Disclaimer: This is not for those ww barb/range barb out there that uses Battle Rage only for Into the fray proc.

First, let's consider the two runes of Battle Rage:
Marauder's Rage: +3% critical chance, +30% damage done.
Bloodshed: +3% Critical chance, +15% damage done. When critical does 20% of damage done to nearby enemies.

I got curious as to whether bloodshed can become more favorable against Marauder's Rage, and if so at which point? So I did a little calculation. Things to consider:

Weapon damage (dmg) - This includes all the buffs, weapon dmg% modifier from the skill you use.
Critical hit Chance (cc) - This is your critical hit chance from your gear, passives, as well as 3% from battle rage.
Critical hit dmg (cd) - This is your critical hit bonus dmg granted by gear and passive.
Mobs hit (n) - The number of mobs affected by your skill that is capable of critical hit and proc Bloodshed.
Spread (p) - The number of how many mobs affected by the proc generated by Bloodshed rune.

*WARNING* Heavy math inc

First, let's consider the dmg done by an ability with Marauder's Rage buff:

Marauder's Rage dmg = (dmg)*(1+cc*cd)*n*1.3

Next, let's consider the dmg done by the same ability, but with Bloodshed rune. Each hits has (cc) chance to proc additional aoe hitting (p) enemies for (dmg)*(1+cd)*1.15*.2 damage.

You can see that how much critical chance is needed to equalize the dmg bonus depends on critical dmg bonus and the spread from your proc (the more packed the mobs are, the more mobs the proc will hit). On the other hand, it does not depend at all on whether how hard your skill hits, or whether it's aoe or single target skills, as long as it is capable of critting (rend for example, while can tick with "critdmg bonus", is not considered crit for the sake of proc).

Let's take a more concrete example. Say your frenzy hits for 50k dmg on a mob unbuffed and you have 50% chance to critical hit with 100% critical dmg bonus (you crit for twice the damage).

With marauder rage you hit one normal and one crit, you do 65k+130k = 195k damage
With Bloodshed you hit one normal and one crit that procs a nearby enemy (p=1) for 57.5k+115k+23k = 195.5k damage.

You can see that Bloodshed does slightly more damage at 50% critical hit and 100% critdmg with spreading to only 1 mob. This scale even better if the proc can hit more than 1 mob, requiring less critical chance and critdmg to equalize the benefit.

Putting the formula to calculate the required critical chance for other spread and critdmg we get

20% crit chance is easily attainable with weapon master+ruthless+battle fury buff alone, so with only expecting to spread to two or more mobs, bloodshed gives superior damage. In a more packed situation the crit requirement is even less and bloodshed keep doing even more damage.

Conclusion
If you have some crit stats on your gear, bloodshed will almost always give superior damage in aoe situations, regardless on whether you're using single target or aoe spells. Bloodshed also has the perk of being able to hit that mob that just missed your aoe or gives some aoe effect to your single target spell. Obviously, bloodshed give no bonus damage against single target, so if you plan on bursting on the last elite standing or the bosses marauder's rage will still be the best option for you.

While under the effects of Battle Rage, Critical Hits have a chance to cause an explosion of blood dealing 20% of the damage done to all other nearby enemies.

So it's either horribly worded, a fixed chance for direct damage abilities or, what I'd expect, the proc chance depends on the proc coefficient of the ability, just like CM does for Wizards.

You're right. The crit chance needs to be modified by the proc coefficient. A skill with proc coefficient will still leaves the math unchanged. However a skill with, say, proc coefficient of 0.5 will require (roughly) twice as much crit chance to gives more damage.

That being said, I can see that if you have 300% critdmg or so lots of crit, it's easy to see that bloodshed rune will outdmg marauder's rage in many situations.

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First, let's consider the two runes of Battle Rage:

Marauder's Rage: +3% critical chance, +30% damage done.

Bloodshed: +3% Critical chance, +15% damage done. When critical does 20% of damage done to nearby enemies.

