Fire blast vs. Sonic attack (ST Attack Chain)

I have been doing some calculations between these two blaster primaries considering resistance debuffs, defiance damage boost and incarnates. Now my calculations come out to fire besting sonic, but it's not that much off... 20-25 DPS. I'm on my cell phone now, so I'll post my calculations later; but I wanted to ask everyone what their calculations come to when comparing these primaries' best attack chains. The ones I compared were shriek-scream-shriek-shout vs. Flare-fireblast-blaze. I used the apocalypse damage process in flare and shriek.
Here are the assumptions I used:
Enough recharge to make each attack capable of a recharge time 1/4 of its base (300%).
Using assault, musculature 45% and an estimated enhancent values and set IOs; each attack has 148% damage bonus above base.
I didn't factor in accuracy as I figured comparing between the two the effects would be the same

I did these assumptions to avoid making mids builds and having to choose a secondary. I wanted a general analysis while being allowed the flexibility to choose a build to fit my other needs, whatever they may be.

Also feel free to tell me of better attack chains

Here are my calculations.

I make the following assumptions when calculating an attack chain’s Overall DPS.

First off, I assume the character will have enough recharge to accomplish 300% recharge enhancement overall for each power (so that the recharge of each power is 1/4 of its base recharge... such as making Drain Psyche perma). This is extremely high, but I give the character the benefit of the doubt that it could get enough set bonuses and perma-hasten (which provides 70% already) to accomplish this. It will take a lot of purples and other IOs, but assume 90% from enhancements, 70% from hasten, and 140% from set IOs such as LotG, purples, decimations and positron’s blast. Again, I am only giving the character the benefit of the doubt that they COULD get to 300% recharge enhancement if they wish to go for it… but likely the recharge won’t have to be that high. But I will provide what recharge enhancement is necessary for each attack chain I speak to below.

I assume the character will use the 75% Damage / 25% -resistance interface proc. For a fast enough attack chain, I assume (from prior calculations not included here) the average DPS added by this damage would be 30 (this assumes no pets while soloing) and the average resistance debuff to be about 4% (this is slightly rounded down than my prior calculations, but we'll attribute that to the occasional miss). I could go into the math deeper, and get more specific, but for benefit of the doubt let’s assume these values for all attack chains (Faster attacks per second would have higher DPS and resistance debuffs, but I'll assume its negligible enough to not complicate these calculations further).

I assume the character will have the musculature 45% damage enhancement alpha. With E.D. saturation, I assume each attack will have an average of 125% base damage improvement using the alpha and regular enhancements. Along with this, I also assume the character will have assault for 10.5% damage bonus and will achieve about 12.5% damage bonus from set IOs for a nice 148% overall damage enhancement to all attacks. This is an estimate that is reasonable while not using MIDs to make a full build, just to evaluate an attack chain with some mitigating factors incorporated.

I treat resistance debuffs as a damage bonus. So -10% resistance is the same as a 10% damage bonus, but is a multiplicative bonus, not an additive bonus. What I mean by that, the resistance bonus is factored in after all base damage in cumulated (this includes the damage enhancements and damage procs). For instance, say you have 10% damage bonus to a power and a 15% resistance debuff applied to the intended target. The overall damage above base value (100%) would be: (100%+10%) then apply the 15% debuff, to make the overall damage (110%)*(100%+15%) = 1.1*1.15 = 1.265. This is an overall 26.5% increase to damage above base instead of 25% if you treated it as cumulative (10%+15% = bad math). This gives sonic a very nice bonus, because it is multiplicative, not additive to base damage (which makes up for its low base damage a lot) and it is applied after everything. Meaning damage procs get the damage bonus (or rather, resistance debuff bonus) too. It’s a double whammy of awesome. Also, when teaming, everyone on your team attacking the target gets this bonus, now making is a triple whammy of awesome.

I assume the apocalypse damage proc is used in the most used attack of the attack chain. I don’t use the PvP proc for these assumptions, but I will assume 1 damage proc from Positron’s blast if an attack chain used a Targeted AoE attack. If I use a melee attack, I'll assume the Hecatomb proc in it. But I'm really only wanting to look at ranged primary attack chains so that I'm not limited to having to be a blapper (within melee range) and I don't want to have to pre-decide what secondaries are to be used.
I won’t incorporate accuracy for the attack chain, I assume that the accuracy to hit for each attack chain is the same and assume it would be approximately the same ratio of difference when accuracy is factored in. It will make the calculations below easier to follow. This is merely a simple enough look at a general comparison between potential attack chains. I welcome you to provide deeper analysis if you choose.

