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harpy
2011-02-15, 12:04 PM
I'm trying to sort out a DPR benchmark based on CR. The idea is to sort out what would be a DPR Target that you would want to reach with a character build at any given level. That way a player could figure out how competent their particular character build is at any given level compared to an average benchmark for the system as a whole.

The benefit to having this benchmark is that it would help GMs and players get an idea of this one aspect of the game at a greater amount of precision. If a GM notices that the hard core min-maxer Barbarian is making every encounter only last two rounds, ending in red mist, then the DPR could be calculated for the character and then compared. If it is well above the benchmark then there would be a data point to use in a discussion about how to tone down things.

On the flip side, if you've got a hard core roleplayer who's used all of their resources to make a vibrant and interesting, yet sub-optimal character, then this would likewise give a datapoint to discuss ways of dialing up the character's ability to contribute in a fight. It might even be an issue of handing this particular player a very potent weapon compared to their level to fix the math, with the assumption that this player isn't going to take advantage of the situation.

However, I'm not totally satisfied with my methodology so far. First, a look at the average hit points by CR in the game as it currently stands. I took all of the creatures on the online database, broke them up by CR and then averaged their hit points:


CR = HP
0.12 = 2
0.16 = 3
0.25 = 3.83
0.33 = 5
0.5 = 8.03
1 = 12.51
2 = 19.17
3 = 29.59
4 = 40.46
5 = 56.49
6 = 68.28
7 = 83.09
8 = 96.84
9 = 115.83
10 = 127.79
11 = 144.89
12 = 161.37
13 = 173.41
14 = 187.29
15 = 226.29
16 = 245.06
17 = 282.46
18 = 308.9
19 = 316.44
20 = 360


The next part is to define the bechmark. The game, as it was laid down in 3.0/3.5 was built with specific assumptions in mind, and playtested to make a CR system that would fit within those specific assumptions. This was:

four characters + four encounters per day + each encounter is roughly five rounds long

In terms of party composition, if you assume the iconics (fighter, rogue, cleric, wizard) then you have two classes that specifically are dealing with outputing damage, with another two that might be outputting damage. The cleric could wade into the fight, but depending the level varies on how competent he is in the battle. He could also be healing and buffing. The wizard could be providing direct damage through spells, but could also be doing some kind of battlefield control type of effect.

Because of this, I'm estimating that overall three party members worth of actions are dealing with damage output, with other possible actions outside of DPR issues taking up one party members full time (counting the cleric and wizard as only contributing half effort for damage output).

Onto the rounds per combat. The assumption is roughly five rounds of combat. To try and standardize this I'm estimating that each party member has to spend at least one round dealing with positional movement. It's either a charge, or moving into a flank, or dealing with terrain. So right off I'd drop it down to four rounds worth of actual attacks. Next, not every attack can be considered a full or flanking attack. Either because of a need to reposition, or just the nature of the battlefield, it seems on a broad level another round needs to be removed to compensate for just standard or non-flanking attacks.

Thus we have:

(three characters) x (three rounds) = 9 attacks in an encounter

Going back to the average hit points, and no dividing them by 9 we get:


CR = HP
0.12 = 0.22
0.16 = 0.33
0.25 = 0.43
0.33 = 0.56
0.5 = 0.89
1 = 1.39
2 = 2.13
3 = 3.29
4 = 4.5
5 = 6.28
6 = 7.59
7 = 9.23
8 = 10.76
9 = 12.87
10 = 14.2
11 = 16.1
12 = 17.93
13 = 19.27
14 = 20.81
15 = 25.14
16 = 27.23
17 = 31.38
18 = 34.32
19 = 35.16
20 = 40


The problem is that those numbers just don't look right at all. DPR is supposed to take into account chance to hit. These numbers are meant to be DPR targets, not DPR themselves. But if you go over the the DPR olympics thread, a single character build for DPR is going to drop an average CR 10 creature (127.79 hp) in two or three rounds on their own. If the rest of the party is backing up that DPR outputter, then the creatures barely going to have a chance of looking menacing.

But perhaps that is simply the nature of the DPR olympics, showing how above the power curve those builds are compared to something less optimized.

So what do people think? Where do the estimations need to be tweaked. Remember, this is a benchmark, it's meant to be a grand averaging of the entire system and thus assumes that there is great variation on either side of the mean. There is also the caveat that it is only a DPR Target that is trying to be nailed down, and not taking into account all the other effects and strategies in the game.

Aldizog
2011-02-15, 12:35 PM
Your numbers are right for what was expected for 3.5. The flaw in the system is that optimization led to too-powerful characters.

