It really does warm my kitty paws to have seen the addition of an AP ratio to Miss Fortune’s ultimate. Hybrid characters have always been a confusing part of the community, but they tend to be the most interesting and flexible of the bunch. Champions like Jax, Katarina, and Nidalee seem to find themselves in heated debate as to whether they ought to be build AD or AP. Very few people are willing to do the math footwork to figure it out, so today I thought I’d walk you readers through some relatively easy math to figure out which builds have the highest DPS and Burst! Even better, I’ve got a pleasant surprise for our readers at the end of the article!

To start off, let me define DPS and Burst. I was surprised to find that a number of people are not familiar with these terms even in ranked level 30 play.

DPS stands for “Damage Per Second”. It’s an average of how much damage your character can put out over a period of time with their abilities and autoattack. If you like, think of DPS as slow damage.

Burst, on the other hand, is how much damage your character can put out instantly or nearly instantly. Like DPS, it involves using both your abilities and your autoattack, but no time is involved, so it is the maximum amount of damage you will be able to put out. Again, if you like, you can think of Burst as fast damage.

However, these two values mean little unless you also include cost efficiency. Building a character for the best DPS or Burst might not help if you can’t afford to build in that direction.

**If you don’t like math skip down to the next section of bold text.**

To figure out Burst and DPS, allow me to mathematically define a few terms. In this way, we can more easily write equations that describe Champion Burst and DPS concisely.

Let X_{x} = Any Specific Ability or Autoattack Base Damage

Let D_{x} = Any Specific Ability or Autoattack AD Ratio

Let P_{x} = Any Specific Ability or Autoattack AP Ratio

Let _{Q, W, E, R} or _{A} = Q, W, E, or R Specific Ability or Autoattack, respectively

Let Y = Champion’s Bonus AD

Let Z = Champion’s AP

Let B = Burst

With these definitions, we can begin writing equations. The damage for one use of an ability is equal to X+(Y*D)+(Z*P). Using different abilities (Q, E, W, and R abilities), we can say that Burst for any single X is equal to X+(Y*D)+(Z*P), since Burst for any single X only concerns itself with the damage of a single use of an ability. However, Burst as we know it includes all Q, E, W, and R abilities going off, plus one autoattack. This means that the equation for a Champion’s full ability Burst will look like this:

X_{Q}+(Y*D_{Q})+(Z*P_{Q}) + X_{W}+(Y*D_{W})+(Z*P_{W}) + X_{E}+(Y*D_{E})+(Z*P_{E}) + X_{R}+(Y*D_{R})+(Z*P_{R})

We also need to include one autoattack for completeness sake, which is the base autoattack damage plus the AD bonus at a ratio of 1 to 1:

X_{A}+Y

The final equation is as follows:

B = X_{Q}+(Y*D_{Q})+(Z*P_{Q}) + X_{W}+(Y*D_{W})+(Z*P_{W}) + X_{E}+(Y*D_{E})+(Z*P_{E}) + X_{R}+(Y*D_{R})+(Z*P_{R}) + X_{A}+Y

Let us condense this before moving onto DPS.

Let Q = X_{Q}+(Y*D_{Q})+(Z*P_{Q})

Let W = X_{W}+(Y*D_{W})+(Z*P_{W})

Let E = X_{E}+(Y*D_{E})+(Z*P_{E})

Let R = X_{R}+(Y*D_{R})+(Z*P_{R})

Let A = X_{A}+Y

Therefore, B = Q + W + E + R + A

So with Burst figured out, we move onto DPS. To find DPS, we must consider that abilities are governed by cooldowns. Cooldown reduction reduces this cooldown by a percent which can not exceed 40%.

Let C_{x} = Any Specific Ability or Autoattack Cooldown

Let R = Champion’s Cooldown Reduction in decimal form if Cooldown Reduction in decimal form is < or =0.4.

Let R = 0.4 if Cooldown Reduction in decimal form is > 0.4

Let S = Champion’s Attack Speed in decimal form

Let P = Champion’s Bonus Attack Speed in decimal form

Let F = DPS (ran out of letters!)