Here are my formulas for calculations (along with what is known and unknown):

Base Damage = 62.56 (This is the base damage for a blaster’s ranged attack)

Chain DMG Scale = ??? (This is the accumulated damage with in the attack chain, in terms of its ratio to base damage - it'll make sense when I go through the calculations)
Chain duration = ??? (how long is the attack chain?)

Defiance Chain Damage Bonus (DCDB) = ??? (Assumes a consistently hitting attack chain and averages the inherent damage bonus over the duration of the attack chain)

Damage Bonus = DCDB + 148 (from the assumption mentioned above, assault, enhancements, and musculature)

Resistance Damage Bonus = ??? + 4 (from the assumption mentioned above, reactive proc. This calculates similarly to ICDB for sonic attacks)

Proc DPS = (Cummulated average Proc Damage in chain)/(Chain duration) + 30 (from the assumption mentioned above, reactive proc) (Apocalypse Damage Proc averages to 35.7 damage per hit)

Chain DPS = (Base Damage)*(Chain DMG Scale)*(Damage Bonus)/(Chain duration) + Proc DPS (This is the total DPS of the attack chain prior to factoring in the resistance debuffs)

Final DPS = (Chain DPS)*(Resistance Damage Bonus)

Reiterating what some of these knowns/unknowns are:

Base damage for ranged blaster attacks is 62.56

The Chain DMG Scale is the cumulative damage of the entire chain (i.e. a Shriek-Scream-Shriek-Shout chain would be .84+1.32+.84+2.12 = 5.12.

Damage Bonus is the cumulative damage enhancement for each power. This includes enhancements, IO set bonuses, and powers (assault). I make the assumption that each power will have relatively the same overall damage enhancement so that I don’t have to make a complete Mids build to analyze… just gives me a rough overall estimate.

NOW FOR THE REAL FUN --- The attack chains:

*SONIC ATTACK*
*Note* I know that Scream does DoT and that some of its ticks of damage gets the benefits of its own resistance debuff. I did not factor this in for the calculations, so keep that in mind when my final numbers are presented. Its actual DPS will be a little bit higher if I did factor this in.

Shriek à Scream à Shriek à Shout Requires recharge enhancement of 172.5% above base (reasonable)

Base Damage = 62.56

Chain DMG Scale = (0.84 + 1.32 + 0.84 + 2.12) = 5.12

Chain Duration = (1 + 1.67 + 1 + 2.67) = 6.34 seconds

DCDB = (6.6%*8.5s + 11%*9.17s + 6.6%*8.5s + 17.6%*10.17s)/6.34s = 61.8394%

Damage Bonus = 148 + 61.8394 = 209.8394%

Resistance Damage Bonus = (13%*5s + 13%*7s + 13%*5s + 13%*10s)/6.34s + 4 = 59.3628%

Proc DPS = (35.7+0+35.7+0)/6.34s + 30 = 41.2618 DPS

Chain DPS = (62.56)*(5.12)*(1+2.098394)/6.34s + 41.2618 = 197.7977 DPS

Final DPS = (197.7977)*(1+0.593628) = 315.2161 DPS

*FIRE BLAST*

(I didn’t use fireball because of high recharge and low defiance damage bonus, although it does have a great individual DPS)

Flare à Fire Blast à Blaze Requires a recharge of 274.5% above base (very high)

Base Damage = 62.56

Chain DMG Scale = (1.01 + 1.48 + 3.02) = 5.51

Chain duration = (1 + 1.67 + 1) = 3.67s

DCDB = (6.6%*8.5s + 11%*9.17s+6.6%8.5s)/3.67s = 58.0572%

Damage Bonus = 148 + 58.0572 = 206.0572%

Resistance Damage Bonus = 4%

Proc DPS = (35.7 + 0 + 0)/3.67s + 30 = 39.7275

Chain DPS = (62.56)*(5.51)*(1+2.060572) + 39.7275 = 327.1924 DPS

Final DPS = (327.1924)*(1+0.04) = 340.2801 DPS


Now, I don’t know what the best attack chain would be for Fire Blast using the above formulas, but Flare-FireBlast-Blaze may not be optimal. It may be best to replace FireBlast with FireBall or to incorporate a melee attack from the secondary (let’s assume the MM secondary because it’s popular for soloing AVs and GMs). Here’s some looks at other Fire Blast attack chains.

