EDIT: idlewild found my error, the correct math and graph updated
Chart:
Now obviously Archery isn't the only factor in determining which weapon type is best for your build and playstyle, but if you were wondering (like me) which weapon would give you the best DPS at a certain gear point, now you know.
I am not sure that you have modeled the damage calculations correctly. Think of it this way, if you have 100 dps before crit/dmg modifiers, 100% crit and 50% crit damage, the xbow bonus takes you from 150dps to 200 dps whereas the bow bonus takes you from 150 to 172.5. At 100 dps, 50% crit and 50% crit damage, the xbow takes you from 125 dps to 150 dps whereas the bow takes you from 125 to 143.5. Similarly, at 0% crit, you go from 100dps to 100dps with the xbow and from 100 dps to 115 dps with the bow bonus.
From these examples, we can see that crit% does indeed have an impact on the viability of bows vs xbows. The issue in your calculations is that you are multiplying non-crits by the crit damage modifier.
It should be more along the lines of:
1.15(baseDPS)(1 + critChance * critDmg) = (baseDPS)(1 + (critChance)(critDmg + .5))
1.15 + 1.15(critChance * critDmg) = 1 + .5critChance + critChance*critDmge
.15 + .15(critChance*critDmg) = .5critChance
So your break-even depends on your existing crit chance and crit damage modifier. Also, the crit chance you have is a bit harder to model due to sharpshooter.
If my math is correct (and I'm not positive it is), it means that the damage bonus from Archery for bows beats the damage bonus for Xbows until you reach 333.33% crit damage (before Archery).
If this is true, I'm pretty sure there are a lot of players out there using Xbows that probably shouldn't be.
Can someone please double check this?
Math is right, conclusion is wrong. Xbows are better until you have 333% bonus crit damage without the passive.
I am not sure that you have modeled the damage calculations correctly. Think of it this way, if you have 100 dps before crit/dmg modifiers, 100% crit and 50% crit damage, the xbow bonus takes you from 150dps to 200 dps whereas the bow bonus takes you from 150 to 172.5. At 100 dps, 50% crit and 50% crit damage, the xbow takes you from 125 dps to 150 dps whereas the bow takes you from 125 to 143.5. Similarly, at 0% crit, you go from 100dps to 100dps with the xbow and from 100 dps to 115 dps with the bow bonus.
From these examples, we can see that crit% does indeed have an impact on the viability of bows vs xbows. The issue in your calculations is that you are multiplying non-crits by the crit damage modifier.
It should be more along the lines of:
1.15(baseDPS)(1 + critChance * critDmg) = (baseDPS)(1 + (critChance)(critDmg + .5))
1.15 + 1.15(critChance * critDmg) = 1 + .5critChance + critChance*critDmge
.15 + .15(critChance*critDmg) = .5critChance
So your break-even depends on your existing crit chance and crit damage modifier. Also, the crit chance you have is a bit harder to model due to sharpshooter.
Thank you! I knew I just needed someone else's eyes on it.
You're right, my original formula was wrong. Substituting y for crit damage and x for crit chance, your formula simplifies to:
Bows are better above the line, which means that for most players, bows still beat Xbows as far as Archery is concerned. Basically until you hit 35% crit, bows are better, and after that bows still win as long as you have enough crit damage from gear (which you probably should be stacking if you have 35% crit).
You're right that sharpshooter makes things a bit more complicated, but not by much, since at the crit levels required to make Xbows better, Sharpshooter resets pretty often.
Here's the basic explanation:
Above the Red line, hand Xbows are best.
Below the Black line, Xbows are best.
In between Red and Black, Bows are best.
The blue line compares hand Xbows to Xbows, 1-hand above the line, 2-hand below the line.
Now obviously Archery isn't the only factor in determining which weapon type is best for your build and playstyle, but if you were wondering (like me) which weapon would give you the best DPS at a certain gear point, now you know.
Here's the basic explanation:
Above the Red line, hand Xbows are best.
Below the Black line, Xbows are best.
In between Red and Black, Bows are best.
The blue line compares hand Xbows to Xbows, 1-hand above the line, 2-hand below the line.
Now obviously Archery isn't the only factor in determining which weapon type is best for your build and playstyle, but if you were wondering (like me) which weapon would give you the best DPS at a certain gear point, now you know.
Where is the legend? What do the axis represent? I'm not sure I get this
Where is the legend? What do the axis represent? I'm not sure I get this
Sorry about that, I couldn't find a online graph program that would let me label anything. X-axis is your crit chance, y-axis is your crit damage. Original post updated.
One simple conclusion is that if you have more than 250% crit damage, you'll get a higher damage bonus from Archery with a bow over a 2H Xbow, even at 100% crit chance.
