I am trying to figure out the best way to maximize damage per second for a physical dps character, such as Tristana.

Or rather, trying to figure out how to calculate it.

I understand the general principles but not exactly how they are applied to this game. I'm also not sure about damage tables...

Examples:

You show 100 damage on your stats, so therefore you will do 100 damage each strike against a target with 0 armor. If you hit it 100 times over 100 seconds (1.000 attack speed in stats), that's 100 dps (damage per second), assuming no crit, masteries, etc.

**Crit**

Each % of crit will make one more strike crit in this example. Assuming a crit is a flat 100% of the base damage, for each 1% you will have a strike that does 200 damage (out of 100). Therefore if you increase the crit chance from 0 to 1% you get 10100 in 100 seconds or, 101 dps, or a 1% increase in damage per second. This is elementary but it is essential for this discussion that I make it clear.

**Attack Speed**

Now attack speed, for each 1% you get 1 more strike in 100 seconds, therefore it will again show 10100 damage in 100 seconds.

**Damage**

And damage is even more easily calculated, for each 1 point invested, 1 more point in damage. In this example 1% more damage.

This means 1% of attack speed = 1 damage = 1% crit in terms of dps. All increase dps equally.

**Armor**

Ok now this is where I start to get confused. Let's simplify armor into being 1% of damage mitigation per 1 armor point. Now, if you're doing 100 dps against a 0 armor target, then now you're doing 80 dps against a 20 armor target.

Each percent of crit would make 1 strike out of 100 strikes of 80 damage do 160 damage. So... 8080/100 = 80.8. That's still a 1% increase in damage. The calculations are the same for attack speed and damage.

Now for future calculations; AS= Attack Speed (as shown on stats), D = Damage, C= Crit, P=DPS, M = armor, R=Crit Damage, P = Armor pen.

**So... P = (D*AS*((1+(C*/100)*(R/100))*(1-((M - P)/100))) .... right?**

Now I'm not sure what all the caps are, AS is 2.5 attacks a second, Damage is.. undetermined.... I reckon it'd be 600 as the highest damage item is Bloodthirster and that caps at 100 damage, add that to base damage and it'd be your cap. Crit is something like 100%.

I don't know the crit damage cap. I'll assume 250% of base damage. Armor penetration is self explanatory, as it caps at the point which the target has 0 armor. Now to calculate the maximum possible damage in a game before masteries and runes.

THIS IS WHERE I MAKE HUGE LEAPS OF FAITH AND LOGIC

This is where I'll need help.

Let's say you're a Tristana with 100 base damage, 10% chance to crit, .7 attacks per second. You have no armor pen, nor crit damage. Your target has 30% damage reduction from armor. You attack this person for 10 seconds.

P = ((100*.7*1.1)*.7) = 53.9 damage per second. If you buy Berserker's Greaves (25% IAS) that would then be... I assume... .7*1.25.. so .875 attacks a second. This makes the new dps .... 67.4 a 25% increase. Ok looks good so far. So now you're liking attack speed and get a recurve bow (40% IAS).

Now that'd make.... 0.7 * 1.65 ( as they are additive from what I can see)... New P = 88.9, a 65% increase over no IAS items but .... only a 32% increase from just greaves.

You buy another because you still think it's a good increase. 0.7x2.05 then. P = 110.5, this is only a 24% increase from where we were a second ago.

"But Dine, any idiot could tell you that stacking attack speed without damage or crit is stupid."

Indeed it is. Now we buy a Pickaxe, +25 damage. P = 138.1, or a 25% increase. Neato! Now we get another, P = 165.7, or a 20% increase. But you add another recurve, you end up doing... 198 dps. A 20% dps gain.

"That's an even smaller gain, where are you going with this?"

Ok ok, so the first item increased DPS by about 135. That's .54 dps per point invested in attack speed. The next item increased dps by 21.5, so about .54 dps per point as well. The next item is the same.

NOW we get to the damage portion. So 25 damage increased dps by 27.6, making each point of damage worth 1.1 damage per second. If there were no attack speed items then 25 damage would only increase dps by 13.5

So this line of logic states that investing in one stat makes the other stats more valuable.

What I'm going to try to figure out now is....

What combination of items and runes increases physical dps the most?

I'm talking theoretical highest dps.

Right now let's just work with items.

Set variables are.... 30% damage mitigation from armor, all HP runes, and no masteries that increase physical dps.

Boots are required. The only that increase DPS are berserker's Greaves. An Infinity Edge is without a doubt required for any physical dps. So therefore 2 items are set in stone.

based on This (http://www.leaguecraft.com/builder/Tristana/5e700b48f06a18258db0a7377590cbde) a level 18 Tristana does... 203 dps.

P = (176*1.117*(1+ ((31.66/100) * (150/100))) * (1- 0.3)) = 202.96

Adding a Bloodthirster would bring it to 318.29 DPS, Adding a Last Whisper would bring it to... if i calculate the 40% armor pen correctly....

P = (296*1.385*(1+((31.66/100)*(150/100)))* (1 - (0.3*0.6))) = 495 DPS

Hmm I dont have the time to figure out the last 2 items but I believe these 4 items make up the highest possible DPS for the first 4.

I'll try to continue this later...

As it stands right now

Right now my questions are what two items would best fit in those slots for the highest possible dps and much further down the line, what runes and masteries?