DPS Guide

DPS Guide

Posted: Thu Oct 29, 2009 2:17 am

DPS GUIDE

DPS stands for damage per second. Simply put, it is the raw damage your hero can deal, per second. This is before armor reductions, evasion, etc. For information on that, see Caspian’s guide:
http://www.dotastrategy.com/forum/ftopic12672.html
ExG_Tamahome's guide:
http://www.dotastrategy.com/forum/ftopic4382.html

Stats and base damage are two of the most important things to know to calculate DPS.


Attack Speed
Attack speed is how fast a hero attacks. It is measured by the cooldown in between attacks. There are two major parts to attack speed. IAS, and BAT.

IAS
IAS stands for Increased Attack Speed. It is generally found as a percentage. Each point of agility increases IAS by 1. Most abilities that affect attack speed deal with IAS. The five exceptions to this are Chemical Rage on Alchemist, which lowers BAT, Shapeshift, which also lowers BAT, Berserker Rage, also lowering BAT, True Form, also lowering BAT, and Metamorphosis, which increases BAT. The maximum IAS is +400%, and lowest is -80% IAS.
To calculate IAS, everything is additive. So if you have a Hyperstone and gloves of haste, you have 55%+15%=+70% IAS, NOT (1.55*1.15)-1=+78.25% IAS. Thus, 6 Hyperstones provide +330% IAS, not +1286.7 (400)% IAS. Negative effects also stack additively. So attacking Enchantress with maxed out Untouchable means that you subtract 80%, not multiply IAS by 0.2.

BAT
BAT stands for Base Attack Time. This is the amount of time it will take in between each attack, if IAS is 0. Most heroes have a BAT of 1.7, but exceptions are as follows:
Syllabear(True Form), Huskar, Terrorblade(range): 1.6
Troll(melee): 1.55
Windrunner, Terrorblade(melee): 1.5
Anti Mage, Chemical Rage level 1: 1.45
Lycan(Shapeshift): 1.4
Chemical Rage level 2: 1.35
Chemical Rage level 3: 1.2

The only notable nonhero unit is the Spirit Bear, as he can hold items. BAT is as follows:
Level 1: 1.75
Level 2: 1.65
Level 3: 1.55
Level 4: 1.45

Calculating attack speed:
Attack speed is measured in seconds in between attacks. The formula is:
BAT/(1+IAS), where IAS is in decimal form. This means that

I shall now poke at the DS database to prove how whoever found Clockwerk’s base attackspeed found the number of attacks per second, seconds between attacks, and to use it as an example, as well as providing the correct value.

Clockwerk, with no items, at level 1, has 13 agi. At 1% IAS per agi, 1*13=13% IAS =0.13 as a decimal (ooh, difficult maths!).
Clockwerk is a normal hero with a BAT of 1.7.
1.7/(1+0.13)=1.7/1.13=1.50 seconds/attack. This is the type of value on every single other hero in the database.

What was really found with Clock was the number of attacks per second, found by (1+IAS)/BAT, or the inverse of the number of seconds per attack. This is more useful and easier to use when calculating DPS.
So, (1+0.13)/1.7=0.6647 attacks/sec.


Damage
Base damage:
Base damage is the number displayed next to your hero’s stats. The hero has a base damage, and stats add to the damage. In the DotAStrategy database, the base damage is calculated after the base stats are added in, so only added stats need to be calculated. Every point in a hero’s primary attribute provides 1 damage. For base damage, items and attribute bonuses do not count in determining base damage. It has a lower and higher value, as the value is slightly random. The only way to increase/decrease this is by leveling up, and gaining stats that way, or by gaining stats from an ability, like Silencer’s Last Word Intelligence gain, or Decay’s Strength gain.

Damage added
This is what gets added on to your base damage. This is the number next to your base damage, usually + a number. This is what gets added on from items, and attribute bonuses. Attribute bonuses to the primary stat from items end up getting added here as well. It is generally given, and can easily be found by adding all the item effects up. So an Agility based hero with Butterfly gains +30 damage, and +30 AGI (and 30% IAS, and 30% evasion). The +30 AGI also provides +30 damage, because it is part of the primary attribute. I’m currently not counting things that add a percent of your damage, as I calculate them as damage modifiers. This does include things like Empowering Haste and Enrage, which adds damage by a percentage, but not a percentage of your damage.

Damage modifiers
These are things that modify your damage, such as Command Aura, Empower, Double Damage, etc. These generally deal in percentages, and only with damage gained by stats. These stack additively, casting Empower on a player who is Bloodraged will NOT provide 288% damage.

As you can see, having command aura does not affect the damage from Rapiers.

The important thing to remember is that the damage is stat based only. So to calculate damage provided by this, the formula for damage added is (PrimaryStatBoost+AverageBaseDamage)*DamageIncrease, where DamageIncrease is the % damage, as a decimal. AverageBaseDamage is… the average base damage, so just (MinimumBaseDamage+MaximumBaseDamage)/2

So… Luna is level 25, with +20 stats (level 10 attribute bonus). She has a Divine Rapier. She is also standing next to a Vengeful with Command Aura, and Drow with Trueshot Aura. Base damage I will already calculate (fine, look it up), and it is 110-116.

The average base damage is (110+116)/2=113 damage
Lunar Blessing provides 27% extra damage. (113+20)*0.27=36 damage.
Command Aura provides 36% extra damage. (113+20)*0.36=48 damage.
Trueshot Aura provides 28% extra damage. (113+20)*0.28=37 damage.

Luna’s damage will therefore show as 110-116 (+20+250+36+48+37), or +391 damage.