*FIRE BLAST #2*

FlareàFire BlastàFlareàBlaze Requires recharge of 172.5% above base

Base Damage = 62.56

Chain DMG Scale = (1.01 + 1.48 + 1.01 + 3.02) = 6.52

Chain duration (1 + 1.67 + 1 + 1) = 4.67

DCDB = (6.6%*8.5s + 11%*9.17s+6.6%8.5s+6.6%*8.5s)/4.67s = 57.6381%

Damage Bonus = 148 + 57.6381 = 205.6381%

Resistance Damage Bonus = 4%

Proc DPS = (35.7 + 0 + 35.7 + 0)/4.67 + 30 = 45.2891 DPS

Chain DPS = (62.56)*(6.52)*(1+2.056381)/4.67s + 45.2891 = 312.2422 DPS

Final DPS = (312.2422)(1.04) = 324.7319 DPS

*FIRE BLAST #3*

FlareàMind ProbeàFlareàBlaze Requires recharge of 215.5% above base

Range Damage Base = 62.56

Melee Damage Base = 55.61

Ratio Melee to Range = 55.61/62.56 = 0.8889

Mind Probe Damage Scale = 1.64*0.8889 = 1.4578

Chain DMG Scale = (1.01+1.4578+1.01+3.02) = 6.4978

Chain duration = (1 + 1.17 + 1 + 1) = 4.17s

DCDB = (6.6%*8.5s*3 + 7.7%*8.67s)/4.17s = 56.3691%

Damage Bonus = 148 + 56.3691 = 204.3691%

Resistance Damage Bonus = 4%

Proc DPS (35.7 + 14.35 + 35.7 + 0)/4.17s + 30 = 50.5635 DPS

Chain DPS = (62.56)*(6.4978)*(1+2.043691)/4.17s + 50.5635 = 347.2704 DPS

Final DPS = (347.2704)*(1.04) = 361.1612 DPS

*NOTE* This is the best Final DPS So far, if you’re willing to blap. (Also, you could put much more procs into Mind Probe for additional DPS).

*FINAL SUMMATION*
Fire is still best for ST damage. It also is king for AoE damage which is great for the appropriate content. But the pros for Sonic Attack show that it is great for ST damage as well, and it is great when teaming (everyone gets the resistance debuff bonus). Sonic Attack also doesn't require as much global recharge to accomplish its top attack chain, but you may still need high global recharge for other needs such as perma-Hasten/perma-Drain Psych/perma-PB/etc.

I like your methodology. It's similar to mine, and having spent the last couple of days mulling over various attack chains and slotting options for Defender Sonic Blast, I find your post especially interesting.

That said, I see two potential hiccoughs in your calcs: first, you're not taking into account Arcanatime, which is a pet name for the way the server influences cast times (named after Arcanaville, who invented the method for accounting for those server ticks). Second, and this is a less solid assertion on my part, but AFAIK you're underselling Reactive's DoT a bit.

On the first point, your Sonic attack chain should go from this:

"Chain Duration = (1 + 1.67 + 1 + 2.67) = 6.34 seconds"

to this: "Chain Duration = (1.188 + 1.848 + 1.188 + 2.904) = 7.128 seconds"

I don't have time right now to go over the implications of that change, but I imagine it'll make a pretty big difference, given that the duration of your attack string affects both DPS and average -RES debuff.

On the second point, this post describes how Reactive's DoT most likely works given the available evidence at the moment. In any case, it seems pretty clear that as long as we're not discussing scenarios with multiple Reactive-proccing attackers (oodles of pets/teammates), the Reactive DoT will not reach its stacking limit of 8 -- and thus what determines Reactive's DPS in this sort of calculation is the character's attack speed. It's basically a normal proc for our purposes.

I'll come back later when I have more time.

Quote:

Originally Posted by Iggy_Kamakaze Nice build

blaze-blast-probe requires 252% in blaze (using Mids' Arcanatime), and might do a little better for fire.

It's also very much assuming a solo situation. Fire's DoT adds only to your damage, sonic's -resist adds to everyones damage on the target.

While it dealt with Defender Sonic Blast this is a very detailed thread dealing with the attack chains possible with Sonic Blast.

http://boards.cityofheroes.com/showthread.php?t=195250

I am more interested in Beam Rifle in comparison to Fire. If you take Disintegration into consideration, how does it compare to Fire?

