Weapon Damage Vs Weapon Speed

[Yaldi]

Ok so on my way home from work I had a sudden thought. When is Weapon Damage better to get than weapon speed.

 

I don't have the knowledge of mechanics of some people here so i can't do the maths myself. So can anyone answer if there is a point where it becomes more cost efficient to but weapon damage items like galactic defender or contamination shard over weapon speed? Or is it just better to get to weapon speed cap then get damage?

 

Also where do crits come into all of this? And Items with stats?

 

There is so much to cover so hopefully we will get some surprising answers

[Mus]

I gave this a bit of thought and came up with a basic formula to answer your question.

 

Let wpn dmg = x , wpn speed = y. Then DPS = x/y.

 

Increasing wpn dmg is additive, ie '+35 wpn dmg'. This corresponds to wpn dmg going from x to x + dx.

Increasing wpn speed is multiplicative, ie '+25% wpn speed'. This corresponds to wpn speed going from y to ky.

 

Hence we can see what happens to the DPS when we increase wpn dmg, or wpn speed:

 

For an increase in wpn dmg, DPS goes from x/y to x/y + dx/y ... (1)

For an increase in wpn speed, DPS goes from x/y to (1/k)(x/y) ...(2)

 

So we want to see when (1) is better than (2), i.e when is it better to increase wpn dmg rather than wpn speed.

Simply set (1) > (2) and we end up with a simple condition on dx and k:

 

dx > x[(1/k)-1] ... (3)

 

So you only need to know your current wpn dmg, and the increases in wpn dmg and wpn speed that you are considering to see which is better. If (3) holds then the increase in wpn dmg is better than the increase in wpn speed.

 

Note: To calculate k: Say you are considering an increase in wpn speed by s%. Then k = 1 - (s/100). eg increase wpn speed by 25% implies k = 0.75.

[eSeS]

Wow. Can you explain that for Mathfobics?

[residente]

meh, int > weapons

 

@op i guess the speed is better, just from experience

[Mus]

There isn't a whole lot of explanation to add. Everything you need is in my post, I merely skipped out the algebra. You don't really need to follow the Maths involved, just use the formula at the end.

 

Residente, wpn speed is not always better than wpn dmg. The Maths has proven that.

[heimdallr]

you can do a linear programming formula that will find the point/pointS at which the changes occur.....BUT regardless of math you got to count other stuff too.....for example....if you have pyre and you have attack speed you increase pyre procs frecuency....you cannot increase the pyre damage with your weapon damage(i mean the unique)....think other stuff too...like if you have an item that stuns or an item that reduces enemy resistance(yeah u know what 2 items I´m talking about)....you want to proc those effects as often as possible.....therefore most of the time attack speed will be better...theres like no way you go 100% non procable items on any build...they are too good to not have them

[Mus]

I was only considering the change to your DPS. If you wanted to consider effects of item passives then it seems the wpn speed will become more useful, not necessarily for DPS, but for their stuns etc. The Maths would become very complicated (especially for Pyre) so there's not much point trying to do it. But the formula still holds for computing DPS increases, which I think is useful.

[Yaldi]

@Residente I think from experience that this is true but that doesnt mean we are right maybe we should get to like 75% max weapon speed and then get more damage for the most efficient DPS.

 

@Mus your math seems to make sense but it doesn't take into account whether or not weapon speed items or damage items cost more or less than each other:)

 

@hemidallr yes items passives count alot. But Contam shard gives no weapon speed so when does it become efficient to buy that item if weapon speed is such a big factor

[Doom]

There are some things to note:

 

1: Weapon speed has a cap, while weapon damage does not (yes once you are level 18, and have 6 masumes as well as potions, you will not be able to get any higher weapon damage, however it is POSSIBLE, while for weapon speed you cannot go over attack per 0.47 seconds or whatever the number was. Yes, you can add time, but time items and abilities are much less abundant than weapon damage ones).

 

2: Weapon damage is affected by physical resist, weapon speed is not.

 

3: How do you compare the two? 1% weapon speed vs 1 point of damage? In that event the amount of added weapon damage should be looked at as a percentage vs that already existing to know truly (For example, say a hero has 1000 weapon damage and an attack every 1.8 seconds. Adding +10 physical damage would be way worse than 10% weapon speed, because it is only a 1% increase in weapon damage vs a 10% increase in weapon speed. But if that hero has 10 weapon damage, and an attack ever 1.8 seconds, that extra 10 weapon damage is way better than 10% weapon speed, because it increases weapon damage by 100% while weapon speed only by 10% still.