I got curious as to whether bloodshed can become more favorable against Marauder's Rage, and if so at which point? So I did a little calculation. Things to consider:

Weapon damage (

dmg) - This includes all the buffs, weapon dmg% modifier from the skill you use.Critical hit Chance (

cc) - This is your critical hit chance from your gear, passives, as well as 3% from battle rage.Critical hit dmg (

cd) - This is your critical hit bonus dmg granted by gear and passive.Mobs hit (

n) - The number of mobs affected by your skill that is capable of critical hit and proc Bloodshed.Spread (

p) - The number of how many mobs affected by the proc generated by Bloodshed rune.*WARNING* Heavy math inc

First, let's consider the dmg done by an ability with Marauder's Rage buff:

Marauder's Rage dmg = (

dmg)*(1+cc*cd)*n*1.3Next, let's consider the dmg done by the same ability, but with Bloodshed rune. Each hits has (

cc) chance to proc additional aoe hitting (p) enemies for (dmg)*(1+cd)*1.15*.2 damage.Bloodshed dmg = (

dmg)*(1+cc*cd)*n*1.15 + ((dmg)*(1+cd)*1.15*.2)*p)*cc*nWe want to see when bloodshed dmg > Marauder's Rage dmg, so the turning point is when

(

dmg)*(1+cc*cd)*n*1.15 + ((dmg)*(1+cd)*1.15*.2)*p)*cc*n= (dmg)*(1+cc*cd)*n*1.3Simplifying the equation gives:

(1+

cd)*0.23*p*cc= (1+cc*cd)*0.15or,

cc= 0.15(0.23*p(1+cd)-0.15*cd)*MATH MODE OFF*

You can see that how much critical chance is needed to equalize the dmg bonus depends on critical dmg bonus and the spread from your proc (the more packed the mobs are, the more mobs the proc will hit). On the other hand, it does not depend at all on whether how hard your skill hits, or whether it's aoe or single target skills, as long as it is capable of critting (rend for example, while can tick with "critdmg bonus", is not considered crit for the sake of proc).

Let's take a more concrete example. Say your frenzy hits for 50k dmg on a mob unbuffed and you have 50% chance to critical hit with 100% critical dmg bonus (you crit for twice the damage).

With marauder rage you hit one normal and one crit, you do 65k+130k = 195k damage

With Bloodshed you hit one normal and one crit that procs a nearby enemy (p=1) for 57.5k+115k+23k = 195.5k damage.

You can see that Bloodshed does slightly more damage at 50% critical hit and 100% critdmg with spreading to only 1 mob. This scale even better if the proc can hit more than 1 mob, requiring less critical chance and critdmg to equalize the benefit.

Putting the formula to calculate the required critical chance for other spread and critdmg we get

Critdmg\Spread 1 2 3 4

100% 0.48 0.19 0.12 0.09

200% 0.38 0.14 0.08 0.06

300% 0.32 0.11 0.06 0.05

400% 0.27 0.09 0.05 0.04

20% crit chance is easily attainable with weapon master+ruthless+battle fury buff alone, so with only expecting to spread to two or more mobs, bloodshed gives superior damage. In a more packed situation the crit requirement is even less and bloodshed keep doing even more damage.

ConclusionIf you have some crit stats on your gear, bloodshed will almost always give superior damage in aoe situations, regardless on whether you're using single target or aoe spells. Bloodshed also has the perk of being able to hit that mob that just missed your aoe or gives some aoe effect to your single target spell. Obviously, bloodshed give no bonus damage against single target, so if you plan on bursting on the last elite standing or the bosses marauder's rage will still be the best option for you.

You're right. The crit chance needs to be modified by the proc coefficient. A skill with proc coefficient will still leaves the math unchanged. However a skill with, say, proc coefficient of 0.5 will require (roughly) twice as much crit chance to gives more damage.

That being said, I can see that if you have 300% critdmg or so lots of crit, it's easy to see that bloodshed rune will outdmg marauder's rage in many situations.