Archer Optimization Math...

[felwred]

Before anyone critiques this as being math-geek heavy - that's the audience
I am hoping reviews this to correct my maths and show me what I am missing.

I have a level 15 AL character that is focused on being an archer.
In a recent convention, I sat with a player who built a similar
concept but with assassin levels. Using the same weapon, he seemed
to dramatically out-damage my character. The math to it starts
getting complicated due to the number of variables as to how often this would
be true (are there surprise rounds, how many rounds of combat between short rests,
average AC of opponents, etc.). I wanted to get some thoughts about if there
was a much better damage dealing version of the archer concept than what I built.

He's level 11 fighter, level 1 cleric, level 3 ranger.
Feats: Sharpshooter, crossbow expert
Fighter/Ranger styles: Archer (+2 to hit)/Defense (+1 to AC)
+2 Longbow (PoTA)
Fighter - Battle Master with maneuvers meant to focus on battlefield control (D10)'s
Ranger - Horde Breaker to take extra attack against adjacent foes to target.

Right now, when using sharp-shooter he is +9 to hit for 17+D8(weapon)+D6(hunter's
mark)+(often) D10 for maneuver for 3 shots per turn. Average damage of 29 per hit
when using a maneuver, 24 when not.
If you assume 50% of the time, horde breaker can be used (pretty normal) - that
means he averages 3.5 attacks for 1.75 hits per round for 46.4 average damage per
round (assuming maneuvers used half the time).

It seems like the better DPS build with a bow would have been a fighter/assassin/ranger
build. If you went fighter 5 (2 attacks), ranger 3, assassin 7 assuming the same feats,
stats and equipment, it would be +9 to hit for 17+d8 (weapon)+d6(hunter's mark)+
4d6 (sneak 1/round per opponent)+D8 maneuver. Average damage for first attack on primary opponent is 38, then 35 on secondary opponent (via horde breaker) (all assuming sneak is easy
to set up), then 28 for second attack. If you assume the same hit rates and horde breaker utilization rates, that means an average of (first number is hit percentage) (.5*38)+(.25*35)(horde breaker half
the time)+(.5*28)= 41.75 damage.

The assassin seems to come in at lower damage steady state but would hit more on
rounds where he went first due to advantage. Those rounds, he likely hits 75% of the
time increasing damage to around 54 for the first round.

Anyone have thoughts on how these compare? If the player had gone with champion,
that first round of assassin damage would be huge (if he had surprise) but that doesn't appear to be the case.

Thanks!

Fred
case.

 

[Yunru]

Pet peeve (especially given you're from Westminster): It's maths. It's short for mathematics, which is plural because you're performing more than one operation.

 

[mellored]

Maths is the preferred method of communication on the char-op forum. Nothing to apologist for.

And if your interested in damage, you should take precision strike. Turning a miss into a hit does about 4x as much more then an extra d10 damage would. Menacing strike and trip certainly has it's uses but it's not DPR.

Hunter's Mark requires a bonus action, which means you don't get to use your crossbow expertise that turn. Unless you have 1 big target it's probably not worth losing the action to keep moving it around. Ensnaring strike is quality though.

You also might be seeing the assassin do more damage because his 1 attack is bigger.
i.e. 30+20+20 might look bigger then 20+20+20+20

I'm not sure what your getting from cleric. Bless is very nice though, if you can pre-cast it. A good replacement for hunter's mark that leaves your bonus action free.

And rolling a 20 on an assassins surprise round is still just a crit. Not 3x or anything. Champion doesn't actually add anything to the surprise round. Doesn't add much afterwards either.

And finally, remember that advantage doesn't stack. So if someone binds the enemy, your damage goes up, but it remains the same for the already hidden rogue.

 

[Blue]

I'm not too fond of either in terms of ASI. The first has 3, all from fighter, and two feats. The second only has two ASI, and two feats. Even if it's starting variant human for one of those feats, the second build has a max dex of 18 with AL point buy and I think that makes the rest of the numbers off. I'll pretend it's right for the rest of the post to do a comparison, but I really doubt it is.

BTW, if they don't get hit all that much as a ranged combatant, the first one can cast and maintain bless for a better chance to hit AND help out two others in their party, an option the second one doesn't have. Also could toss out a bonus action heal to stand someone up. The second one may required party resources get sneak attack. So the first seems to have better team synergies.

The first not only has a larger superiority die, it has one more of them, and two more maneuvers.

Action surge doesn't allow SA to be dealt again in the same round, so the first gets much more out of Action Surge.

First option should be: 17 + d8 (4.5) + d6 (3.5) = 25 (not 24), and 30.5 with a d10 (5.5) maneuver adding it.
So it's 3.5 * 0.5 * 25 = 43.75 without maneuvers, up to 53.375 with maneuvers on all hits.

