I made a post about a day ago about most efficient rune combinations and got alot of feedback. After reading through the comments I realized that DPS cannot be calculated without taking into account the base stats of each champion. So I wrote a program in Mathematica 9 that takes into account: base stats, starting item and offense masteries. I used constrained optimization of multiple variables with multiple constraints to find the combination ofattack speed and attack damage marks and quintescences that maximizes DPS (damage per second) of fighters, assassins, tanks and marksmen at level 1 – all in one click. However, I did not take into account champions’ abilities.

I’m deciding whether I should upload the program or not. Also, for someone to use the program they must have Mathematica 9. Here’s a preview of how it looks:

here’s a graph

If anyone wana help create an app or web application of this program, message me. .

Fun Facts

• Maokai has the highest DPS (73.8488) of all junglers, given that he starts with Hunter’s Machete, have all [21] offense masteries (as shown in the preview above), and a combination of 9 AS marks + 3 AS quints.
• Twitch has the highest DPS (60.6584) of all marksmen, given that he starts with Doran’s Blade, offense masteries, and a combination of 7 AD marks + 2 AS marks + 3 AS quints (I guess that’s why he’s getting nerfed in 4.10)
• Shaco’s optimal rune combination for maximum DPS at level 1 (67.7924) is 6 AS marks + 3 AD marks + 3 AS quints (and yes its the same if you factor in his backstab passive – just a 20% increase in his DPS)
• Scaling health per level seals are efficient at level 6 (breakeven point with flat health seals)
• AS quints OP
• Rule of Thumb: The higher base AD is, the more efficient AS runes are; The lower base AD is, the more efficient AD runes are.

Now feel free to ask for optimal combinations of other champions.

Also I can create other programs that would optimize various rune combinations such as armor/health/health regen seals/quints, magic pen/ability power marks/quints, magic resist/CDR/mana regen glyphs/quints/etc; But I just don’t think its worth the time. Maybe sometime in the future; I just did this one for fun.

EDIT: I’m not an expert, so don’t take my advice as written in stone – I’m only doing the math. Again, I did not factor in champions’ abilities so even though these runes maximizes basic attack DPS, ability scaling was not considered. That being said, efficiency was calculated for only level 1 where only one ability is unlocked (level 1 damage comes mainly from basic attacks). However, it may be the best for champions that rely mostly on basic attacks.

EDIT 2: The whole point of this is just to show how useful math can be to solve problems, not to make strong judgements on best rune combinations – the math in this program isn’t powerful enough yet to determine that as there are some variables left out and other runes to consider, but still may be used as a guide to better strategies and theory crafting

EDIT 3: I’m tired calculating DPS lol XD if this post gets popular, I’ll consider uploading the program.

EDIT 4: Someone asked for a graph that shows the trade off between AS runes and AD runes, well here it is:

Note that the axes are labeled AS marks and AS quints but it already takes into account AD marks/quints (for example at the origin where AS mark = 0 and AS quint = 0, AD marks = 9 and AD quints = 3…AD marks = 9-AS, AD quints = 3-AS). Also this is holding base AD and base AS constant. All I did was maximize this function, subject to the constraints {0 <= ASmarks <= 9, 0 <= ASquints <= 3}, as base AD and AS varies to get optimal DPS for each champ.

I’ll update this post with more facts as time go by

UPDATE: Here’s the program:

After getting much feedback from my first post, I decided to create a program in Mathematica 9 that shows the various combinations of Attack Speed and Attack Damage marks and quints, that maximizes DPS (damage per second) from basic attacks for various AD champions.

The computations take into account:

• Starting items
• Masteries
• Base stats

(You gotta click on the file name at the top of the page where is says “Download: DPS rune efficiency.cdf”, click on “DPS rune efficiency.cdf”)