And, to prove it, here is the screenshot:

Bashes, Criticals, and other damage adding abilities.
Pulverize is a skill used by Tidehunter in the Anchor Smash skill. To figure out how much damage it provides, we must use probability and expected value. Expected value says that if there is a chance for something to be happen, the outcome on average can be found by ChanceOfOccurrance*Effect. So Anchor Swing deals 0.2*200 damage, or 40 damage on average, per hit (Anchor Swing is Magical Damage, don’t forget that!). Same thing with Bashes and extra damage. Monkey King Bar has a 35% chance to do a 100 damage ministun. This means that it provides 0.35*100 damage, or 35 damage extra on average.
Criticals are a slightly different story. They do damage based on the hero’s damage, not a constant amount. They are therefore calculated as a percentage or decimal. It can be found by (1-Critchance)+(Critchance*Critmultiplier). For example, Phantom Assassin’s crit has a 15% chance to deal 4x damage. So (1-0.15)+(0.15*4)=1.45, or a 45% damage increase due to criticals. To calculate total damage, multiply this by the damage found AFTER damage modifiers, but BEFORE adding Bash and Pulverize damage.
When a player has multiple criticals, only the latest effect works. So if a Phantom Assassin gets a Buriza, and both criticals happen on the same hit, the Buriza was acquired last, and the Buriza will take effect. When a player has both a Bash and a Critical happen on the same hit, both will work. Acquiring a skill means putting a single skillpoint into it or every time you pick up the item.

Technically, the probability calculations in this section are wrong, because the Warcraft 3 engine does not generate a random number every time a unit attacks. See Flodian’s guide on Pseudo-Random Distribution at http://www.dotastrategy.com/forum/ftopic18287.html for more information.

FINAL RESULTS:
The final formula, for calculating DPS, is (AttacksPerSec*DamagePerAttack)=DPS.

For a complete step by step method:
1. Find the hero's base stats.
2. Find all the effects of the items on agility and the primary stats, as well as effects on damage.
3. (1+IAS+(AGI/100))/BAT=attacks per second, where IAS is a decimal.
4. Base Damage=Level 1 base damage+(PrimaryStatGain*Level) You can usually find this stat online.
5. Find the average base damage (now referred to as ABD), by adding the minimum base damage and the maximum base damage, and dividing by two.
6. Damage adding items, and primary stat items, as well as primary stat boosting abilities and damage boosting abilities, are added on here, where 1 point of the primary stat is equal to 1 damage.
7. Percentage based damage adding things, such as Command Aura and Double Damage are added on by (IncreasePercentage*(ABD+PrimaryStatsFromItemsOrAbilities))
8. Critical damage is found as a percentage. (1-critchance)*(critMultiplier) is the total damage, as a multiplier.
9. The critical multiplier is multiplied by the total damage so far.
10. Things that have a chance to happen on every attack, such as Anchor Smash or MKB ministun are added to damage, as (ChanceOfHappening)*(DamageWhenHappens)
11. The final damage is multiplied by the number of attacks per second.


Credits:
The guides linked in this guide,
http://web.dota-allstars.com/2009/07/14/critical-strikes-and-bashes
PlayDotA
DotAStrategy, ofc.

Feel free to comment on this, and point out places where I have screwed up.

*Fixed, Luna's base damage was different than I thought.

Last edited by bobbob247 on Thu Oct 29, 2009 6:35 am; edited 6 times in total

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Posted: Thu Oct 29, 2009 2:23 am

Great job man! About time we got a guide like this!
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Posted: Thu Oct 29, 2009 2:29 am

whoosssshhh...


good job dude...this time...a wall of text is pretty interesting
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My Latest Hero
LoL ID: dare18
HoN ID: dare18

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Posted: Thu Oct 29, 2009 2:39 am

I could add pictures of what I am talking about, but that would take some more time. Maybe some other day. (Procrastination skills)...

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Posted: Thu Oct 29, 2009 2:41 am

Awesome info, I love it.
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Posted: Thu Oct 29, 2009 2:48 am

a useful guide.

just a suggestion: try to lessen the wall of texts. lol
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SENTINEL VS NEUTRAL VS SCOURGE

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Posted: Thu Oct 29, 2009 3:14 am

*clapclapclap*

Now we can tell new members what "contributing to the forums" means .
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Starting on Lion guide.

PM me for help with guides, item/hero ideas. willing to help, but bug/annoy me on purpose and die .



I can stalk you.

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Posted: Thu Oct 29, 2009 3:16 am

Someone needs to move this sucker to the library/sticky this!
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Posted: Thu Oct 29, 2009 3:39 am



Yeah, I'll add some more info, such as useful links and a few diagrams of what I am doing at some point. But those are cosmetic, and not too important to the guide. Therefore I can post this without losing a lot of the value of the guide.

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Posted: Thu Oct 29, 2009 3:40 am

Moved to the Library. Great info... Demo'ing some stuff using screenies (gifs) would be even better. Do it do it!
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--Voting begins Nov 22--
Keep the entries coming!

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Posted: Thu Oct 29, 2009 4:54 am

i always new that am and TB had low bat but wasnt aware of wr and huskar... Or sylla...

zZZZ

Gj on the guide anyway,.

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Posted: Thu Oct 29, 2009 6:36 am

I added a couple of pictures now... will add more some other time. Now I have graphic proof!

Unfortunately, DS owns wide screenshots hard, so just click on them for now.

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Posted: Thu Oct 29, 2009 7:17 am

wow. this gets better and cooler. this is the advantage of library guides, you update and we can see it instantly. keep it up.
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SENTINEL VS NEUTRAL VS SCOURGE

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Posted: Thu Oct 29, 2009 9:03 am

goog job mate....nice work.!
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