[Yaldi]

3: How do you compare the two? 1% weapon speed vs 1 point of damage? In that event the amount of added weapon damage should be looked at as a percentage vs that already existing to know truly (For example, say a hero has 1000 weapon damage and an attack every 1.8 seconds. Adding +10 physical damage would be way worse than 10% weapon speed, because it is only a 1% increase in weapon damage vs a 10% increase in weapon speed. But if that hero has 10 weapon damage, and an attack ever 1.8 seconds, that extra 10 weapon damage is way better than 10% weapon speed, because it increases weapon damage by 100% while weapon speed only by 10% still.

 

very good point but how does this relate to the actual game in real terms? Is early weapon damage better because you have less damage or does it mean you should raise you attack speed to a point then you get a better % increase in dps by getting a damage item?

[Midknight]

Weapon damage is good early on and after you've capped speed. Keep in mind that weapon "speed" is a misnomer since it doesn't determine how "fast" you attack but rather how "slow" you attack because it's a measure of the cooldown between attacks. If your weapon cooldown is 2 and you have a +20% bonus, it calculates as 2 / 1.2 = 1.67 cooldown. In turn, a 20% attack speed bonus translates into 20% more DPS. So, to compare the two, you need to convert the Weapon Damage bonus into a percentage of your current weapon damage. For example, if you have 100 weapon damage, +10 weapon damage is a 10% increase and would match a 10% attack speed bonus, not counting proc'ed effects. But another +10 weapon damage to the 110 value is only a 9.09% increase while another 10% attack speed bonus is a composite value, it is +10% to the current value after the previous +10% was calculated, yielding a net 21% increase rather than just 20%. In other words, weapon damage diminishes in value while attack speed accelerates. However, your composite attack speed bonus cannot go above a +400% bonus. If you ever need to pick between attack speed and weapon damage, attack speed wins out about 9 times out of 10. For a simple comparison, consider a 20% attack speed bonus. To match that, you'd need a weapon damage bonus greater than 20% of your current weapon damage. If your current weapon damage is 300, you need better than +60 weapon damage bonus to match +20% weapon speed. But if you only have 100 weapon damage, you only need to beat +20. If your attack speed bonus is already at +400%, then more will not help you and you can default to weapon damage if need be.

 

Agility also gives weapon speed; 0.29% per point of Agi and it also composites as other attack speed bonuses do. With 400 Agi, your Agi composite speed bonus sits at +218%. Add on, say, a +15% and two +20% and you get +427% which breaks your cap. If you had 300 Agi, your base speed bonus is +138% and the same 15% and 2x 20% bonuses will bring you to +294%. You'd need an additional +25% composite bonus to fall just below the speed cap.

[Mus]

For example, if you have 100 weapon damage, +10 weapon damage is a 10% increase and would match a 10% attack speed bonus

 

No this is not correct. Plug this into the formula I gave and you see that the +10% wpn speed gives greater DPS increase than the +10% wpn dmg. Another way to see this is by noticing that 1.1 < 1/0.9.

 

bzzt, wrong. -Midknight

Edited January 15, 2013 by Midknight
Disinformation

[TungVu]

It depends on team comp. You are assuming that your enemy will let u stay in 1 spot during a team fight and shoot at them. So let me cut it out for u:

If your team can peel for you/enemy team only has soft initiation then you should get a hybrid of weapon dmg and weapon speed.

If enemy team has an assassin/hard initiation/or your team can't protect you very well leading to u having to kite for most of the time in a team fight then its better to skip weapon speed to the later part of the game.

Ofc I'm only talking about early game, late game ADC build should be standard. Its just that you should prioritize weapon dmg b4 weapon speed on your way to the full build if you have to constantly move/kite in a team fight.

[WhaleTits]

It depends on team comp. You are assuming that your enemy will let u stay in 1 spot during a team fight and shoot at them. So let me cut it out for u:

If your team can peel for you/enemy team only has soft initiation then you should get a hybrid of weapon dmg and weapon speed.

If enemy team has an assassin/hard initiation/or your team can't protect you very well leading to u having to kite for most of the time in a team fight then its better to skip weapon speed to the later part of the game.

Ofc I'm only talking about early game, late game ADC build should be standard. Its just that you should prioritize weapon dmg b4 weapon speed on your way to the full build if you have to constantly move/kite in a team fight.

 

SHHHHHH don't tale them why i build nova like i build novaaaaaaaa

[Midknight]

No this is not correct. Plug this into the formula I gave and you see that the +10% wpn speed gives greater DPS increase than the +10% wpn dmg. Another way to see this is by noticing that 1.1 < 1/0.9.

 

The inherent problem being that the formula you gave is incorrect. This has been tested by myself and others. So don't spread disinformation.