Specific abilities Q, W, E, and R, all have cooldowns in common. By dividing the ability damage by the cooldown of the ability, we can find out the base DPS of that specific ability. With Q, for instance, the base DPS equation would be equal to Q/C_{Q}. Cooldown Reduction must also be accounted for, and is a percent multiplier to C_{x}. Taking Q again, the final base DPS of Q would be Q/(C_{Q}*(1-R)). The full equation for all abilities’ DPS with Cooldown Reduction included is then:

Q/(C_{Q}*(1-R)) + W/(C_{W}*(1-R)) + E/(C_{E}*(1-R)) + R/(C_{R}*(1-R))

The Autoattack is calculated differently than abilities. Instead of the autoattack cooldown being measured as a cooldown, it is instead measured as the number of attacks over one second. This significantly eases our calculation, as the base Autoattack DPS is equal to A*S. When we include the Bonus Attack Speed, which is a percent modifier to the original Attack Speed, the total Attack Speed = S*(1+P).

Let T = S*(1+P)

Remember that while the base Attack Speed will never exceed 2.5, the bonus attack speed may push the total Attack Speed above 2.5. However, the total Attack Speed may never exceed 2.5. Therefore, we must add this to our definitions:

Let T = S*(1+P) if S*(1+P) < or = 2.5

Let T = 2.5 if S*(1+P) > 2.5

The final Autoattack DPS equation equals A*T.

With this, we may complete our final DPS equation:

F = Q/(C_{Q}*(1-R)) + W/(C_{W}*(1-R)) + E/(C_{E}*(1-R)) + R/(C_{R}*(1-R)) + A*T)

With Burst and DPS calculations complete, the rest is relatively simple. By finding the most efficient basic items for AD and AP and dividing their gold cost by their relative bonus, we can find out how efficient our Burst and DPS is with either AD or AP.

The B.F. Sword, the most efficient basic AD item, costs 1650 gold and provides +45 AD. Therefore, its efficiency is 36 and 2/3 gold per AD. The Needlessly Large Rod, the most efficient basic AP item, costs 1600 gold and provides +80 AP. Therefore, its efficiency is 20 gold per AP. Since we are looking to compare the two, we shall multiply both examinations by their respective items, then subtract the value of the respective item to find the effective Gold value gained or lost. Therefore the equation for the B.F. Sword Burst and DPS is as follows:

Let Z = 0

Let Y = 45

B*1650-1650 = Extra or Lost Effective Gold Value From AD Burst

F*1650-1650 = Extra or Lost Effective Gold Value From AD Burst

The equations above, in layman’s terms, give you how much effective Gold you gain or lose beyond the original cost of a B.F. Sword when using abilities. So if you have lots of abilities with high AD ratios, you’ll notice you end up with a much higher effective Gold value than a character with lower or even no abilities with AD ratios. In some cases, you may end up with negative effective Gold values. In these cases, the B.F. Sword gives you less effective Gold value than its original cost, making it a poor choice of item. The greater the effective Gold value, the more cost effective the item is. By comparing effective Gold of the AD equation with the effective Gold of the AP equation, you can figure out which build, AD or AP, is generally more efficient.

Remember, the multiplier value for Burst and DPS is the item you are using, while the subtrahend is the item it is being compared to. You can switch out the multiplier and subtrahend to compare relative item efficiencies.

**The math is over, you can come out from under the bed now.**

By using the calculations above, I’ve worked out the AD and AP Burst and DPS for a number of hybrid characters. Champions have been placed below in the Burst and DPS categories based on which one is more cost efficienct: building only B.F. Swords (AD) or only Needlessly Large Rods (AP). Some of the numbers were slightly off due to the difficulty of measuring certain skills, percent damages, and other skill oddities, but the results on these characters were still crystal clear. While these categories are good guidelines, keep in mind that characters often have abilities that have not or cannot be measured with mathematic spreadsheets alone. Still, I found some interesting results that are contrary to popular opinion and common sense.

Better at AD Burst: Kayle, Miss Fortune, Shaco, Yorick

Better at AP Burst: Akali, Blitzcrank, Cho’Gath, Evelynn, Ezreal, Jax, Kassadin, Katarina, Leona, Kog’Maw, Master Yi, Mordekaiser, Nidalee, Poppy, Sion, Skarner, Teemo, Tristana, Twisted Fate

Better at AD DPS: Blitzcrank, Evelynn, Ezreal, Kassadin, Katarina, Kayle, Leona, Kog’Maw, Master Yi, Miss Fortune, Mordekaiser, Nidalee, Poppy, Shaco, Sion, Skarner, Teemo, Tristana, Twisted Fate

Better at AP DPS: Akali, Cho’Gath, Jax, Yorick

Generally speaking, the results line up with what we’d expect: Akali and Cho are best built AP, AD tends to have higher DPS than AP, AP tends to have higher Burst than AD, etc. But here are the more interesting results you might not believe:

Morde’s AD Burst efficiency is very close to his AP Burst efficiency. It would appear to me that AD Morde is actually better than AP because of AD’s much higher DPS.