Thank you Obitus for the excellent replies and for performing the new calculations incorporating arcanatime. I wanted to look at the Reactive DoT interface proc some more to get an accurate assessment of its DPS. Now I don't know what the facts are for this proc, but assuming you're correct (stacks up to 8 times, there are 5 ticks for each proc where each tick has a 75% chance at firing, and each tick of damage is 13.36 damage) then I figure the character has no chance at saturating the number of DoT procs on a single target... so I will look at what the DPS added for each attack would be using binomial probability of a 75% Dot 25% -res proc (T4)

Here is my formula:
DPS added (prior to -res buffs) = (13.36)*[5C0*(.75^0)(.25^5)*0+5C1*(.75^1)(.25^4)*1+5C2*(.75 ^2)(.25^3)*2+5C3*(.75^3)(.25^2)*3+5C4*(.75^4)(.25^ 1)*4+5C5*(.75^5)(.25^0)*5
Which equals:
13.36*[1*1*0.0009765625*0 + 5*0.75*0.00390625*1 + 10*0.5625*0.015625*2 + 10*0.421875*0.0625*3 + 5*0.31640625*0.25*4 + 1*0.2373046875*1*5]
Which equals 13.36*(3.75) = 50.1

So you're right Obitus, you can expect a 50.1 Damage increase for each attack. Instead of using 30 DPS, I will calculate the number of attacks per second, and multiply it by 50.1 for my calculations.
As for the -res debuff. That will stack up to 4 times for a 10 second duration I believe (maybe 8.3 seconds). Now this could saturate, so I need to keep that in mind with my calculations. Also, this is also dependent on the number of attacks per second... or better yet, the number of attacks in a 10 second duration (or 8.3 seconds if my assumption of the -2.5% resistance debuff is wrong). Now, I won't bog down this post with all the numbers, but I will look at what the expected -res debuff % would be if one can achieve 5, 6, 7, or 8 attacks per 10 seconds. I'll show how it's calculated for the 8 attacks, but after that I'll just post the results.

For 8 attacks over 10 second duration:
average -res debuff would equal:
0*8C0(.25^0)(.75^8) + (-2.5%)*8C1*(.25^1)(.75^7) + (-5%)*8C2*(.25^2)(.75^6) + (-7.5%)*8C3*(.25^3)*(.75^5) + (-10%)*8C4*(.25^4)(.75^4) + (-10%)*8C5*(.25^5)(.75^3) + (-10%)*8C6*(.25^6)(.75^2) + (-10%)*8C7*(.25^7)(.75^1) + (-10%)*8C8*(.25^8)(.75^0)
Which equals : -4.920196533203125% resistance debuff.

For 7 attacks over a 10 second duration: -4.33929443359375%
For 6 attacks over a 10 second duration: -3.73779296875%
For 5 attacks over a 10 second duration: -3.12255859375%

Now, I don't have time now to do all my numbers again, I'll leave that for a later post. But using my Fire Blast #1 attack chain of Flare - Fire Blast - Blaze, my attacks over a 10 second period would be about 7 (using arcana time and rounding down from 7.102). Using my Sonic #1 attack chain of Shriek - Scream - Shriek - Shout, my attacks per 10 second period would be 5.612.
Using these numbers, my Fire Blast should have proc DPS to be 7.102*50.1/10s = 35.58 DPS and the resistance debuff would be approximately the -4.3393% (from above).
My Sonic Attack should have proc DPS to be 5.612*50.1/10 = 28.11 DPS and the resistance debuff would be between -3.12255% and 3.73779%.
So, as you can see, having more attacks per second is much better when using the reactive interface proc, and as the attack chains for Fire Blast are very good in this area, it pulls further away from Sonic Attack.
Now, as mentioned before, the Sonic Attack is still very good ST DPS while solo, but it just can't quite compare with Fire Blast... however its benefits are far better with a team (as everyone gets the buff) and when using a pet. So there you have it, for now (as I continue my overuse of the word "now"). I'll run more numbers later but this week I'm away from home and don't have easy access to a computer. If you have attack chains that you'd like me to calculate, post them, and I'll jput out final numbers using the methods mentioned in this thread.

Sonic is my favorite blast set by far.

The way I see it, I'm not losing much damage by playing Sonic instead of Fire, especially on teams, and solo, few sets have as much utility to go along with good damage like Sonic.

When calculating a set's damage, it also pays to consider what that set brings to the table to keep you alive, because dead toons deal no damage. And Siren's Song is HUGE in that regard.

This thread was a great read . I'm laughing to myself because I HATE math and yet I have found myself doing this very thing when it came to builds I wanted to work on in mids.

