D&D 4e Strikers: Math First

UPDATE: I initially did the calculations using the wrong figures for Sorcerer Chaos Bolt bounce damage. Both weapon pluses and the Sorcerer secondary attribute bonus are added to the bounces. In addition, the secondary attribute bonus gains +2 at paragon tier. This makes the Sorcerer stack up very, very well, though the Ranger and Avenger still beat it on the difficult targets.

In a bit of a departure, I'm going to talk about tabletop RPG, and I'm going to indulge my love of math and graphs and analytics. You have been warned.

Both Ameron and Sndwurks of Dungeon's Master have claimed that the Avenger class is "broken". Ameron wrote "Avenger - worst striker ever" last March. I thought comments to that post had pretty effectively rebutted the claim, until recently Sndwurks posted a redesign of the Avenger class.

We engage in redesign or tweaks of classes all the time, so I have no issue with that. By all means, people should not play classes they don't like, and feel free to fiddle with them to get classes they do like.

But I have a problem with the idea that Avengers are "broken" - meaning that they don't acheive the damage output that other striker classes, particularly the Rogue and the Ranger, do. I think this is mistaken. So, I made a spreadsheet and a bunch of graphs. (I told you this post was going to be geeky!)

This post is going to cover the math. In the graphs below, I look at damage output of Rogues, Rangers, Avengers, Barbarians, Warlocks and Sorcerers.

I present graphs of damage per Standard Action (DPS) versus the roll needed to hit the mob. I think that mostly pluses to hit even out between the classes. There may be a few exceptions to this, but they will be relatively easy to deal with after the fact.

Arcane classes don't get the proficiency bonus to their attack modifier, but they generally attack defenses other than AC, which means that these effects tend to cancel each other out. It isn't perfect, but that's the assumption we're going with. For now.

In the scenarios below, I've generally assumed no feats are chosen to that add damage. I think these feats generally even out between the classes, and their effect is usually pretty easy to incorporate. Ability modifiers are assumed to be 5 in heroic tier and 6 in Paragon tier. The Paragon tier graphs assume that characters have picked up another +2 to damage (other than magic weapons/implements) somewhere along the line.

All damage calculations are based on using the expected value of any die roll. So Rogues are assumed to use a Short Sword (1d6 = 3.5) plus 2d6 (=7), plus Ability modifier damage (5).

Barbarians and Avengers are modeled with Greatsword. Greataxe is arguably better, but the proficiency modifier is one smaller. That can be modeled as a tax of 5% of damage output, that makes Greataxe damage output equal to .95*(6.5+5)=10.95 versus Greatsword = 5.5+5 = 10.5. High crit makes it a little better still, but the effect is pretty small. Barbarians use Devastating Strike, which adds an additional 1d8(4.5) damage to every hit. Avengers use Oath of Enmity, which allows them to roll twice and use the better roll, including crits.

Warlocks use Eldritch Blast plus their Curse (1d10(5.5) + Ability(5)+1d6(3.5)).

Sorcerors use Chaos Bolt and add a second ability score. I assumed that the second ability modifier was equal to 3. I think such builds are possible. Chaos Bolt will bounce when an even number is rolled and attack a nearby target, dealing 1d6(3.5) damage on a hit, with a possibility of further bounces. No target may be hit more than once. This is (1/2 + 1/4 + ...)*3.5 = 3.5, assuming there are enough targets. But there aren't enough targets, so we'll call the damage contribution from bounces 2, which is roughly equivalent to saying there's an average of two extra targets.

For Rangers, we face two separate questions. First, should we use melee attacks, for which scimitar is the best one-handed (all Rangers dual wield, right?) or do we use longbow with its superior damage? Second, do we Twin Strike or not?

The math works out like this: let

W be weapon damage, including any magical plusses, etc. that would be counted on both damage rolls of a Twin Strike,

Ph be the probability of a hit,

A be the Abiility score modifier,

HQ be Hunters Quarry damage, and

MHQ be (1-Ph)*HQ.

