You may have heard that the best day to buy an airline ticket is a Tuesday.

Other things you may have heard: Polaroid cameras now let you see photographs shortly after you take them, and bloodletting is no longer an accepted cure for fever.

In other words, it’s outdated information. The standard explanation for the Tuesday theory was that airlines release their bargains early in the week and competitors scramble to match them. But even if there’s still some truth to that, other variables have complicated things.

There are plenty of companies out there offering reports and tools to help you navigate this and other airfare decisions — Google’s Explore Flights engine and Kayak’s price trend feature among them. But a few months ago, some smart people at a company called Hopper, whose primary business is aggregating blog posts for travelers, started releasing intriguing reports about how to lower your travel costs. The reports (available at hopper.com/research, by signing up for their mailing list or following their chief data scientist on Twitter, @patricksurry) are coming with a frequency, transparency and detail I haven’t seen in other reports that try to answer similar questions — and I’ve looked.

And while static reports provide only broad conclusions, Hopper also provides customizable tools that are as powerful as they are simple to use. Hopper’s detail and customizability mean more specificity, whether you know exactly where you’re flying or still haven’t decided. And they’re doing it with a huge amount of data, about a billion price points delivered to them every day. After taking the reports and tools for a long spin, I came up with some conclusions; here are a few of the most useful.