The Final Puzzle Piece: PC Damage

So far there have been articles about power options (non-damage riders on powers) for both PCs and MM1 and MV monsters. There have even been articles on monster damage. So if we’ve taken care of status effects, and we’ve taken care of monster damage, what’s left? To-hit and defenses scale pretty much statically all the way to level 30, so what now? PC damage. If power options are important but vastly insignificant compared to to-hit, defenses, and damage, and to-hit and defenses are static, that leaves damage. We’ve already investigated what makes monster damage tick (or the lack thereof), so that leaves PC damage. How does PC damage scale by level, especially as compared to monster hit points? Read on to find out.

The first, and most obvious, problem with determining PC damage by level is there isn’t really an expected value, or if there is, it’s difficult to find. There are so many variables, as Mr. Ross mentioned in the comments section of my last article, that to tackle this problem you would need untold hours of dedicated analysis work – it would be so time-consuming that no single blogger could possibly do it.

Or could we?

Thankfully, one group of many individuals has, in fact, already done the work of determining what expected player damage looks like! They are members of the Character Optimization board, who, while I don’t generally approve of the concepts of “builds”, are pretty well versed compared the majority of people about how to create a PC that can do things – such as damage. Rather than having to re-combinate the thousands of magic items, feats, paragon paths, powers, and epic destinies that exist on the dozens of classes, I can instead simply reference their handy-dandy DPR by level threads (in this case I will be using “DPR King Candidates 3.0”).

But wait! “Stop HydraDM, you’re crazy!” you say? “You shouldn’t use optimized characters like that!” you say? Well, actually, this isn’t a problem like you would expect. Why isn’t it a problem? Because: I am not comparing player damage to anything else, I am comparing player damage to itself as it relates to monster hit points. Comparing player damage to monster damage will come later and use “expected” values rather than solely values submitted to a thread designed to be about damage-per-round.

So, before I start on the damage, first I need to determine the average suggested monster hit points for a given level. Using our handy-dandy DMG (and updated tables where appropriate), this comes out to… well, actually there is no standard amount. The problem here is that despite damage, attack, and the defenses all using crisp and easy to use formulae, hit points on monsters arestill determined by constitution score. Blegh. Come on now 4th edition, you’re letting me down here. Anyway, a quick browse of the compendium (and my previous data on the matter) shows that we are given 213 standard monsters in MV and, just to round things out, 228 standard monsters in MM3 (I’m using modern monsters because this is an analysis of modern damage – no point in including MM1 stuff here). Therefore, consider total standard monster count to equal 441. This set of monsters is composed of 85 skirmishers (19.3%), 84 soldiers (19.0%), 84 controllers (19.0%), 55 artillery monsters (12.5%), 54 lurkers (12.2%), and 79 brutes (17.9%). Ignore the fact that we’re missing .1% from rounding error here – my actual calculations use the entire number.

Using this information, we acquire some figures: 7.86 (approx) base hp for any given monster, plus 7.86 (approx) hp per level, plus constitution score. So what the heck is the constitution score going to be? “On average, the highest ability score of a [Non-AC Defense’s ability score] pair is equal to 13 + one-half the monster’s level.” So, if Constitution is the higher of our STR-CON pair that means, what, 13 hp at first, 14 at second, 14 at third, 15 at fourth etc.? Sure, why not, let’s go with that. It’s as good a guess as any, and really we only need a yardstick. Being a handful of HP off shouldn’t be too bad, assuming there’s actually a noteworthy problem to be found.

One final assumption: I am going to ignore area damage. There is no way to tell how many monsters might be hit by such attacks, and thus calculating their expected damage value is frankly difficult at best.

The following values are Damage-Per-Round (DPR) that can be continued indefinitely. I will therefore equate this damage with the Monster Single-Target Damage expression. The values posted in the practical DPR Kings thread (done by averaging submissions) are for levels 1, 6, 12, 16, 24, and 30.

Expected % of Expected Monster HP (practical) –

  • Level 1: 68.4%
  • Level 6: 51.9%
  • Level 12: 54.4%
  • Level 16: 56.1%
  • Level 24: 69.2%
  • Level 30: 161.8%

So, from our practical submissions, what seems to be the pattern here? Well, your given DPR Kings submission seems to do quite well at level 1 (I imagine this is because of the plethora of experience concentrated in optimizing level 1 characters), then dips down (again, probably due to less experience), and rises steadily until it reaches level 30, at which point it spikes off the charts primarily because of a few ridiculous character concepts, such as the one that expects an average DPR of 3,857 (yes you read that right) currently holding first place for level 30. This particular build, as a result, is technically speaking a statistical outlier (outside of 3 standard deviations from the mean; in this case it is at around 5), but I have included it anyway because I think despite being a statistical outlier it is also very important. The “smiley-face” nature of these numbers (high at the start, high at the end, kind of low-ish in the middle) seems to reflect that the center of the graph should be higher than it is, except that very few people use those levels as a target goal in comparison to level 1 or level 30. So, while we might be wise to ignore the outlier at level 30, we also might be wise to include it. In this case I have kept it included. A special thanks to commentor “Sentack” for pointing this oversight out to me 🙂

