The guidance for off-topic questions has this to say about the use of statistics:
Asking for a link to something or statistics
This is a subtler meaning of the 'favorite off-site resource' part of the wording of the close reason. Asking a question that doesn't draw upon the community's expert knowledge as programmers but rather asking it to be a crowdsourced search engine falls into this area.
Links to things suffer from link rot. Statistics become out of date over time. Neither of these contribute significantly to the collective knowledge of problem solving that the Q&A format provides.
I don't understand what the issue is with questions that invite answers that involve statistics. To me that guidance is bad for the quality of answers on this site. Allow me to illustrate.
Take for example this question about code reviews: How to deal with no code reviews in my new place when I come from that practice?
In my view, having to argue in favor of the best practice of code reviews is something programmers are likely to face (hence on-topic) and the best possible answer to this question is to provide provable statistics that demonstrate the value of the practice of code reviews (and possibly statistics that compare the different ways of performing code reviews). This way the asker has better than anecdotal arguments in favor of code reviews as a best practice. In my opinion statistics are a higher quality answer when it comes to best practices answers, because they remove the bias inherent in an answer that is a sample of 1.
I can understand forbidding link-based answers, and requiring that the statistics are repeated in the body of the answer (citing the off-site resource where they were obtained), but why is it a good thing for P.SE to automatically close questions about best practices which can best be answered through statistics?