I think Magic 8-Ball would give best chances XD.
That said, I don't think the game is truly won until a Nexus falls.
But let's say that you stand to win 20 LP from a game or lose 15 LP.
How bad would your chances of winning have to be to make it worth the dodge?
A simple question, a simple calculation: basically you would have to have a <35% chance of winning to consider the dodge mathematically close to worth it.
And that's insane: you would have to be so incredibly confident from champion select that you would lose the game that chances are you are actually be better off playing the game to see if you can get a lucky win in those cases when you suspect that the odds are not in your favor.
So if such an app were to exist that could give you recommendations on dodging than I suspect that it would almost always tell you that it is better to play the game than dodge it. I think that it is just better to use your own intuition during champion select to decide if dodging is worth. Just keep in mind that it is rarely worthwhile to dodge (even in ELO Hell).