It’s not the irrelevant backlinks that helped your web pages rank well on the SERP. The irrelevant backlinks provide no direct benefit at all, it is the relevant backlinks that provide all the benefits.
If you take a closer look at your own methods I’m sure that you will discover that you have been channeling link juice through relevant backlinks. Perhaps your success came through unwitting use of effective techniques and you did not realize many of your backlinks were in fact relevant.
Even a blind squirrel finds a nut every once in a while.
Again, much confusion comes, from misunderstanding how search engines work. For example, the website topic is not a signal used by search engines for relevancy, and this applies specifically toward backlink relevancy. All signals are page level. A backlink from a page that contains the targeted keyword in or near the anchor text is a relevant backlink. An irrelevant backlink has no direct influence on ranking. It is only after link juice is channeled through a relevant link that you will receive the ranking benefits.