Second option should be: 17 + d8 (4.5) + d6 (3.5) = 25 for base attacks (including hordebreaker, not sure why you put it as 35 - what am I missing?). d8 (4.5) Manuever can bring it up to 29.5, and sneak attack if you get at least one hit a round is 4d6 (14).
So pre-SA it's 2.5 * 0.5 * 25 = 31.25, up to 36.775 with maneuvers on all hits. SA requires at least one to hit. With 2 attacks it's 75%, with 3 attacks it's 87.5%. With 2.5 attacks it's the ugly 82.3%. (1 - 0.5 ^ 2.5). So expected SA damage per round is 14 * .823 = ~11.5.
So final damage is 42.75, up to 48.275 with maneuvers.

First does slightly better damage with or without maneuvers. With the team synergy stuff I pointed out, more superiority dice, the better Action Surge, plus the fact that the second doesn't really have the ASI for the 20 Dex and both feats so it's actual damage output is even lower, I'll take the first build as stronger in practice.

Side note, both could improve their damage by switching from a longbow to a hand crossbow if range allowed it (and you have a +2 hand crossbow). Crossbow Expert can't grant a bonus action attack for a Longbow, but d8 to d6 is a 1 point reduction per attack, but you get +17 static damage +1d6 weapon damage and +1d6 hunters mark, which absolutely eclipses that minor reduction. Does take up the bonus action.

 

[FrogReaver]

Before anyone critiques this as being math-geek heavy - that's the audience
I am hoping reviews this to correct my maths and show me what I am missing.

I have a level 15 AL character that is focused on being an archer.
In a recent convention, I sat with a player who built a similar
concept but with assassin levels. Using the same weapon, he seemed
to dramatically out-damage my character. The math to it starts
getting complicated due to the number of variables as to how often this would
be true (are there surprise rounds, how many rounds of combat between short rests,
average AC of opponents, etc.). I wanted to get some thoughts about if there
was a much better damage dealing version of the archer concept than what I built.

He's level 11 fighter, level 1 cleric, level 3 ranger.
Feats: Sharpshooter, crossbow expert
Fighter/Ranger styles: Archer (+2 to hit)/Defense (+1 to AC)
+2 Longbow (PoTA)
Fighter - Battle Master with maneuvers meant to focus on battlefield control (D10)'s
Ranger - Horde Breaker to take extra attack against adjacent foes to target.

Right now, when using sharp-shooter he is +9 to hit for 17+D8(weapon)+D6(hunter's
mark)+(often) D10 for maneuver for 3 shots per turn. Average damage of 29 per hit
when using a maneuver, 24 when not.
If you assume 50% of the time, horde breaker can be used (pretty normal) - that
means he averages 3.5 attacks for 1.75 hits per round for 46.4 average damage per
round (assuming maneuvers used half the time).

It seems like the better DPS build with a bow would have been a fighter/assassin/ranger
build. If you went fighter 5 (2 attacks), ranger 3, assassin 7 assuming the same feats,
stats and equipment, it would be +9 to hit for 17+d8 (weapon)+d6(hunter's mark)+
4d6 (sneak 1/round per opponent)+D8 maneuver. Average damage for first attack on primary opponent is 38, then 35 on secondary opponent (via horde breaker) (all assuming sneak is easy
to set up), then 28 for second attack. If you assume the same hit rates and horde breaker utilization rates, that means an average of (first number is hit percentage) (.5*38)+(.25*35)(horde breaker half
the time)+(.5*28)= 41.75 damage.

The assassin seems to come in at lower damage steady state but would hit more on
rounds where he went first due to advantage. Those rounds, he likely hits 75% of the
time increasing damage to around 54 for the first round.

Anyone have thoughts on how these compare? If the player had gone with champion,
that first round of assassin damage would be huge (if he had surprise) but that doesn't appear to be the case.

Thanks!

Fred
case.

I need more info to adequately compare the classes in your game.

How many combats per day do you typically have? How many short rests? How many rounds do combats last? Are you using a longbow the whole time or sometimes hand crossbows too? How often do you have to use your bonus action during combat to move hunters mark to a different enemy (or lose it's benefit from not moving it)? How often do you win initiative over at least 1 enemy in combat?


I can say for sure that champion is typically worse at damage than battle master.

 

[FrogReaver]

Using my standard assumptions:
6 combats a day at 4 rounds each and 2 short rests that are evenly distributed. Assume 16dex gives you 50% chance to hit without any other modifiers. 20 dex and archer style will be 70% to hit. The addition of a +2 longbow will be 80% to hit. This will be 50% chance to hit with the -5/+10 feat.

