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Dec 17, 2014

How Many Possible Matchups are in League of Legends?



Earlier today, user forscience0 posted up an interesting calculation on reddit, calculating that there are 46 quadrillion possible 5v5 matchups in League of Legends. This is interesting in itself, but I think his calculations can be refined a bit further...


Original Inputs
Total Champions: 123
Teams: 2
Size of Teams: 5 players

Additional Inputs
Number of Champions with >10% popularity: 36

Original Calculation

With the current champion pool of 123 champions there are 216,071,394 possible team compositions which leads to 46,686,847,305,103,236 possible 5v5 matchups in League of Legends (blind pick).
Yes, you read right:
46 quadrillion 686 trillion 847 billion 305 million 103 thousand and 236.
With an average game time of 30 minutes, you would need more than 2,662,950,450,895 years of playing 24/7 if you wanted to play all possible matchups one time.
This is more than 2.6 trillion years! In comparison: this time span is approximately 190 times the age of the universe or 586 times the age of the earth(!).
EDIT: yes guys, you are right. My calculation is not entirely correct because matchups where only the sides of the teams are swapped are counted twice.
The right number of possible 5v5 matchups in blindpick is the following:
(123 nCr 5)² / 2 + (123 nCr 5) / 2 = 23,343,423,760,587,315 (23 quadrillion...)

Modified Calculation

In calculator mode, his formula can be arranged as follows: (nCr(123,5))^2/2+(nCr(123,5))/2

Therefore, as adjusted for champion popularity, (nCr(36,5))^2/2+(nCr(36,5))/2 = 71,061,672,528 (71 billion) different possibilities just for the top 30% of champions!

If that's not incredible enough, that's the calculation for normal games. The calculation for ranked games would be as follows:

nCr(36,5)*nCr(31,5)/2+(nCr(36,5))/2 = 32,027,732,351 (32 million) games to play.

Sounds like I still have quite a ways to go...anybody else out there close to that number? At 20 minutes a game that'll only take 1,218,711 years :]

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  1. SquirrelNutkinsDecember 18, 2014

    I r8 8/8 plz dont h8 i just wanted to convers8 and maybe demonstr8 how much i love to read your math and masturb8.

  2. give this squirrel a nut plz!

  3. SquirrelNutkinsDecember 18, 2014

    Did......did you say nut? I like those.

  4. Nice m8 sorry if I irrit8 u but I just love ur rhyming. I r8 8/8 m8, your rhymes are gr8!

  5. Daniel BarcelosDecember 18, 2014

    If you join all the games tath ever happened in the whole world, how many years had already been played and how many games.
    Well, even if LOL could be played for 1 trilion years, not even god would see a match with Galio, Urgot, Yorick, Skarner and Anivia in the same team anyway

  6. a question that does not relate to this post. after 5 drags if u do another drag does t give u any buff??

  7. disqus_uc8SPs7S3iJanuary 04, 2015

    I'm not sure if you already got an answer to your question, but here is the answer:
    The fifth time you take dragon, it grants a temporary buff that lasts three minutes (it is similar to the old Baron Buff). The dragon won't respawn for six minutes, and by then your buff will have worn off. If you take it again, it gives you that temporary buff for three minutes again. Hope that helps!


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