[akanna]

I think it also depends what hero you are using

 

For example:

 

With leo attack speed is far more important to get first because his ult procs on attack, so more speed = way more damage, you can actually do quite well maxing attack speed before getting any damage items at all.

 

With cain though you are better off going for a damage item first, since he relies a lot on doing mass damage in a few seconds for easy kills, then getting an attack speed item to boost his speed after E

 

With darpa his grenade(E) boosts damage for a few seconds, but his mine(Q) does DOT

So you can choose to go for damage first to maximize grenade hits and leave them weak for the DOT, or attack speed to proc a full mine/nade faster

 

With zera you are better off getting attack speed to maximize damage during his ult (just make sure to have lots of agi)

 

Etc Etc

 

I am mostly talking about second to third item decisions, since you always want to max attack speed as an AA

[Azrael]

Ok so on my way home from work I had a sudden thought. When is Weapon Damage better to get than weapon speed.

 

I don't have the knowledge of mechanics of some people here so i can't do the maths myself. So can anyone answer if there is a point where it becomes more cost efficient to but weapon damage items like galactic defender or contamination shard over weapon speed? Or is it just better to get to weapon speed cap then get damage?

 

Also where do crits come into all of this? And Items with stats?

 

There is so much to cover so hopefully we will get some surprising answers

There is not a unique way to determine wheter is better, to get Raw Damage or ASPD, if you have stun batton, foe, retrofit, shrink ray, pyre, etc.. you would want to have higher aspd (lower cd on attack), but if you have ocelot, BHM, star fury, demigod talent, etc... you are needing Raw Weapon damage.

In terms of DPS, 500 weapon damage against a hero with 50% phys resis deals 250 damage, if you have a Weapon Speed of 1, you are attacking once per second (supossedly), so you deal 250 damage per second. If you have 350 weapon damage but a Weapon Speed of 0.4 and against the same 50% phys resist, you are dealing 175 damage 2.5 times per second, so it is 437.5 damage per second. This is basic layout and very simplified as i didn't take into account many factors of the game.

[Mus]

@Midknight:

 

I am not an expert in the game mechanics, and I realised that I incorrectly formulated an increase in attack speed. i.e the little formula for k that I gave isn't correct, but my derivation of the formula remains correct, as does the formula. Just need to amend k.

 

This is the corrected version: Increase wpn speed by s% implies k = 1/(1+(s/100)).

 

My formula remains correct, the only problem was k. If you check, you will see that my formula now gives precisely the same result as your method does.

 

In fact it simplifies massively to:

 

dx > x(s/100)

 

Which by the way is the same as what you were saying, so this is not 'disinformation'.

[Ironsights]

if you present a formula that relies on a variable or constant, in this case K, that is incorrectly obtained produces incorrect results you have in fact spread disinformation if you attempt to hold the inaccurate formula as correct.

 

an considering that you chose to argue with midknight CITING YOUR FORMULA as the reason he was wrong...when in fact your formula was wrong...

 

you are spreading disinformation.

 

However, the math troll is successful.

[Mus]

My formula was correct. The variable k was incorrectly obtained because I did not know the game mechanics for wpn speed when I posted it. I have now amended the variable k, and the resulting formula is all you need to determine whether or not an increase in wpn dmg is better than an increase in wpn speed.

[Ironsights]

Your not taking into account all factors:

 

unless I am at max weapon speed on toxi, speed is ALWAYS better than damaeg: why? Because his AA slows and poisons, thus it needs to proc as fast as possible. Alternatively, if you are relyign on leeh to survive, again you will most likely want speed until it is capped, since that will be what keeps you alive to continue dealing damage.

 

My point is that there are FAR more variables than just 'will speed here or damage here' grant me more total damage...

 

It is all circumstantial.

 

Sorry boss, but a simple derivative is not the answer to this problem.

[Mus]

I have already said that I was only considering the change to your DPS, and nothing else. Once you know how to get the best DPS, then of course you can decide if you want the speed or the damage based on the other factors that you mentioned.

[BestPlayer]

tung already eksplained to all you small sons, dunno what you're still arguing about

 

if you're in a position where your team kan pik fawourable fights for you, are you're guaranteed the option of sustained damage towards a target, weapon speed will usually be the better option - whereas if you are not in a position where you kan rely on your team to pik the fights for you, and you get kited around/are in danger of being targeted on the outset, weapon damage will usually be the better option.

[Mus]

Why can't you spell properly?

[BestPlayer]

Why can't you spell properly?

 

I kan, if I hawe my eksternal keyboard plugged in. Should you ewer giwe me a reason to kare about anything you post, I will plug it in before I respond.