Three things right off the bat.

I know my students are learning, I'm a teacher

This is a bad analogy, that is not the same at all. We are not talking about agencies, we're talking about the centuries old institution of ADVERTISING. You will need to compare Advertising and Eduction.

So to turn this around on you, actually how old are you? Any way, this is like saying "How can we tell that kids that go to school turn out better educated than kids that don't go to school? What if we think they're just paying attention"

You're not convincing me

This says more about how slow you are than how obvious I should be.

Please link me proof.

First of all, no agencies are not willing to link their statistical data about their clients return on their investments. Again, HOW OLD ARE YOU?

Finally, if I must entertain you, if I must. Here.. This is a centuries old field of work and your delusions of grandeur because you think it doesn't work on you is hilarious.

In fact, you're a FUCKING GAMER and you still think advertising doesn't work?? WOWWWWW!! Ever heard of Call of Duty? Never fucking heard of the hype-train? Actually I'm done.

I'll leave you with this, now please move along.

" I'm guessing, many of your friends -- think advertising doesn't "work" is that they think advertisements are trying to make them do something immediately.

They're wrong.

Successful advertising rarely succeeds through argument or calls to action. Instead, it creates positive memories and feelings that influence our behavior over time to encourage us to buy something at a later date. No one likes to think that they are easily influenced. In fact, there is plenty of evidence to suggest that we respond negatively to naked attempts at persuasion. "