Shaco’s AD Burst is just as high as his AP Burst, but he gets a lot more DPS from AD. Stop building Shaco AP, he is simply less efficient than AD.

AP Sion is more than twice as cost efficient as AD Sion, even with the recent buffs.

Even though Teemo has a higher AD DPS than AP DPS, his AP DPS is almost as high and his AP Burst is double his AD Burst.

Tristana’s AP Burst is one of the most cost efficient builds in the game for an “AD Carry”.

AD Twisted Fate is more cost efficient than AP Twisted Fate with almost as much Burst and much higher DPS. Even though people say that AP TF is superior, I think I’ll be building AD TF from now on.

Yorick actually has a higher AP DPS, but his AD DPS is close and the AD Burst is nearly twice as good as his AP Burst. Don’t build him AP.

Now: the surprise!

For all of you diligent readers I have taken the time to create a simple spreadsheet that allows you to do your own calculations on AD, AP, and hybrid builds. Most of the spreadsheets out there are half complete or difficult to use. You’ll find them scattered about the forums or the web. This one, unlike other spreadsheets and value calculators, only requires you to look on the League of Legends Wiki and to input the base stats from your favorite champion into the colored boxes. At the top, it will automatically calculate effective Gold efficiency with B.F. Swords (for pure AD builds), Needlessly Large Rods (for pure AP builds), a combination of B.F. Swords and Needlessly Large Rods (for hybrid builds), and a Hextech Gunblade (for those of you who still want to use it on hybrid characters: the upcoming Graves patch has nerfed it significantly and these upcoming changes are already reflected in the spreadsheet).

Just below that, there is a section for you to put your own items in. Simply grab the stats from the League of Legends Wiki, plug the numbers in the colored boxes, and everything calculates by itself! These values are efficiencies as opposed to effective Gold values; since they aren’t compared to anything, they merely show how much Gold per point of statistic the items are worth. This allows you to see how efficient the items you are using are; the more efficient, the higher the value, the more efficient the item is. You can always compare them to a B.F. Sword or Needlessly Large Rod by dividing the item’s Gold price by putting in a B.F. Sword or Needlessly Large Rod into an item slot and looking at the AD or AP efficiency (for reference, B.F. Sword efficiency is 36.67 Gold per AD and Needlessly Large Rod is 20 Gold per AP).

One note before you go changing all the values around: only change values in colored boxes! Any other changes may break portions of the spreadsheet.

The real strength of this spreadsheet is that it allows you to tweak both character and item statistics. With this spreadsheet, you can change values on characters and items at a whim, allowing you to view the effects of past, present, and future patches. It also gives users the capability to invent their own items, try out hypothetical character buffs and nerfs, or even invent and balance new Champions!

**The spreadsheet can be found here:** Google Docs Link (Remember you have to download it to use it!)

Download a copy today and try it out in Microsoft Excel, Open Office.org, or any other supported spreadsheet program!

While this spreadsheet is free to use and derive from, you are not permitted to use it for commercial endeavors of any sort. Similarly, if you choose to use this spreadsheet wholly or partially, you must give both myself and the No ELO website credit on any derivative work. I worked hard to create this free spreadsheet, so myself and the site at least deserve some credit for it!

Love the math and the thought. But there are lots of factors which matters but are really hard to put into an equation. Like AoE / single-targeted, skill-shots / non-skill-shots (or ease of landing the ability / attack), range, combo-based bonus / proc effects, etc.

It’s still very helpful as a reference though.

Great job! ðŸ™‚

For AoE effects, merely multiply the AD/AP ratio by the number of targets. As I said in the article:

“While these categories are good guidelines, keep in mind that characters often have abilities that have not or cannot be measured with mathematic spreadsheets alone.”

Read every word, really appreciate the work you went to. Thanks.