@Obitus:

I'm not sure what factors your using to arrive at your DPS, but the way your applying the extra damage done from the -res effect looks wrong. You appear to be calculating your DPS, then adding up how much -res the enemy will have accumulated by the end of the chain, and then multiplying your dps by that accumulated -resistance.

In the game that -res is, I believe, applied after you finish executing the attack. So the first attack you use will have no -res attached to it and do it's basic damage, while the next attack you use will only be multiplied by the -resistance that is applied from the first attack, and so on. So you should have something like:

((Shriek Damage) + (Scream Damage * 1.13) + (Shriek Damage * 1.26) + (Shout Damage * 1.39)) / Total Activation Time = Damage Per Second w/-Res

The actual DPS should be significantly lower than what you are depicting.

Thank you for clearing it up. I can understand, and agree with, why you would adopt that methodology against a single powerful enemy who takes a prolonged period of time to defeat as it does give an apparently more realistic representation of what the Sonic blaster will be capable of doing for that kind of scenario. I apply a similar logic when I am calculating for double stacked Blinding Feint or Follow Up on my melee AT's.

Still, I don't think it's insignificant to, at very least, be aware that a Sonic Blaster has a period of time where he has to stack his -res effect on the enemy before he can achieve a damage per second which factors in a constant -res debuff. Most of the time we are not fighting a single opponent that takes several minutes to defeat, but instead many quick skirmishes against several dozen individual enemies. While you could argue that such a scenario is more relevant to a 'who has better aoe potential' type of discussion, I still think it's important that a Sonic Blaster is aware that he is going to have to rebuild his -res debuff every time he has to target a new enemy, which is going to happen frequently during most combat scenarios in the game. His calculated DPS is going to more often resemble what his 'first' attack chain returns, rather than what he is capable of against an Arch Villain.

Guys, I think this discussion should include Beam Rifle! My Beamer is lvl 24 now and I swear his ST attack is so high.

How do you calculate -regen effect to show its "DPS" number, assuming the less the target heals back, the more "dps" you have?

I really think Beam rifle's ST can beat Fire Blast if we include Beam's -regen effects.

Ok, here's the info I copied down from in-game data. You are right that regen effect is target specific. I guess I can care less about minions and lieuts and maybe even bosses. But let's start with boss and higher ranks?

Single Shot
92.72 Damage
1s Cast
4s Recharge
-75% Regen when the target is Disintegrated

Charged Shot
132.76 Damage
1.62 Cast
8s Recharge
+15.39 bonus damage when the target is Disintegrated

Disintegrate
135.13 damage over 10.50s
1.9s Cast
10s Recharge
-150% Regen for 15s
(you can stack this attack for more DoT damage. I don't think the -regen part stacks but I am not 100% sure)
(12.50% Defiance buff for 9.4s)
* I just double check. You cannot enhance -regen buff with +healing enhancements but not sure about Power Boost. If Power Boost can improve -regen, then I really regret taking /Fiery. I just haven't tried /Fiery so I chose it)

Lancer Shot
162.79 Damage
1.9s Cast
11s Recharge (100% chance mag 3 stun!)
+26.53 bonus damage when the target is Disintegrated
(12.50% Defiance buff for 9.4s)

Not sure how Piercing Shot works into the equation but there you go.

Piercing Beam
115.11 Damage
2.33s Cast
18s Recharge
-13% Resistance to all for 10s (which means it is possible to keep it on the same target)
+37.99 bonus damage when the target is Disintegrated (the bonus damage is quite high)
(5.90% Defiance buff for 9.83s)


Ok, do your math! Basically, you start the fight with Disintegrate and I assume you follow with Piercing to get the debuff and then tier 1, tier 2 and 3 and cast Disintegrate again, although I am not really sure how long the Disintegrated effect lasts. Maybe it's just 15s so you have to cast Disintegrate again? The mobs die too fast for me to notice if Dis ever "expires" on the same target. lol My Beamer is only lvl 24 ATM.

Interesting analysis... one thing I'm curious about is how Sonic and Fire compare when dealing with more typical builds that don't have any purples and don't have the recharge to do a T1 -> T2 -> T3 attack chain. Basically, something more like Flares -> Fire blast -> Flares -> Blaze vs Shriek -> Scream -> Shriek -> Shout, with no procs other than Reactive (since so many Blaster builds use 6 Thunderstrikes in their ranged attacks). I find those sort of comparisons more interesting because that's sthe sort of build I'm likely to be running... even if I do plan to spend two or three billion on a Blaster I'm still running Thunderstrikes because I like to solo, and not being hit is good for soloing.