My hypothesis is that in informal writing (say something like Stack Exchange questions) "it's" is massively more common than "its".
Is this true? Are there any data to support it? Concrete percentages?
Is there a heuristic that a very simple program¹ can use to detect when "its" would be appropriate?
The purpose of this question is that it is one of the more frequently confused pairs of words. I'm designing tools for flagging potential spelling mistakes, so if one was a lot more frequent than the other and I had indicators that the piece of text was poorly spelled then it might be a valid suggestion.