Consider the sword-and-boarder. He's often talked about as being unable to do enough damage to get enemies to notice him. But consider this: with a starting 16 Str, a bastard sword, the WF/WS feats, and NO magic, he does about 11 points of damage per round at 6th level against an AC of 19 (using the MM guideline of 13+CR), and the same at 7th against AC 20. At 8th, he does about 14.5 points against AC 21, and by 12th it's 22 against AC 25. All of this with NO magic, no stat-boosters, no magic weapons, no Inspire Courage or Haste. That's a really sub-optimized PC and he's still exceeding your damage levels (also note that he's roughly comparable to the wizard's Magic Missile spell, or the warlock's Eldritch Blast). In other words, he does enough that a party of him and his allies will drop a CR-appropriate foe in 3 or 4 rounds, not one-shot it. The greatsword user does about 19 per round at 8th and 27.5 per round at 12th without Power Attack (though without magic or Shock Trooper, the optimal power attack amount is quite low).

So, the point is that the monster HP totals and AC were balanced for a totally unoptimized sword-and-boarder and a party of somewhat less-effective allies (such as an unbuffed mace-wielding cleric). The potential for optimization is a flaw in the system that wasn't properly accounted for.

Chen
2011-02-15, 12:47 PM
So, the point is that the monster HP totals and AC were balanced for a totally unoptimized sword-and-boarder and a party of somewhat less-effective allies (such as an unbuffed mace-wielding cleric). The potential for optimization is a flaw in the system that wasn't properly accounted for.

A robust system would have made optimization scale linearly. Clearly they can't publish a book, recommend an appropriate encounter and then have 90% of the population that plays be unable to defeat said encounter. So the encounters need to be setup in a such a way that the guy who grabs a fighter and throws random feats at it can still participate.

This issue is still present in what little 4th ed I've played. The difference between a Wizard who takes the blasty spells and the controller spells is HUGE, even just with the PHB1. Similarly some powers are just plain worse than others at the various levels (in some cases they are almost strictly worse). The monster's manuals are clearly made up to cater for the person who chooses a non-optimized and non-complementary array of powers.

I recall making an encouner where our 5 person party destroyed a beholder and some skeletons things. The encounter was supposed to be a Level + 4 encounter. If I hadn't practically doubled the beholder's hp AND added another beholder (with similar HP) the fight would have been over with the PCs having practically no losses. This isn't even a lack of tactical play on my part. The numbers just don't work out well.

And hence back to my point about optimization needing to be linear. If you have linear optimization its easy as you can just say something in the monster manual like "Adjust all creature stats by X and their HP by Y if your group is well optimized" or somesuch. Clearly the system would need to be designed from the start this way, but I certainly think it would help with balance issues.

Darastin
2011-02-15, 01:55 PM
The problem is that those numbers just don't look right at all.
Yeah, they're far off from what the system actually provides. 40 DPR for a level 20 character is ridiculous. And that's not speaking from a point of view that considers any amount of actual optimization.


DPR is supposed to take into account chance to hit.
Of course it is. The math is rahther simple, but doing it all by hand (or Excel :smallcool: ) takes time. I actually took the time to write a little Java application (wizace.de/downloads/damalyzer_2.6.zip) for this (no instructions included; use at your own risk).


These numbers are meant to be DPR targets, not DPR themselves. But if you go over the the DPR olympics thread
then you go too far. I'd rather try to find out what the developers actually intended. It's from 3.0, but the old Bastion of Broken Souls module contains pregenerated 18th-level-characters. I'll be taking their equipment, advance their stats to 20th level and use a very conservative build to determine intended baseline DPR.

So, for basic melee, you start with STR 15. Put all stat increases into it, add a +6 stat booster and a +5 tome. That gives you an actual STR of 31. Take a +5 two-handed weapon, Weapon Focus and Power Attack. This results in an attack bonus of 20 (BAB) + 10 (STR) + 1 (focus) + 5 (weapon) = 36. It's supposed to be a damage dealing type, so we go with a +5 greatsword dealing 2d6 (base) +15 (STR*1.5) + 5 (weapon) = 2d6+20 points of damage on a successful attack. As you can see, a very conservative build using expected equipment; and not considering any special abilities of actual warrior-type classes - no rage, no weapon specialization, no smite, no favored enemy and so on.

Now, let's determine DPR for one full attack. This thread is meant for Pathfinder, so I'll be using Pathfinder rules for Power Attack.