I'm assuming this doesn't model any kind of an attack, right? The numbers tell me I should use a hand crossbow, (350% crit dmg, 30% crit) but honestly I have nothing to be gained from attacking faster for less damage. I use Cluster Arrow and Spike Traps as my damage dealers, which are solely dmg scaling based. So, switching to a hand-xbow with a considerably lower damage range and a faster attack speed might increase my hungering arrow damage, but it would ruin my frontloaded damage from these 2 big hitters as far as I know.
Yeah, it doesn't model anything beyond which weapon type would give you the greatest bonus to DPS from Archery. It's a much simpler comparison between 2h Xbows and Bows, since they can be used interchangably, but 1h Xbows have a lot more to consider, such as having a second Xbow for another potential 200% crit damage bonus. The chart most accurately compares using any of the weapons with a quiver, for the case where you have otherwise equal weapons of type.
Beyond that, there's other gearing considerations such as hatred efficiency and crit chance proc rates to consider when gearing your character, I just thought it was interesting to look at how the Archery bonuses stack up against each other.
Wrong math.
1.15(baseDPS)(1+ critChance * critDmg) = (baseDPS)(1+ (critChance)(critDmg + .5))
Why 1 here?
From N attacks you do N * critChance - crit, and not 1, or N, but N * (1 - critChance) - non crit.
So if we calculate dmg for 100 attacks it be:
100 * (1 - critChance) + 100 * critChance * critDMG.
True equation is:
1.15(baseDPS)((1-critChance) + critChance * critDmg) = (baseDPS)((1-critChance) + (critChance)(critDmg + .5))
and final: y = (-0.15/x + 0.65) / 0.15
Wrong math.
1.15(baseDPS)( 1 + critChance * critDmg) = (baseDPS)( 1 + (critChance)(critDmg + .5))
Why 1 here?
From N attacks you do N * critChance - crit, and not 1, or N, but N * (1 - critChance) - non crit.
So if we calculate dmg for 100 attacks it be:
100 * (1 - critChance) + 100 * critChance * critDMG.
True equation is:
1.15(baseDPS)((1-critChance) + critChance * critDmg) = (baseDPS)((1-critChance) + (critChance)(critDmg + .5))
and final: y = (-0.15/x + 0.65) / 0.15
Here's a simulation:
100 shots, 100 damage per shot, 30% crit chance, 50% crit damage, non crit damage
baseDamage = 100*100 = 10,000
Total damage = 70 normal hits for 7000 damage, 30 crits for 4500 damage, total damage = 11500.
Your formula seems to be attempting to calculate normal hit damage and adding critical hit damage, just like I showed in the example simulation, but the formula doesn't work the way you've written it.
If you want to think about it that way, the formula should look like this:
(baseDPS) [(1-critChance) + (critChance * (1 + critDmg))] ::: the key here is that the critical hits do 100% + bonus crit damage.
but when you simplify that you get:
(baseDPS) [(1-critChance) + (critChance * (1 + critDmg))]
(baseDPS) [(1 - critChance) + (critChance * 1 + critChance * critDmg)]
(baseDPS) [1 - critChance + critChance + critChance * critDmg]
(baseDPS) [1 + critChance * critDmg]
So I'm just going to try to tl;dr this for people. Xbow is only better if you have > 33% crit chance, before that bow is better.
Am I correct in what you're saying?
Well, partly anyway. Bow beats Xbow below 35% crit chance or so no matter what. Above that, it depends on your crit damage bonus, but even a small amount of crit damage from items can pretty easily push you into bow territory.
So for most players, bows are probably better than 2H Xbows, at least as far as Archery is concerned. But Archery certainly isn't the only variable to consider in making a weapon choice, just part of it.
Your formula seems to be attempting to calculate normal hit damage and adding critical hit damage, just like I showed in the example simulation, but the formula doesn't work the way you've written it.
If you want to think about it that way, the formula should look like this:
(baseDPS) [(1-critChance) + (critChance * (1 + critDmg))] ::: the key here is that the critical hits do 100% + bonus crit damage.
but when you simplify that you get:
(baseDPS) [(1-critChance) + (critChance * (1 + critDmg))]
(baseDPS) [(1 - critChance) + (critChance * 1 + critChance * critDmg)]
(baseDPS) [1 - critChance + critChance + critChance * critDmg]
(baseDPS) [1 + critChance * critDmg]
Which is what my formula is.
Man you misunderstand me.
When i wrote "critDmg" - i mean it full coefficient, multiplier. So +50% bonus dmg = 1.5 critDmg in my equation.
Then:
100 shots, 100 damage per shot, 30% crit chance, 50% crit damage, non crit damage
baseDamage = 100*100 = 10,000
Total damage = 70 normal hits for 7000 damage, 30 crits for 4500 damage, total damage = 11500.
its transform to :
((1-x) + x*y))*1.15 = ((1-x) + x*(y+0.5))
Try to solve this, your result must be y = (-0.15/x + 0.65) / 0.15
This true graph, your y = ((-0.15/x)+ 0.5)/.15 - wrong.
