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I have decide to find out how may games of league are possible. Here are my results.

Jump··3 votes·948 views
How many games of league possible

Just over two weeks ago I decided to investigate how many normal games of League are possible on Summoner's Rift. After extensive research and a 11 page report here is the final number.

Total number of games possible : 2,308,992,582,707,252,059,690,092,587,664,558,027,538,550,531,393,292,273,268,088,091,072,621,354,215,937,854,404,154,903,493,669,004,911,386,284,469,254,650,231,824,520,014,035,482,932,439,742,257,481,289,519,749,911,334,961,921,642,910,372,479,902,331,051,517,893,513,011,717,811,935,782,065,090,940,906,492,906,915,049,974,383,136,688,947,875,495,414,615,934,554,912,335,029,062,363,200,995,445,763,696,261,977,587,008,253,411,284,578,063,342,616,976,280,550,290,347,859,965,940,226,101,919,259,736,221,750,278,039,883,876,849,438,916,426,414,777,850,784,185,892,821,773,219,087,104,091,393,007,282,629,905,544,671,768,078,394,127,624,798,765,273,360,184,033,452,188,209,182,645,019,749,609,785,588,980,595,360,853,593,627,519,947,075,338,672,727,867,718,870,239,421,842,480,884,949,235,927,642,504,404,193,131,101,719,875,340,359,505,737,345,063,173,208,793,170,221,356,944,177,095,753,282,636,085,680,838,808,824,033,040,973,931,930,541,366,192,235,136,726,360,047,550,020,558,945,219,701,687,665,440,807,222,842,209,720,706,646,647,508,893,906,988,216,894,099,600,601,977,254,401,866,462,948,920,551,946,488,657,399,211,013,285,501,917,897,075,158,726,071,726,297,591,759,911,387,135,409,584,896,406,002,299,902,095,221,156,653,978,452,943,649,749,881,825,303,490,493,445,226,007,297,351,782,886,007,986,611,814,400,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

To get this number, I had to formulate a massive equation and then substitute different numbers into it to get this final result of 2.3 trecentresexagintillion or 2.3 x 101092 .

TL;DR: There are 2.3 x 101092 possible games of normal on Summoner's Rift.

If anyone has any questions about research or information please ask and I will respond as soon as I can. Also any suggestions for future working would be very appreciated :) (only because I'm not very creative XD)

6 Comments

ModThe Djinn2 votes

Interesting, but not entirely accurate. Averaging champion skins isn't reliable, as they are heavily skewed towards older and/or more popular champions. Additionally Master isn't applicable, because if someone has already achieved 5+ Mastery than they can NEVER play a game with that champion with 1-4 mastery ranks, taking that out of the equation. You've also neglected things like Vintage Skin overlays, ranked borders, honor ribbons, and special features like Project Skin Release effects, which are all important to consider if we're considering things like mastery rank and player icon (which I personally wouldn't consider for something like this, as those don't affect the game at all).

League's MMR system also skews who can play against whom, so that data isn't accurate either. You'd need to find out the percentages of players in each MMR bracket and estimate accordingly for a true estimate.

Also, it seems a bit unreasonable to account for all potential future players, but NOT all potential future skins/masteries/champions. I'd have suggested sticking with the current number of players. If you DID use this method, however, you need to account for the fact that non-english characters are (or once were) permissible, which increases the number dramatically.

You also missed Dragon / Baron / Herald buffs and numbers of towers/inhibitors taken, which are things you could easily account for even if you can't account for actual creep score. I believe you also failed to account for champions in different roles: a game with Nami Support plays out fairly differently from one with Nami Jungle, for example.

So, fun though the exercise is, the number is staggering inaccurate, even with everything you accounted for. And, by your own admission, there are a number of more important factors you CAN'T account for.

Definitely a fun read though. :P

Jump1 votes

Hi thanks for the super critical feedback I like it, so let me go over everything you said one by one. :)

For champion skins and mastery system, creating a more reliable system is a lot hard than it looks on the surface, mainly because of the heavy math involved. For the same reason I didn't include Viktor's hex cores I cant for skins either, because there is a probability to the number of skins possible on the champion, it means your creating a variable of a variable which mathematically sucks and would require some form of supercomputer to allow for it. Also, as much as I would like to be more accurate with the Champion mastery system, I wouldn't know how to put that in a mathematical form in terms of the leveling up system, but currently it works on that there will be repeats to allow for it (If you do know how to do that though, please tell me it would be super helpful).

However for most of the improvements points put here are forgiven by the statement I made very on into the report which states, “I can not predict games with different outcomes based on skill, strategy, synergy or meta used". This does rule out a lot of options such as Dragons, Barons, Rift Heralds, MMR matchmaking, Vintage skins, Ranked Borders and special effects. I'm sorry I wasn't 100% clear in this statement, but it also assumes that all players are on equal footing with no vibration. This once again is because it will be a variable of a variable.

The thing I do like in here is talking about characters for different regions. I was looking to expanding the other two maps into this report and I can definitely add this variable

Thanks for the review of the document however, it is very much appreciated and ill be looking to improving it in volume 2. I would love it so much if you could look at it once I am finished, in about 2 weeks, because your review is the best I have had so far. :)

KidPhantomhive1 votes

Wowza. So much crazy math. Please join NASA. We need smart people.

Jump1 votes

Hahaha, thanks man but thats too hard for me :P

Miku Lv991 votes

How is it not infinite? There's no maximum game length.

Jump1 votes

That is true. :) But i did say in the report that "I can not predict games with different outcomes based on skill, strategy, synergy or meta used", and game length does unfortunately fall under this.

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