Primary set: +5 greatsword; 20th level generic warrior; using BAB of 20 with Pathfinder rules:
Weapon 1: to hit: +36/+31/+26/+21; avg. damage 27.0 (19/x2); power attack x 3.0
------------------------------------------------------------------------
AC avg. damage best PA avg. PA damage
10 112.8600 6 188.1000
11 112.8600 6 188.1000
12 112.8600 6 188.1000
13 112.8600 6 188.1000
14 112.8600 6 188.1000
15 112.8600 6 188.1000
16 112.8600 6 188.1000
17 112.8600 6 188.1000
18 112.8600 6 185.6250
19 112.8600 6 183.1500
20 112.8600 6 180.6750
21 112.8600 6 178.2000
22 112.8600 6 175.7250
23 112.8600 6 170.7750
24 111.3750 6 165.8250
25 109.8900 6 160.8750
26 108.4050 6 155.9250
27 106.9200 6 150.9750
28 105.4350 6 143.5500
29 102.4650 6 136.1250
30 99.4950 6 128.7000
31 96.5250 6 121.2750
32 93.5550 6 113.8500
33 90.5850 6 103.9500
34 86.1300 6 94.0500
35 81.6750 6 84.0375
36 77.2200 0 77.2200
37 72.7650 0 72.7650
38 68.3100 0 68.3100
39 62.3700 0 62.3700
40 56.4300 0 56.4300
41 50.4225 0 50.4225
42 45.9675 0 45.9675
43 41.5125 0 41.5125
44 37.0575 0 37.0575
45 32.6025 0 32.6025
46 28.0800 0 28.0800
47 25.1100 0 25.1100
48 22.1400 0 22.1400
49 19.1700 0 19.1700
50 16.2000 0 16.2000

So unless you're only fighting rather hard targets (ACs in excess of 40), that's quite a lot more than 40 DPR. And that's without any buffs, cool item effects, class abilities or even feats beyond the most basic ones.

Fights against single opponents don't ever last three rounds of actual combat (not counting any rounds purely spent on positioning, atempting to avoid combat, countering said attempts etc.). If you want your fights to last longer, use multiple opponents.

Just my two €-cents;
Darastin

NichG
2011-02-15, 02:20 PM
This is why if I'm going to have a single opponent fight the party, I inflate hitpoints by a factor of 10.

D&D as written is a game where any single target without some way of being immune to attack or able to avoid attacks will go down in one round of being focused upon. So you either run battles with large numbers of enemies so that it doesn't matter if the barbarian does 40 or 400 damage per hit, thats still just one monster down, you give cascading resistances and immunities that need to be removed before anyone can hurt it (displacement, stoneskin, delay death, berserker frenzy, indomitability, death pact, contingent blah, abrupt jaunt, ...), or you give it more hitpoints to be more in line with what a party can really deal out.

harpy
2011-02-15, 05:15 PM
Great responses! Thanks for all the analysis, I've got more to chew...

Thanks for highlighting the solo issue. The big problem with solo monsters is that it generally makes for a poor encounter due the fact that the action economy is lopsided to the party's favor far too much. With one creature against four PCs, the sheer action economy can make it too easy for a party to win.

So, I went back and worked out the hit point totals that would happen if you had four creatures to fight at CR. These would be four creatures that are three steps down in CR, which combined end up having the same value as level appropriate CR in the Pathfinder system.

Having four PC versus four monsters is a much more interesting and dynamic encounter. One of the results of this is that the overall pool of hitpoints that the PCs have to contend with increases over that of just a solo monster rated at CR level.

The table below has the CR listed, along with two numbers. The first one is the total number of hit points for all four creatures, and the second number is the value of that hit point pool divided by 9, giving a DPR target.

CR = 4 creatures / DPR target
1 = 15.32 / 1.7
2 = 20 / 2.22
3 = 32.12 / 3.57
4 = 50.04 / 5.56
5 = 76.68 / 8.52
6 = 118.36 / 13.15
7 = 161.84 / 17.98
8 = 225.96 / 25.11
9 = 273.12 / 30.35
10 = 332.36 / 36.93
11 = 387.36 / 43.04
12 = 463.32 / 51.48
13 = 511.16 / 56.8
14 = 579.56 / 64.4
15 = 645.48 / 71.72
16 = 693.64 / 77.07
17 = 749.16 / 83.24
18 = 905.16 / 100.57
19 = 980.24 / 108.92
20 = 1129.84 / 125.54

true_shinken
2011-02-15, 06:38 PM
You, sir. Remove your Wow 4e DPS from my Pathfinder. :smalltongue:

harpy
2011-02-15, 07:23 PM
You, sir. Remove your Wow 4e DPS from my Pathfinder. :smalltongue:

Heh... I know. Actually, the reason I want to do this analysis is so that a metric can be made to help GMs with these kinds of issues. If a baseline is established, then it's a lot easier being able to point to an over-optimized build and saying, "see, this is why it is going too far... tone it down."

It's pretty easy to optimize and push the envelope, but it's a lot harder for the GM to be able to eyeball what is going to far until it's already causing problems.

"Treat the disease, rather than the symptoms."