As i say, y - full multiplier before Archery. And x - crit chance. For example my DH has 167% = 1.67.critDmg and 41.5% = 0.415 crit chance.
its transform to :
((1-x) + x*y))*1.15 = ((1-x) + x*(y+0.5))
Try to solve this, your result must be y = (-0.15/x + 0.65) / 0.15
This true graph, your y = ((-0.15/x)+ 0.5)/.15 - wrong.
As i say, y - full multiplier before Archery. And x - crit chance. For example my DH has 167% = 1.67.critDmg and 41.5% = 0.415 crit chance.
Since we're using different values for what critDmg means, our graphs are going to be different. It's not that mine is wrong and yours is right, it's that they're coming from different values.
As you can see, it's the same curve, yours is just 1 unit above mine, which is exactly what we'd expect given what the critDmg variable stands for in our respective formulas.
If we count ONLY archery passive I could agree that Xbows are the best end game cos I have 45% crit and crit easy can be done 50%. But if we take a look on a bow with cold dmg the math going little bit diffrent cost you got 15% from bows, 20% from steady aim than your dmg is calculated and cult of the weak is counted at last for 15% over the slowed mob than you can use HA with Devoult and the dmg become unbelivable high I am able to crit with HA for 240k dmg and also to slow the target my NT crits for 100-150k and also slow the enemy. I have attack speed 2 per sec. The damage with X-bow with cold dmg is less I tryed this with better X-bow than my bow. For Hand crossbow there is no good Hand-crossbow with cold to test.
Well firstly I didn't say I thought Xbows were the best endgame. In fact, I think for most players Bows are probably best. At your crit level, you only need 75% crit damage from gear to push you into bow territory, which can be done with a single gem pretty easily.
Let me see if I understand you: you're saying that if you have a weapon with cold damage, and you're using culling the weak, that the cold weapon is better? I mean, I guess that's true, but it has nothing to do with archery. As I said in the original post, the bonus from Archery is only one part of what you should consider when gearing, but if you want to know what weapon is going to give you the best bonus from archery based on your current gear point, the chart tells you that. I think that's useful information, because if you're shopping for a weapon, you might want to know which weapon type is going to be best for you based on your current gear.
If you already know you want a cold damage weapon because you plan on using Culling the Weak, then comparing equivalent DPS cold bows to cold Xbows shouldn't make a difference. If you have testing that indicates otherwise, please share.
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Chart:
Now obviously Archery isn't the only factor in determining which weapon type is best for your build and playstyle, but if you were wondering (like me) which weapon would give you the best DPS at a certain gear point, now you know.
From these examples, we can see that crit% does indeed have an impact on the viability of bows vs xbows. The issue in your calculations is that you are multiplying non-crits by the crit damage modifier.
It should be more along the lines of:
1.15(baseDPS)(1 + critChance * critDmg) = (baseDPS)(1 + (critChance)(critDmg + .5))
1.15 + 1.15(critChance * critDmg) = 1 + .5critChance + critChance*critDmge
.15 + .15(critChance*critDmg) = .5critChance
So your break-even depends on your existing crit chance and crit damage modifier. Also, the crit chance you have is a bit harder to model due to sharpshooter.
Thank you! I knew I just needed someone else's eyes on it.
You're right, my original formula was wrong. Substituting y for crit damage and x for crit chance, your formula simplifies to:
y = ((-.15/x)+ .5)/.15
Which I've graphed here: http://fooplot.com/plot/k87can8y8r
Bows are better above the line, which means that for most players, bows still beat Xbows as far as Archery is concerned. Basically until you hit 35% crit, bows are better, and after that bows still win as long as you have enough crit damage from gear (which you probably should be stacking if you have 35% crit).
You're right that sharpshooter makes things a bit more complicated, but not by much, since at the crit levels required to make Xbows better, Sharpshooter resets pretty often.
Here's the chart! http://fooplot.com/plot/asrikurc1t
Here's the basic explanation:
Above the Red line, hand Xbows are best.
Below the Black line, Xbows are best.
In between Red and Black, Bows are best.
The blue line compares hand Xbows to Xbows, 1-hand above the line, 2-hand below the line.
Now obviously Archery isn't the only factor in determining which weapon type is best for your build and playstyle, but if you were wondering (like me) which weapon would give you the best DPS at a certain gear point, now you know.
Where is the legend? What do the axis represent? I'm not sure I get this
Sorry about that, I couldn't find a online graph program that would let me label anything. X-axis is your crit chance, y-axis is your crit damage. Original post updated.
One simple conclusion is that if you have more than 250% crit damage, you'll get a higher damage bonus from Archery with a bow over a 2H Xbow, even at 100% crit chance.
