I'm no data person, but I imagine storing say 5 clips for each of 1,000,000,000 players might be rather burdensome.  Why not just record your own screen action on your device?

It would not store the data as a video clip for obvious reasons...  ... and would only be saved locally.

Are you aware of how games like StarCraft2 can store an entire match in a tiny data file for playback?

 Recording all your games into video isn't practical.

No I'm notaware of how other games store.  Like I said I'm not a computer guy, but it works for me.  I wouldn't object to it if they rolled it out.

Well, for what it's worth, I am a "computer guy". It would be trivial to record, at least as long as the recording is for the current patch (cross-patch would be trickier, but solvable). All you'd really need to save is the RNG seed, a copy of all initial champion stats, and the sequence of player actions. Everything else is deterministic based on those variables, and could be fully reconstructed. You could records hundreds of matches and the resource consumption would be a rounding error compared to what the game uses normally.

Not that I see that much use for the feature, but I guess it might occasionally be useful for some people to rewatch a recent loss to see what went wrong.

Even just a rewatch button, appearing after arena battles, I'm sure would benefit all. Once a missed outcome is different from what was expected it's natural to want to be able to see what you've missed.