Or you could do what I do and use IP for runes/champions and RP for skins that are on sale. Depending on how many champions you own/play, there should be a decent skin on sale every few weeks, and you can get a lot of skins for cheap (292 or w/e) when they're on sale.
But that's just me.
But that's just me.

Thanks to Jovy for the sig!
agreeing with Psi on the matter, however to answer your question: It's not random, it's all about business. I think they are putting those champs on sale that are selling less, just to get more of them sold and get it going more (more of a champ played -> more people wanting to play that champ).
I'm back!
Its all Marketing, if they know a certain champion was popular lets say during a free week then bam a few weeks later he will be free.
Its not on a rotation set in stone because some champs have never gone on sale lol.
Its not on a rotation set in stone because some champs have never gone on sale lol.
Just wait, and if you can't why not e-mail riot about it?

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I will Ryze to the occasion... hur hur
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i.e. Lee Sin was on sale at the very start of September. At 85 champions and 6 champions on sale each week, it would take ~14 weeks for him to be on sale again (AKA, mid January).
Should that be when I should expect him to be on sale again at that point? Or is it possible it'd be earlier?
I have 975 riot points, and I want to spend it on two 6300 IP champions who are on sale (So I can get two rather than just one); The two I want though are Irelia (Last on sale October 14th) and obviously Lee Sin (September 2nd), so I'm sad because I believe they won't be on sale for another 3-4 months :(
Second question is, how long does it normally take for a new champion to go on sale? I'm also interested in Graves, but I have a feeling new champions don't go on sale until they've been out for awhile.
Edit: Just googled and saw Nocturne was on sale just two months ago, at the end of August. So, I guess it is random. Part of me likes that because it means it could be sooner; Other part realizes that means it could be longer :(