For maximum damage output, Rangers should use Twin Strike instead of any other At-Will power (or Basic Ranged Attack) when W+MHQ is greater than A. That is if the weapon damage, plus the proportion of Hunter's Quarry that you aren't going to lose is bigger than the rangers Ability score modifier. Here's a chart of MHQ and W+MHQ for Heroic and Paragon tiers.



As the caption says, rangers should pretty much always use Twin Strike. For a longbow, which is what's shown, W+MHQ starts out at slightly over 5 and improves as targets become more difficult, because taking two shots gives you a greater chance of dealing HQ damage. At paragon tier, W+MHQ starts at 8, assuming only a +2 weapon. Do you think an ability score modifier is going to be 9 at paragon tier? I don't. With a scimitar, W+MHQ starts at 4, not 5, so it might be the case that the easiest targets should be attacked with something else, but it's not going to matter much.

The second issue is which weapon to choose for the Ranger, longbow or scimitar. (They're going to be dual wielding, so scimitar is the clear melee choice.) Longbow has more base damage (1d10 vs 1d8) but scimitar is high crit, dealing 1d8 extra damage on a critical hit. Here's the chart:



Longbow wins over Scimitar. Any pluses to damage apply equally to both weapons, typically. No particular Ranger can switch like this between weapons, because they use different ability scores. (Unless they have twin 16's or something.) Both builds are fine builds to play. But for purposes of comparison with other striker classes we want to put the Ranger's best foot forward, and that best foot is Twin Strike longbow.

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Ok, that's all the preliminaries. Now for actual data. First with non-magical weapons, like you might be a first level.



There's no real big winner, but the Ranger is at the top of the pack. The Avenger is below par for the easiest third of targets, but after that climbs to the top on the hardest targets. If you're saying to yourself, "but those never come up", I'll address that later. This is just the data.

Soon characters get magic weapons. Magic weapons are modeled by adding 1 to damage, and an extra 1d6(3.5) of critical damage per magic plus. Just for fun, let's look at some +2 magic weapons, appropriate for higher heroic tier.



The Twin Shot longbow Ranger has now emerged from the pack. This isn't spelled out directly in the PH, but pluses to damage add to all damage rolls and since the attacks in Twin Strike are rolled separately, each damage is a damage roll. So they count twice.

The Avenger with Oath has caught up, being slightly behind only on those targets needing only a 2 to hit. Rolling twice means an Avenger is never actually missing these targets. Everyone else (except the Ranger) has those "I rolled a 1" moments. Additionally, the Avenger, like the Ranger, is getting a lot more criticals. So the Avenger is at the top of the pack on the harder targets.

The Barbarian is the laggard. However, the extra damage die of the Barbarian is built-in, it does not depend on any circumstance or positioning. it does not have to be set up, it can't be taken away by any normal means, so that's probably an ok tradeoff.

The Ranger in one campaign I run has a Vicious longbow +2. Vicious weapons deal an extra 1d12(6.5) per plus on a critical hit, rather than 1d6. So let's model that.



This doesn't change things much relative to each other, other than boosting the Ranger and the Avenger, who make two rolls per standard action, doubling the chance of a critical hit.

Let's look now at paragon tier. I assume that key ability scores are now providing +6 to damage, and that the Sorcerer has boosted his secondary as well, giving him +10. I also add another +2 to damage for things like Weapon Focus and damage type specialization. Sneak Attack does 3d6(10.5), Hunters Quarry and Curse do 2d6(7). Devastating Strike add now 2d8(9) damage. Can the Avenger keep up?



Yes, it can. The Ranger continues to excel, but the Avenger is right there in the pack on the easiest target, and matches the Ranger on the difficult targets. The big surprise for this tier is the Barbarian. Because he gets extra damage in d8's instead of d6's, it starts to tell.

We haven't discussed either the effect of tactics and cooperation, or the difficulty of enemies. That will have to wait for another post. Looking at these graphs, I'd have to say the Avenger is working as intended, and not broken at all. If anything is broken, it's the Twin Striking Ranger.

That's all for now.