Let’s see some numbers that ads work.

Companies have tested this. A DIY chain ran an ad and people complained it was annoying, so they stopped running it. Their sales started to decline. Started running the ad again and sales went up.

Probably you're not the target audience and just collateral damage in the ad war, but for the population in general they work.

Just because I have heard of NordVPN doesn’t mean I’ll necessarily use it (in fact I use arch mullvad, btw.)

No it does not mean you will pick it. It means you are more likely to pick it. Given all else being equal you are vastly more likely to pick something familiar than something unfamiliar. And it all comes down to trends and statistics. The hope is that more people will go for your brand that leads to more sales then the cost of the marketing in the first place. You might not go for NordVPN for other reasons, but can you say that about every product you have been advertised to? If anything the more you know about a product the less advertising will affect you in the familiarity sense - these adverts are not so much meant for you as they are for people not familiar with VPNs at all.

But there are a lot of studies on the topic like this and this meta analysis that seem to conclude that advertising is effective. And there are a lot of studies on what various aspects of adverts make them more effective. I am yet to see any research that says adverts are ineffective overall, though I have not dug that deeply into it.

There used to be a business joke you’d hear in the ‘60s, often attributed to John Wanamaker, a pioneer in marketing:

“Half the money I spend on advertising is wasted; the trouble is, I don’t know which half!”

The joke highlights the dilemma many businesses face in evaluating the effectiveness of their advertising spend. It’s remained relevant in the advertising and marketing industries, reflecting the challenges in measuring the impact of advertising efforts.

You just became an ad for mullvad...

2 second google for some numbers: “In 2022, global internet advertising revenue stood at 484 billion U.S. dollars”

One of the metrics you measure when running ads is return on investment, and companies will soon go bust if you aren’t making money on your ad spend.