I am not sure about believing in astrology, you mentioned this:
Even if you can't understand why it works, it is simply too consistent to be mere chance
What do you mean by "consistent"?
I do have family (a lot of them) who believe in this, but if I am being honest I do have serious doubt about this subject.
I would love to know some examples of that consistency you mentioned :P
Well like Eugene and I were discussing in his comment, Mercury Retrograde. I tried denying it had any influence for years because I simply found it too inconvenient to want to believe in it, but even times when I didn't know it was MR, once I found out it had been it explained all the miscommunications, messed up travel, and general problems with anything involving travel or communication. And that's what MR does.
After many years resisting the idea, I finally said to myself, "Ok, how can I work with this?" And now whenever MR is upon us I plan to do more planning, writing and reflecting and never, ever plan a product launch for that period.
It's purely anecdotal, but I think that may be where those systems of astrology came from. Many people collecting anecdotal correlations for thousands of years.