Something else important to note: a “fair” striker is considered one that can sustain an expected DPR/Monster HP of .4, or killing 40% of a standard monster per round, every round, indefinitely. At 20% you are considered “garbage” compared to standards of play they have established, and at 60% you are considered “optimized”. 80%-100% and above is suggested to be particularly impressive and potentially necessitating an adjustment by WotC due to its power relative to the majority of builds. As a cursory example of this in action, a Warlock at level 1 using Eldritch Blast with an ability score modifier of 4, accurate implement for +1 to hit, and attacking a cursed target will deal an average of 8.8 DPR, which translates to 27.5% of an expected monster’s HP at level 1 (roughly) – not quite “fair”.

So, yes, as expected PC scaling increases faster as the level gets higher. But what, then, does their damage look like compared to monster damage? Thankfully I happen to already have those numbers, so let’s have a look (In % opponent hit points):

Level 1

Monster Single Target (Normal): 34.3%
Monster Single Target (Brute): 42.9%

PC Single Target (“Fair”): 40%
PC Single Target (“Optimized”): 60%
PC Single Target (Practical): 68.4%

Level 6

Monster Single Target (Normal): 27.6%
Monster Single Target (Brute): 34.5%

PC Single Target (“Fair”): 40%
PC Single Target (“Optimized”): 60%
PC Single Target (Practical): 51.9%

Level 12

Monster Single Target (Normal): 24.7%
Monster Single Target (Brute): 30.1%

PC Single Target (“Fair”): 40%
PC Single Target (“Optimized”): 60%
PC Single Target (Practical): 54.4%

Level 16

Monster Single Target (Normal): 23.6%
Monster Single Target (Brute): 29.5%

PC Single Target (“Fair”): 40%
PC Single Target (“Optimized”): 60%
PC Single Target (Practical): 56.1%

Level 24

Monster Single Target (Normal): 21.9%
Monster Single Target (Brute): 27.3%

PC Single Target (“Fair”): 40%
PC Single Target (“Optimized”): 60%
PC Single Target (Practical): 69.2%

Level 30

Monster Single Target (Normal): 21.4%
Monster Single Target (Brute): 26.8%

PC Single Target (“Fair”): 40%
PC Single Target (“Optimized”): 60%
PC Single Target (Practical): 161.8%

In chart format, that looks a little something like this (with high single target brute limited damage tacked on for scale; it says maximum, but it’s the average of that maximum set of dice and modifiers) –

Eugh. That looks kind of gnarly, doesn’t it?

Tune in next time for the capstone article of the series, which will combine expected damage and expected power options into the ultimate graph of monster versus PC (by-the-book) power.


Posted on March 6, 2012, in Monster Design, Rules Design and tagged , , , , , , , , , . Bookmark the permalink. 2 Comments.

  1. These are some really interesting numbers although I think the level 30 “practical” has to be an statistical anomaly. To the point that it should have been filtered out of your data. Maybe then the level 30 practical would have looked a bit more normal. It looked like it was shooting for maybe 85% – 95% (Which is insane still) but not the “So you kill them and bloody it’s unborn children” value of 160%.

    I’ve also noticed that the Character Opt boards are also going by a “Monsters Killed in 5 Rounds” scale now, instead of a “Damage Per Round” scale. Apparently this is because while high DPR is nice, if you’re still only able to kill 1 monster every 2 rounds, then you’re build isn’t that much better then the guy next to you with a lower DPR but with better status effects. Damage doesn’t overflow. Interesting concept.

    Keep up the work though, yes going by the Char-Op boards is questionable but some of the data that comes out of there is very interesting.

    • I would have changed it, but honestly level 30 being a bit of an outlier just like level 1 makes sense. Level 30 “builds” are complete – you can’t get a higher level by the book. Level 1 “builds” are going to be common-place since most games begin at level 1. Both ends of the spectrum have more experience (and drastically more submitted “builds”) than the middle levels do. If anything I would expect each of the middle points to, in actuality, be higher than they are, rather than the beginning and end be lower.

      A cursory glance at the data I used indicates that the top level 30 build does seem to be statistically an outlier (taking the 3 minutes to actually compute standard deviation my rough guess here seems to be substantiated), but there are other builds that kill more than a single monster per turn at level 30 as well… just not more than 10 of them. The practical in this case would dip down to 1.25 rather than 1.61 – thanks for pointing that out! I’ll edit the article with a note.

      This is correct, they are using a “monsters per round” scale. However, the monsters per round scale is simply a straight conversion of expected damage divided by expected monster hit points (their expected monster hit point value is slightly too low for use with my model so I corrected it for when I expressed values in percent of expected monster hit points). In this case, then, damage does in fact overflow. Your implementation would’ve been cooler, though!

      Glad you like what I’ve created, and I hope you stick around for my capstone article of the series, which will be a fairly good comparison between monster and PC expected value per round.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: