The "science" of advertising is one into which I haven't looked... but it does seem kind of baffling. Like, I presume the companies paying for advertisements have done the actual work of checking to see what the marginal return on ad-dollar-spent is, as opposed to, say, the marginal dollar price reduction, since from the standpoint of the seller they are identical to the bottom line:
That is, if I spend $1 in ads, I get $X more in total revenue. If I drop prices $1, I get $Y in more total revenue. The interesting thing is that to drop prices, I don't actually even need cash to do it, so it's arguably a more sustainable choice; in order to pay for ads, I actually need cash...
The brand recognition aspect is very interesting though, because it seems like it would be very difficult to tie sales at a future date to a particular ad campaign. Like if I pay $1 for ads today, how do I know the sales growth I have in 3 months is due to that ad, compared to any of another factors? Do companies buying ads actually track the data enough to make these determinations?
I think ads only really work in a few cases:
1) Announcing new products
2) Announcing availability of products
3) Appeals to emotion for truly discretionary purchases, where a product doesn't have a "taste" lock-in factor (e.g., if you prefer the taste of Coke vs Pepsi, no amount of advertising will change your taste buds).