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edxs' Graph
For damage normalized by gold costs, see Macrohard's Graph
Last edited by ElementUser; 05-08-2010 at 02:53 PM.
It all comes down to your attack damage without the items.
Late game Riftshards will normally out-DPS a Savage Mace.
Before then, when your DPS is low-medium, Savage Mace will be better...
The Math.
Riftshards (MAX) - +75 damage, 10% to proc 2.4x Critical Strike
Savage Mace - +80 damage, 35% chance to deal an additional 100 damage.
Let's look at 100 base damage
Potential damage on a single strike:
Riftshards - (100 + 75) x 2.4 = 420 Damage
Savage Mace - 100 + 80 + 100 = 280 Damage
Factoring in proc'ing chance:
Riftshards - (100 + 75) + (100 + 75) x .24 = 217 average damage per hit.
Savage Mace - (100 + 80) + 100 x .35 = 215 average damage per hit.
Conclusion
As you can see, even with just 100 base attack, your average output with Riftshards will be slightly higher then with a Savage Mace.
Remember though, this is theoretical damage, based off the assumption that the items proc evenly (eg. Savage Mace will proc 35/100 times), which, in practice, does not happen.
Last edited by Rilian; 05-05-2010 at 08:32 AM.
Your math is flawed.Originally Posted by Rilian
You ignored armor, true strike and the +15 attack speed.
Which is obviously very disadvantageous for savage mace.
Also, savage mace is +88 damage not +80.
Last edited by `patrick`; 05-05-2010 at 08:37 AM.
Why will this not happen?
"If you PSR is higher then mine, you obviously don't have a life.
You are a looser and probably a virgin."
For the same reason that some ppl never win the lottery even if they played more than enough times, statistically.
On topic:
im not so good at maths and it's kinda tiring to follow up
the equations, so so far what's the damage point where Riftshards takes over?
so you get a six every 6th time you roll the dice?^^
it's the thing with statistic, it will become true with great numbers, but you cannot rely on the % with the though of "I didn't get a procc the last 10 attacks, so now it should procc!"
for more see Wiki: Law of Large Numbers
btw: it's different in DotA
afaik it's this post, so it's around 96-97 dmg
"Imagination is more important than knowledge. For knowledge is limited [...]." - Albert Einstein
We are a nation of thinker, because we always think about what others are thinking about us. - Gerhard Uhlenbruck (*1929) - german aphorist
i think riftshards is better at any time on full level
Considering most heroes have over 100 base attack by Lv 25, theoretically it's true.
Armor is assumed to be zero, and all attacks are assumed to hit. Better?
Also, the attack speed is almost negligible, especially when you consider that as base damage increases, as does the damage gap.
As I glazed over at the start of my post, when your damage is high enough, Riftshards wins outright. All due to the fact that Savage Mace's proc adds a static 100 damage to your total damage output, while Riftshards takes your total damage output and multiplies it by x2.4. Which means the more damage items you have already means the wider the damage gap.
Last edited by Rilian; 05-05-2010 at 08:47 AM.
In the best case +15 attack speed is +15% dps - that's not negligible.
All the things you ignore are what makes a savage mace good - the point at which riftshards takes over is much higher than 100 base damage.
(assuming average 25% armor reduction, which is much more likely than 0%, at the point you get a savage mace/riftshards; 1 attack/second)
(188*0.75 + 100*0.35)*1.15 = 202.4 DPS
[(100 + 75) + (100 + 75) * 0.24]*0.75 = 164.75 DPS
=> Without any other attack speed increasing items, at 25% average armor reduction, ignoring the true strike savage mace is better than riftshards 5, in terms of dps, until you have a base damage of >500.
I think thats a very different result than 100
Looks like I was slow and the big boys finished the math...
Last edited by Rilian; 05-05-2010 at 09:32 AM.
1. In general, +15 AS is not equal to +15% DPSIn the best case +15 attack speed is +15% dps - that's not negligible.
All the things you ignore are what makes a savage mace good - the point at which riftshards takes over is much higher than 100 base damage.
(assuming average 25% armor reduction, which is much more likely than 0%, at the point you get a savage mace/riftshards; 1 attack/second)
(188*0.75 + 100*0.35)*1.15 = 202.4 DPS
[(100 + 75) + (100 + 75) * 0.24]*0.75 = 164.75 DPS
=> Without any other attack speed increasing items, at 25% average armor reduction, ignoring the true strike savage mace is better than riftshards 5, in terms of dps, until you have a base damage of >500.
