This same post came up last year.. It seems like it's a revolving door. First of all if there is one thing I have learned about asking Riot any question is that the way you phrase your question heavily dictates the answer you get. So if you ask them does Riot make money off of LCS then the answer is no.
BUT!!! what you are forgetting is that $$$$ and making money isn't a straightforward concept. TLDR: Return on Investment (ROI).
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Riot wants to extend LoL's presence as much as possible and would like to not develop LoL 2 anytime soon.
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LCS is Riot's way of not only gaining increased exposure because let's face it BBC had an article about LoL Championship. It does get attention outside of its current fanbase. You can easily check this with the growing numbers over the past years.
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In order to extend LoL presence and avoid the game from A) Dying, and B) developing LoL2 is supporting the game, more importantly supporting the community aka Prize Money. This keeps people invested, helps secure your market share and potentially grow it. If you want an example look at Capcom, Street Fighter and the Capcom Cup which is their global tournament. Now look at Marvel vs. Capcom 3.... which is dead. Capcom decided to put their marbles into Street Fighter and now it's the most dominant fighter. If you are going to play one fighting franchise in your entire life in this era 7/10 it's going to be Street Fighter.
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Professional players are role models plain and simple. When you play Ryu you want to be Daigo etc. etc. that's keeping you invested keeping your buy in. Showing that the impossible is possible makes people want to attain it.
This is the same logic with Riot, LCS is an investment to keep their community engaged, invested attracting more people and putting up with Riot's cyclical bullshit from time to time ,and continuing to buy content.
So for you to say Riot does not make money off ESports without actually understanding how Investments pay off is foolish. Imagine if Riot didn't have LCS or if DOTA's prize money far exceeded LoL year after year I am sure I wouldn't be tearing down your post, because LoL would be dead aka no $$$$$$.
TLDR: Esports makes Riot money over time, which is better than money up front.