actions on 1 HP monsters. They speed up play only if they replace a normal monster 1:1 not 4:1. AoE can help this, but only if the little buggers are closed in well.

A better idea – and one that’s been thrown around in weeks past – is damage flattening. Your 1d8 sword always deals 5 damage. (Or 4, or 4 one round then 5 the next. Whatever) There’s still some wasted damage, but it’s significantly reduced. Now your actual results match the statistical model used by both system designers and back-engineers. If you don’t want to do this by math, the players should act so that strikers always hit high-HP targets and then move on once their opponent is about dead, letting the lower damage folks clean up the stragglers.
 
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Umbran

Mod Squad
Staff member
Supporter
The basic reason for is that damage can be wasted. If I hit a monster that has 3 HP left for 15 HP damage, that 12 HP doesn’t go anywhere else. It simply disappears into the void. In terms of speed of killing multiple monsters, I only did 3 HP worth of elimination, not 15. Why does this matter? It matters because the average damage calculations are exactly that. Averages.

What you say is true, but I am not sure it is relevant. In my experience, grind happens not because you are wasting damage on minions, but because the somewhat larger critters have so many hit points - you have to whack away at one of them for several rounds before you get any tactical advantage out of it.

For example, the BBEG in Kobold Hall, in the DMG. He's got a whole lot of hit points, compared to how many the PCs can dish out. That fight dragged on and on. My players (who don't read these boards) used the term "grind" to describe it all on their own.
 

A better idea – and one that’s been thrown around in weeks past – is damage flattening. Your 1d8 sword always deals 5 damage. (Or 4, or 4 one round then 5 the next. Whatever) There’s still some wasted damage, but it’s significantly reduced. Now your actual results match the statistical model used by both system designers and back-engineers. If you don’t want to do this by math, the players should act so that strikers always hit high-HP targets and then move on once their opponent is about dead, letting the lower damage folks clean up the stragglers.

Ummm... I thought I'd just say that this doesn't sound like much fun (and nor do I think it would work very well). You may as well just say this creature takes two hits, this creature takes three hits or something equally unexciting.
Although I suppose distance was replaced by squares so hit points could just be replaced by... hits.

Not a fan of this entire line of thinking.

Best Regards
Herremann the Wise
 

RyvenCedrylle

First Post
I didn't say it was very exciting, now did I? ;)

My point is just that I felt that directly equating 'average damage' and 'speed of combat' is a poor analogy, much the way Rechan did.

Honestly, I'm not sure what I would use to estimate speed of combat. The dice make it very unpredictable.
 

FireLance

Legend
Honestly, I'm not sure what I would use to estimate speed of combat. The dice make it very unpredictable.
In theory, you could translate the distribution of attack and damage rolls into the probability that the fight will end on the 1st, 2nd, 3rd, 4th, etc. rounds.

As a very simple example, assuming a fight between a fighter (+8 attack bonus) and a giant rat minion (AC 15), The fighter has a 70% chance of hitting the minion with each attack, so the probability distribution of when the fight will end will look something like this:
Round 1: 70.00%
Round 2: 21.00%
Round 3: 6.30%
Round 4: 1.89%
Round 5: 0.57%

and so on.​
For a slightly more complicated example, for a fight between the same fighter and two giant rat minions, you get something like the following distribution (assuming discrete attacks only, and no use of cleave):
Round 1: 0.00%
Round 2: 49.00%
Round 3: 29.40%
Round 4: 13.23%
Round 5: 5.29%
Round 6: 1.98%
Round 7: 0.71%

and so on​
I don't have the math or computing skills to work out what it would be like for five PCs and five monsters, though.
 

Cadfan

First Post
Your comments about wasted damage are entirely correct. And they do have an interesting tidbit hidden in them- they're a great endorsement for the use of enemy-only area of effect attacks as cleanup powers, because these attacks hit multiple foes, generally for lower damage per hit compared to regular attacks, thereby wasting less damage.

