Levels 1-10: How much damage does a character gain? (heavy math)

Stalker0

Legend
Edit: There was a mistake in my original post which led to an inaccurate conclusion!

The idea of "grindyness" has been talked about a lot recently, and I too have noticed some issues with the massive number of hitpoints monsters seem to have relative to player's damage. However, the effect didn't seem to be as noticable at 1st level, but at 7th, is now more so. I decided to apply a little math to try and answer the question of scaling...do player's damage keep up with monster hitpoints?

To model this easily, we have to make a great number of assumptions. Here are some that I have made.

1) Each character uses a bastard sword to start and will assume defenders only (as this seems to be the middamage between strikers and leaders).
2) At-wills do 1[w], encounters 2[w], and dailies 3[w].
3) A day of adventuring is 4 encounter of 5 rounds each (20 rounds per day).
4) Characters gain magic items at the normal rate of advancement (I assumed 2nd level for a +1, 6th for a +2).
5) The characters have a static 70% rate of hitting (I think this is a little high overall, but it helps to account for things like situational to hit bonuses, and other misc modifiers I have not entered into my calculations).
6) There will be 1 crit (over 20 rounds this makes perfect sense, I have also factored the chance of criting on an at-will, encounter, or daily in my calculations)
7) Characters will take weapon focus and some other feat at some point that gives them a +1 to damage.
8) Trying to account for the numerous other potential modifiers, I have chosen to grant the character a flat +1 damage/2 levels.
9) We will look at 1 attack per round. I have included 2 more at-will attacks per 20 round cycle to include action points. I am using at-wills because encounter and dailies are hard defined, at-wills are only limited by time.

I have attached my excel for review. Here is the results. Remember, the importance is not how much damage at any particular level, its the change in damage that is the importance.

Code:
Level	Relative	Difference
1	9.2085	0
2	11.8265	2.618
3	12.68	0.8535
4	15.1055	2.4255
5	15.53225	0.42675
6	17.34175	1.8095
7	18.19525	0.8535
8	19.00375	0.8085
9	19.4305	0.42675
10	20.239	0.8085
Total Change		11.0305

So overall, a characters damage increases by roughly 1.23 damage per round per level or about 6 damage more per fight per level. Overall the party then will deal 30 damage more per fight per level. That means that an encounter at 10th level should have roughly 270 more hitpoints total in order to get it at the same length of a 1st level fight.

A 10th level basic monster often has 60 more hitpoints by itself, meaning the total encounter has about 300 more hitpoints, 30 more than our expected estimate. For 10th level characters, it takes 2 party members another round to take out the 30 hitpoints, so it would appears that hitpoints and damage do scale pretty well.
 

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A 10th level basic monster often has 60 more hitpoints by itself, meaning the total encounter has about 300 more hitpoints, 30 more than our expected estimate. Since a party is dealing only 6 more damage per round than at 1st level, that's another 5 rounds of combat. While I doubt the problem is that pronounced, it would seem based on this that combat does increase as the levels go up.

Followed you up to this point. But if the entire encounter has 30 more hit points to go through, rather than each individual monster, wouldn't you need to apply the damage per round and not just the difference to see how many more rounds the combat will take beyond the estimate? Another 30 pts to deal to a 10th lvl party would take 1.5 rounds by your numbers, not 5. Or am I missing something?
 

Followed you up to this point. But if the entire encounter has 30 more hit points to go through, rather than each individual monster, wouldn't you need to apply the damage per round and not just the difference to see how many more rounds the combat will take beyond the estimate? Another 30 pts to deal to a 10th lvl party would take 1.5 rounds by your numbers, not 5. Or am I missing something?

Ah, thank you for catching it! You are absolutely right. At 10th level, a 10th level characters should be doing about 20 damage a round, so 2 character with another round of combat should finish the fight, not 5 rounds. That's a big difference from my original conclusion, with this it appears that the hitpoints do scale pretty well with level.
 
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You're going to run into trouble if you're calculating simply on total hit points vs. total average damage output.

Actions are by far the more important currency in combat, especially when you consider "overkill damage." (ie, Damage delivered in excess of what is necessary to finish off a single combatant.) A creature with 1 hit point still requires an action to kill-- hence, minions.

Throw in Lanchester's Laws, "random number bunching," etc. and it is very difficult indeed to build any kind of predictive mathematical model of D&D.

It's fun, it's worth doing-- but I wouldn't try to draw any conclusions from it.
 



What about the action points players earn every 2 encounters and regain every long rest?

This was factored in to my calculations.

You're going to run into trouble if you're calculating simply on total hit points vs. total average damage output.

Actions are by far the more important currency in combat, especially when you consider "overkill damage." (ie, Damage delivered in excess of what is necessary to finish off a single combatant.) A creature with 1 hit point still requires an action to kill-- hence, minions.

Throw in Lanchester's Laws, "random number bunching," etc. and it is very difficult indeed to build any kind of predictive mathematical model of D&D.

The model is definitely crude I will give you that, and I completely agree that no kind of permanent conclusion should be drawn from just one model. On the one hand I'm not factoring in area damage. On the other hand, I'm not factoring in that players will get hit with harsher conditions like stunning at higher levels that will retard their damage for a round. There is a lot more going on then just this of course, but it was interesting to see how damage does scale in 4e.
 

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