Yeah, it doesn't model anything beyond which weapon type would give you the greatest bonus to DPS from Archery. It's a much simpler comparison between 2h Xbows and Bows, since they can be used interchangably, but 1h Xbows have a lot more to consider, such as having a second Xbow for another potential 200% crit damage bonus. The chart most accurately compares using any of the weapons with a quiver, for the case where you have otherwise equal weapons of type.
Beyond that, there's other gearing considerations such as hatred efficiency and crit chance proc rates to consider when gearing your character, I just thought it was interesting to look at how the Archery bonuses stack up against each other.
1.15(baseDPS)( 1 + critChance * critDmg) = (baseDPS)( 1 + (critChance)(critDmg + .5))
Why 1 here?
From N attacks you do N * critChance - crit, and not 1, or N, but N * (1 - critChance) - non crit.
So if we calculate dmg for 100 attacks it be:
100 * (1 - critChance) + 100 * critChance * critDMG.
True equation is:
1.15(baseDPS)((1-critChance) + critChance * critDmg) = (baseDPS)((1-critChance) + (critChance)(critDmg + .5))
and final: y = (-0.15/x + 0.65) / 0.15
Am I correct in what you're saying?
Noobie#1931
Here's a simulation:
100 shots, 100 damage per shot, 30% crit chance, 50% crit damage, non crit damage
baseDamage = 100*100 = 10,000
Total damage = 70 normal hits for 7000 damage, 30 crits for 4500 damage, total damage = 11500.
My formula: 10,000 * (1 + (0.3)(.5)) = 10,000 * 1.15 = 11,500
Your formula: 10,000 * ((1 - 0.3) + 0.3 * 0.5) = 10,000 * (0.7 + 0.15) = 8,500
Your formula seems to be attempting to calculate normal hit damage and adding critical hit damage, just like I showed in the example simulation, but the formula doesn't work the way you've written it.
If you want to think about it that way, the formula should look like this:
(baseDPS) [(1-critChance) + (critChance * (1 + critDmg))] ::: the key here is that the critical hits do 100% + bonus crit damage.
but when you simplify that you get:
(baseDPS) [(1-critChance) + (critChance * (1 + critDmg))]
(baseDPS) [(1 - critChance) + (critChance * 1 + critChance * critDmg)]
(baseDPS) [1 - critChance + critChance + critChance * critDmg]
(baseDPS) [1 + critChance * critDmg]
Which is what my formula is.
Well, partly anyway. Bow beats Xbow below 35% crit chance or so no matter what. Above that, it depends on your crit damage bonus, but even a small amount of crit damage from items can pretty easily push you into bow territory.
So for most players, bows are probably better than 2H Xbows, at least as far as Archery is concerned. But Archery certainly isn't the only variable to consider in making a weapon choice, just part of it.
When i wrote "critDmg" - i mean it full coefficient, multiplier. So +50% bonus dmg = 1.5 critDmg in my equation.
Then:
10000 * ((1-0.3) + 0.3*1.5) = 10000 * 1.15 = 11500 too.
But my post about graph, and your wrong.
its transform to :
((1-x) + x*y))*1.15 = ((1-x) + x*(y+0.5))
Try to solve this, your result must be y = (-0.15/x + 0.65) / 0.15
This true graph, your y = ((-0.15/x)+ 0.5)/.15 - wrong.
As i say, y - full multiplier before Archery. And x - crit chance. For example my DH has 167% = 1.67.critDmg and 41.5% = 0.415 crit chance.
Since we're using different values for what critDmg means, our graphs are going to be different. It's not that mine is wrong and yours is right, it's that they're coming from different values.
Here's a chart with both your formula and my formula: http://fooplot.com/plot/db7rv3v5xb
As you can see, it's the same curve, yours is just 1 unit above mine, which is exactly what we'd expect given what the critDmg variable stands for in our respective formulas.
Well firstly I didn't say I thought Xbows were the best endgame. In fact, I think for most players Bows are probably best. At your crit level, you only need 75% crit damage from gear to push you into bow territory, which can be done with a single gem pretty easily.
Let me see if I understand you: you're saying that if you have a weapon with cold damage, and you're using culling the weak, that the cold weapon is better? I mean, I guess that's true, but it has nothing to do with archery. As I said in the original post, the bonus from Archery is only one part of what you should consider when gearing, but if you want to know what weapon is going to give you the best bonus from archery based on your current gear point, the chart tells you that. I think that's useful information, because if you're shopping for a weapon, you might want to know which weapon type is going to be best for you based on your current gear.
If you already know you want a cold damage weapon because you plan on using Culling the Weak, then comparing equivalent DPS cold bows to cold Xbows shouldn't make a difference. If you have testing that indicates otherwise, please share.