Well, they have sales data from before the ad ran, and then they get sales data from after the ad ran. It's not a perfectly controlled experiment, but if the ad has an impact (or doesn't) they'll be able to tell.
It's so far from a perfectly controlled experiment as to be useless. You have sales before the ad ran (when it wasn't the super bowl), and you have sales after (when it was the super bowl). That's a huge confounding factor; everybody buys chips, soda and beer on Super Bowl Sunday.
They're not able to tell right away. They pay people like Nielsen millions of dollars to analyze the effectiveness of their ads at super bowl time. Those folks do regression analysis of the sales figures compared to previous years, with the knowledge of how sales in general have been, sprinkle with some bullshit so that the client will hear what they want to hear, and then deliver them back to the companies that ran the ads. (My brother does this job).
My point: they don't really know, and it's not at all easy to know.
edit @jonknee since HN won't let me reply: Except that you're advertising Doritos more than those other brands. How much of that purchase effect spike is due to your other advertisements, how much is due to super bowl ads, and how much is due to people simply feeling like Doritos are an appropriate super bowl snack?
If you have only one type of chip then it would be very hard to tell, but if you advertise for Doritos and Doritos sales spike 4x as much as your 10 other brands that weren't being advertised it's not hard to do the math.
Or you run the ad in some markets, don't run it in other markets, and watch the relative numbers. A/B testing: not just for Internet micro-businesses and Google.
