The honest answer to how far in advance to book a flight is that it depends on the route, and any single number you've been handed is an average dressed up as a rule. "Book 47 days out." "Book eight weeks ahead for domestic, five months for international." These come from averaging a huge pile of fares and reporting the day the average was lowest. Your trip isn't the average, though. It's one pair of cities on one set of dates, and the window that was cheapest across everyone else's flights tells you very little about yours.
Where the low actually tends to land
Across the trips we watch, the cheapest fare rarely shows up either the day the route opens or the week before departure. It usually lands somewhere in the broad middle, weeks out rather than months. That much lines up with the folk wisdom. What the folk wisdom leaves out is how wide and how uneven that middle is. On one route the low might arrive two months ahead and never come back. On another, nearly identical trip, the good price shows up late and the "book early" advice would have had you paying more.
Booking very early mostly buys you a seat, not a deal. Airlines open fares high, before they know how the flight is filling, so the earliest price is often just a placeholder. Booking very late is the other trap: in the final stretch the seats left are the expensive ones, and you're betting against the airline's own pricing. The sweet spot exists, but it's a range, and it moves.
Why a fixed rule can't catch it
A "book N days out" rule is a single guess made once, against a price that keeps moving after you've looked. Even if the number were right on average, you'd still be buying your route, and a fare can swing more inside one week than the early-versus-late gap is worth. The date on the calendar was never the lever. Flexibility and attention are, which is the same reason there's no magic day to book.
So we don't hard-code a countdown. We check your saved routes every morning and price the real combinations, then send the three best fares we found. Some mornings the low lands early. Some mornings it lands late. The point is to be looking when it lands, instead of booking on a day a rule picked for someone else.