Rechan is still wrong though. Hitting more often DOES increase damage dealt per round, and DOES reduce the rounds of combat. That's just how it is, and nothing, not even randomizing to-hit rolls on a flat 20 point distribution, can change that. The law of high numbers may not kick in within a single encounter (though it might, depending on the bonus in question, Lead the Attack is liable create instant statistically relevant results), but within a single DAY of encounters, the law of high numbers is almost guaranteed to make an appearance.

Of course this is actually all off topic a bit from the original conversation, which was about the length of combat one should expect from a party of one leader, one defender, and four strikers, versus a more balanced party with a controller and perhaps another leader.
 

Rechan

Adventurer
It's rare I see "Rechan is Right", much less in a subject heading. But by golly, I like it.

:D

There's also this point made by billd91:
Cadfan said:
But, but... it does. Math says so.

Well, yes and no. Over the long term, math does say so. At least as far as math is able to make the statistical prediction based on certain assumptions of the distribution of the random variables.
But with respect to any single attack or even single fight, it says a whole lot less. Depending on how the random distribution turns out, there will be whole fights in which that hit bonus is completely irrelevant.

So, yes, math says so... but with extensive caveats.
Plane Sailing then followed up with:
Most combats probably don't last long enough for a +1 or +2 here or there to make a statistically significant difference. You've got to have combats lasting 20+ rounds (and that bonus there every one of those rounds) in order to start seeing the mathematical benefits that some have claimed.
 
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Rechan

Adventurer
What you say is true, but I am not sure it is relevant. In my experience, grind happens not because you are wasting damage on minions, but because the somewhat larger critters have so many hit points - you have to whack away at one of them for several rounds before you get any tactical advantage out of it.
As I said elsewhere, I don't think that's the source of grind, necessarily.

The problem comes when everyone's done their thing, used their encounter powers... and the fight's only half over. Certainly monster HP can contribute, but it's more symptomatic than a true cause of grind.

More over, when an hour into a two hour battle, it's obvious the PCs are going to win, but the monsters just aren't dead yet, and the monsters have nothing left that's interesting. For instance, the PCs killed all the monsters except for two artillery monsters, who are still at full health; even if everyone did max damage on every attack, that's still a waste of time because it's shooting fish in a barrel. Add in a miss here and there, and it goes forever.

I say that the hit points factor in only slightly here. The same result could happen if the PCs are fighting 4 minions, and due to the dice, can't hit the minions for 5 rounds.

The problem is: the fight gets boring. The fight is boring because there's nothing left to change things up, make the fight interesting. Powers make the fight interesting. Monster abilities make the fight interesting. Terrain make the fight interesting.

I'm fairly certain that even if the monsters had 1/4 their HP, it would still feel like grind if everyone fought to the death using At-Wills in a 6x6 barren room.

This is also exacerbated by monsters that have debilitating effects. Stuns, grabs, dazes, weakening effects, immobilizing, blinding, auras/powers that decrease hits - anything that prolongs the PCs from killing the monster. They usually result in "Can I get to it/do something to it this round? No? Okay."

I feel this is particularly true when you miss with your encounter/daily powers. You can only use them once in the battle, and if they miss, well, there goes a wasted resource that, due to its absence, makes the fight longer, and frustrating for the player.
 
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Rechan

Adventurer
To extend the issue of "Monsters Have Too Many HP", but taking a left turn, let's try something different.

It's generally taboo to use one edition to compare/explain a problem in another edition; it either leads to edition wars, or it's comparing apples to oranges because the systems had different assumptions/functions. With that said:

Did Grind exist in 2e and 3e? I can recall Many Sessions where the battles took hour, hour and a half to resolve. The monster HP was fewer in 3e, so if there was grind in previous editions, the monster HP wasn't the cause. What made previous editions grind?

And, did the cause of 3e grind continue into 4th, or are the circumstances different?
 

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