Ever wondered how many possible 5v5 hero combinations there are in Dota? Yes it is a lot

I stumbled across this post from six years ago where a user ( /u/Der_Pacifist ) calculated all possible unique hero combinations. I redid the math for our current hero pool (121). Feel free to check the math.

Calculation

(121! / (5! (121 - 5)!))	* (116! / (5! (116 - 5)!))	/ 2	Result: 15942121184925936
possible 5 hero combinations out of 121 heroes	multiplied by the possible 5 hero combinations out of the remaining 116 heroes	divide by 2 since side does not matter	Rounded result: ~16 quadrillion (16,000,000,000,000,000)

Wolfram Alpha Calculation: ((121! / (5! (121 - 5)!)) * (116! / (5! (116 - 5)!)))/2

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How does this number compare?

So it concludes that the number of unique 5v5 dota 2 matchups is 15942121184925936 (~16,000,000,000,000,000). But what does that mean? Here are some very rough estimates to better visualise the number.

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• We currently have around 7 billion people on earth. If EVERYBODY would start playing Dota nonstop without rest or sleep and finish one match every 30 minutes it would take around 130 years to go through all possible 5v5 matchups.

It is also...

• ... ~700 times the number of red blood cells in the human body .
• ... ~80.000 times the number of stars in our galaxy.
• ... including 609357937853574 (~609 trillion) matchups /u/SirActionSlacks- would be exited about (no Windranger but Techies).
• ... half the number of roster changes NaVi went through since TI 4.
• ... the average MMR of users on this subreddit.

submitted by /u/memologic
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