It seems like Seth Kugel's article in the New York Times about "Crunching the Numbers to find the Best Airfare" is quite popular. In this article, he said things like this:
The overall take on the best day to book tickets turns out to be somewhat underwhelming, if you look at the country as a whole. Hopper’s data shows it’s actually Thursday, but don’t expect that fact to save you much money. Reserve a domestic flight on Thursday and you’ll spend, on average, $10 less than if you reserve on Saturday, the worst day to book domestic flights. With international flights, you’ll save, on average, $25 over Sunday, the worst day to book flights abroad. (Those are “maximum averages” that assume you would have booked on the worst day and are now booking on the best.)
This is meaningless navel-gazing.
As I explained in my notes to my Kayak article on 538, talking about best or worst fares is meaningless unless one can describe a strategy with which the traveler could attain those fares. This strategy must work in real time, before it is known that a particular fare would be the best or the worst.
Without such a strategy, we are talking about paper gains and losses.
Analysts who follow Kugel's logic though rarely realize that they are talking about paper money. So, later in the article, Kugel said this:
For the vast majority of routes,... avoid booking on weekends and try midweek; for the average American flier, those savings will add up in the long run.
What savings? Those would appear to be the "maximum averages" defined above, the difference between the best and the worst days for given routes based on a lot of historical data. But there is no strategy to reliably attain the best fare; in fact, there is no strategy to reliably buy the worst-priced tickets either.
As I said before, if the goal is to gain provable savings, you need to write down how you are making the purchase decision today, then you need to define what your new strategy is--whether it is using Kayak, or using Google (which doesn't do predictions)--and then you should compare the two methods.