So you know that in game replay function Riot has been promising us for over a year? That function that is too hard for them to code with the current build and blah blah blah.
Someone got sick of waiting and created a 3rd party replay function for the game. Haven't tried it myself but everything I've read about it has been positive.
It's good and it allows for effective and positive critique of team synergy. You can sit back, watch how a game went, and see what you did wrong.
If you find the thread on the official League forums people are really ripping into Riot (with good reason) in regards to replays, lack of tournaments, server stability, etc. etc. etc. Multiple Riot replies even but most of them a from a head character design guy who has no say in game features.
"Sometimes I think the surest sign that intelligent life exists elsewhere in the Universe is that none of it has tried to contact us."