Damage from single attack with hunters mark: 1d8 + 1d6 + 5 + 2 + 10 = 25
Damage from single attack without hunters: 1d8+5+2+10 = 21.5
Total Damage from battlemaster superiority dice: d10*6(dice)*3(number or long and short rests in day) = 99 damage per day from battle master dice

***Assuming 3 casts of hunters mark per day means you are using it in 3 of the 6 battles per day
25*.55*3 = 41.25
41.25*12 = 495 DPR per day from attack action and hunters mark

21.5*.55*3 = 35.475
35.475*12 = 425.7

action surge:
25*.55*3*3 = 123.75

21.5*.55*12 = 141.9 damage per day from horde breaker

avg damage per day = 445 + 425.7 + 141.9 + 99 + 123.75 = 1235.5/ 24(rounds) =51.47 average DPR (primary fighter build)

 

[FrogReaver]

Rogue primary is a bit more complicated:

25*.55*2 = 27.5 (with hunters mark)
27.5*12 = 330

21.5*.55*2 = 23.65
23.65*12 = 283.8

horder breaker
21.5*.55*12=141.9

extra damage from assassian chance to hit feature (not calculated for sneak attack)**I'm assuming you can use it every battle.
79.75% - 55% = 24.75%

.2475*3*2*25+.2475*3*21.5+.2475*3*2*21.5 = .2475 * (150 + 64.5 + 129) = 85 damage


Sneak attack = 1-(1-.55)^2 = 79.75% chance to land sneak attack with no horde breaker
Sneak attack = 1-(1-.55)^3 = 90.8875% chance to land sneak attack with horder breaker
Weighted sneak attack chance = 85.31875% chance
.8531875*14*24 = 286.671 sneak attack

battlemaster dice
12d8 = 54

286.671 + 141.9 + 283.8 + 330 +85 + 54= 1181.371 / 24 = 49.22 average DPR

 

[FrogReaver]

One reason you likely feel the rogue primary does more damage is that if we looked at a harder to hit enemy his DPR drops less than the pure fighters. However, easier to hit enemies the fighter will do more on. I suspect that you notice how well your character does fighting bosses more than fighting the little enemies before the boss. In that case the boss usually has a little higher AC and you will notice. Also, the rogue will more consistently damage an enemy. 1 attack + sneak attack is good damage and a very good chance to happen. Landind 2/3 or 2/4 of the fighter primaries attacks isn't quite as good of a chance.

***These values can be drastically changed by number of encounters and short rests per day.

 

[felwred]

The character did 1 level of Cleric for a combination of role-play reasons and to use a necklace of prayer beads he earned. The stats and feats, etc. are accurate. Remember that fighters get extra feats/stat bumps at 6th level (thus 1 feat at 1st, stat at 4th, stat at 6th (now a 20), feat at 8th.) His next 2 levels will each result in a feat as well (ranger 4 and fighter 12) (getting hard to decide which feats to pick after the obvious sharpshooter and crossbow expert - thinking Alert and martial adept (for an extra die of maneuvers), observant (increases wisdom stat to the next even number and +5 to passive perception), Resilient (dex to have a much better chance of reducing damage on dex saves), tough (adding another 30 hp), or just take the con stat bonus). He has a +2 bow as well (to hit being +5 (20 dex), +2 bow, +5 (proficiency), +2 archery focus fighter - take the -5 for sharpshooter to get +10 dmg and you have an adjusted +9 to hit).

When you look at tier 3 adventures for AL, you are pushed hard to not take short rests. Typically, you see about 20 rounds of combat between short rests - possibly 30 if the adventure is particularly difficult. Take season 3, for example, Assault on Myrdramira has 1 long rest but no separate short rests. You have 4 major combats without a short rest then another roughly 2 before you are done (but the final fight is dramatically harder than the rest). Normal AC's you are facing are 19-21 with highly mobile targets.

Mellored's post had something I have completely missed on this character for more than 2 years. Precise is almost always more valuable as a maneuver than menacing or many of the others in terms of damage (discounting battlefield control that may be needed at some points). If you are doing 17+D8+D6 (average of 24) - taking a miss and making it a hit is far more valuable than adding another D10 (average 5). Early on, when you have a +1 to hit when using sharpshooter, precise was helpful occasionally but when you missed, it was usually by more than 4 or 5. Now, when you have a +9 to hit, your average miss will result in a die roll of 6 (since a roll of 11 or better will be a hit) giving you a 15 modified - average from a D10 is 5 resulting in a hit. That's a massive increase in damage. Thank you for that insight.

If the dice for precise were used to turn every other miss into a hit (increasing accuracy from 50% to 75%) while reducing average damage per attack by 5, the overall fighter/ranger/cleric damage will outpace the assassin/fighter/ranger pretty consistently (assuming AC 20 or less targets).

Are there any other synergies or bonuses I should be looking for to increase either hitting or damage? What about bless versus hunter's mark? It sounds like bless (against AC 20) slightly out-gains hunter's mark in damage but it would be very close.

Fred

 

[RulesJD]

A few things (we have the same build)

1. Remember to pre-Bless as often as you can, saving you that round in combat. What sort of Cleric are you btw? I'm assuming War for the +wis mod in Bonus attack for your Longbow.

2. If you want to pump this build's damage to the max, use Divine Favor (assuming you're a war cleric) instead of Hunter's Mark. Doesn't use up your Bonus action (which should be used for Crossbow Expert shot anyways) and is only +1 less than HM. If all hit (3 Extra Attack, 1 Bonus) you've lost out on 4 damage, but you easily make up for that when you don't have to burn your Bonus Action each round to move HM. Additionally, DF damage applies to your Horde Breaker target.