I think thats a very different result than 100
2a. ~175 AS is 1 attack per second with a 1.7 sec attack CD, and +15 AS brings you to 10/9 attacks per second
[ (188*0.65 + 288*0.35) ]*1.111 = 247.78 DPS
[ (175*0.80 + (175+175*2.4)*0.20) ]*1 = 259 DPS
2b. Your math was wrong, riftshards is better for the given conditions (e.g. 1 attack per second and 100 dmg without the item in question)
3. Your attack speed and base damage matter for the calculation of DPS
4. For average damage per attack:
[ (x+88)*0.65 + (x+188)*0.35 ] = x + 123
[ (x+75)*0.80 + ((x+75)+2.4*(x+75))*0.20 ] = 1.28x + 111
x = 43 damage without the item in question before riftshards is better for the given condition
Conclusion -
Riftshards at max level is essentially always better than savage mace when calculating average damage per attack.
Last edited by Johnson; 05-05-2010 at 10:03 PM.
You made the same mistake i did. That number i bolded should be 1.4. So your conclusion is incorrect. Check Elementalusers post if you want to see why.
Shockingly, I read the whole thread before posting and verified my numbers in game before doing the math...
I don't think I have any mods installed.
In the " ((x+75)+2.4*(x+75))*0.20 " term:
(x+75) is your damage with riftshards on a non-critting hit
2.4*(x+2.4) is the additional damage from the crit
0.20 is the average chance of occurance
So, the issue may be that I am misunderstanding what a critical strike means in this game.
Is the damage from a crit -
a. regular attack damage + (crit multiplier)(reg attack dmg)
b. (crit multiplier)(reg attack damage)
?
Last edited by Johnson; 05-05-2010 at 10:03 PM.
You multiplied by had a 0.2*(damage+(damagex2.4))
What you calculated there is actually 3.4x crit as you can move the damage on the left hand side into the "damagex2.4" as they are technically like terms. Making it 3.4damag*20% chance. The 2.4 already compensates for your original damage. Make sense? im not very clear when trying to type in the morning.
If b. is correct above, then..
[ (x+75)*0.80 + ((x+75)+1.4*(x+75))*0.20 ] = 1.28x + 96
or
[ (x+75)*0.80 + 2.4*(x+75)*0.20 ] = 1.28x + 96
x = 96.43 damage without the item in question before riftshards is better for the given condition
Agrees with
Last edited by Johnson; 05-05-2010 at 10:07 PM.
When calculating damage from Savage Mace you assume it gives +123 dmg and 15 attack speed. Crit is amazing in that crit is actually a percentage increase to damage which can be worked out by proc chance*crit increase, so 1.4*20%=28% damage increase. So from here its pretty easy
X is your damage before you buy either.
(X+123)*1.075=(X+75)*1.28
So Savagemace is better if you have below 177 or so damage before your purchase either of them. (So most of the time)
I multiply by 1.075 as thats a rough estimate of how much it will increase your damage purely off your base agilities + attackspeed. I really cant be bother to complicate this equation by taking agility gains into account, so dont rage at this fudge factor. I have worked it out for a majority of heroes before and this is a fair estimate but by no means perfect.
EDITED: 1.24 to 1.28 making finally answer 177 pre-purchase.
Last edited by yyr_; 05-05-2010 at 09:07 PM.
It's 28% for level 4 Riftshards. 20% to do 2.4x damage, not 10%. Also, the formula is wrong like Malle informed me when I made the mistake a long time ago.
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Look for my highlighted text (important information) and grey text (interesting but not required information).
I am pretty sure Malle (or for me, Maide) made a graph for riftshards vs shieldbreaker which was pretty cool as well. Ill probably end up doing a full post on all DPS items later.
Hammerstorm with EP and lvl4 Riftshards with galvenize and ulti up is a fun thing to do! =D
yeah, then riftshards would be the best item. but when you're the new FA, then go split-shot lifesteal and mace.
It's really nice that you guys try to break down the numbers, but people should have a feeling for when they should go mace or riftshards.
Normally i buy Mace and Geo on agi carries, to save the modifier for lifesteal.
Riftshards is if, i have had a hard game, cus it's much more easy to assemble. Or if i'm melee without crit, because it's needed from time to time.
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