The way they came up with that number is mildly eyebrow-raising. They looked at box office numbers for the four weeks before and after the Oscar nominations were announced each year, tracking both the Best Picture-nominated films and other "movies that mattered" -- movies they deemed to be "in the running," or otherwise significant. The nominees made, on average, just over $1 million more in the four weeks after the announcement than before, and the other films made, on average, just over $5 million less. Combining those numbers gave Slate their magic figure.
What do you think of this methodology? It's fairly thoughtful, but it also seems a bit circular: much like The Simpsons' theory that alcohol is both the cause of and solution to all of life's problems, box office staying power is often cited as a prerequisite to, and result of, a Best Picture nomination. I think you have to discount Slate's figure a bit by the fact that, on average, the nominees would have had more stamina over the eight weeks than the non-nominees anyway. Sadly it's hard to come up with a precise number since of course we don't know how much, say, No Country for Old Men would have made after the Oscar announcement had it not been nominated.
A good example: this weekend -- the one immediately following the announcement of the 2008 noms -- Slumdog Millionaire saw a nearly 80% box-office boost (and added over 800 screens in a move that certainly preceded the Academy's Thursday announcement). Look what a Best Picture nomination can do, right? Except that last weekend, Slumdog gained nearly 55% without the benefit of any Oscar noms. So I think you have to account for the fact that some of that vaunted nominee staying power is independent of the Oscar nominations, and is rather a result of the word-of-mouth and popularity that garnered the nominations to begin with.