From the looks of it, there is no easy way to find the average time to receive AOR after submission. It depends on the method of submission, processing office, and the total backlog of applicants to fulfill.
Since the Online application was available from December, most of the applicants submitted online during December got AOR within 4 months on average. But there were paper applicants who got it earlier than some of the online applicants.
My guess is, it's very rare to get AOR within 3 to 4 months regardless of paper vs online.
Hope this gives you a broad context for your question.