As an advertiser, I can tell you that Adwords does not always do a good job of targeting the proper pages. I'm actually surprised somewhat but a lot of it has to do with the vagaries of the language. Here's how it most likely works:
Most advertisers will use keywords to target the content network. I advise against that but what can you do? Myself, I target specific pages more likely related to what I'm selling and usually have great success.
As a publisher, you are at the mercy of how advertisers use the system (keywords vs target) and how good they are at it. Not much you can do about that but you can try to help the system give you more relevant ads.
The system basically determines your page's topic (niche as most call it). Note I say page, not site. Each page has a topic even though the site as a whole can be about the same topic. A page can be determine to have many topics but usually will be one or two.
So, if your page is ambiguous, you are not helping it to determine your page's true topic(s). Here, you have to think more SEO-like. Keyword density is important but if you have other keywords that have high density, the system may be "confused". Don't forget too that there is lateral keywords and other things.
Here's an example. A site (which I've actually seen) is about beetle sounds, the noises these insects make. Interesting site. Ads might show on that site about Beatles music. See? Beetle = Beatles (same sound, possible typo...) and sound = music. It's no wonder the system thinks this is relevant, it's being too liberal in its thinking.
I've wondered at times looking at a list of pages where ads showed up what it's thinking. This is always taking over a client campaign and the first thing is that they just use the wrong keywords. That doesn't help of course but even so, often the vast majority of pages are totally non relevant to the keywords. I've never analyzed it so there's something going on I don't yet understand.
So what can you as a publisher do?
First, look at a page from the system's point of view and see what IT thinks may be the topic. Webmaster Tools should help. Are you using a phrase often that has nothing to do with the main topic? Maybe there just isn't a clear topic.
Next, your page's title will be very important. I advise having a description tag as well as a keyword tag. That last tag may not be used much for ranking but it sure could help determining the topic for you as a publisher.
I don't know about Adsense but is there not settings that could help towards being served more relevant ads?
You mentioned browser cookies. There is a component of the network that will serve you ads from other sites you visited (remarketing). There is also another component of "interests" by your visitor. That doesn't appear to be your case specifically although again, you don't know what the system may determine (beetle and Beatles or some other weird relation).
As it's only been a few days, it just hasn't crawled your page yet. I recall something about it won't until someone does. In other words, when you create a new page, visit it yourself. The ads should not be relevant but at least now the system has that page in its database and can start evaluating it.
Finally, your page's topic may be a narrow one where there is no relevant advertisers. I don't opt-in to the content network myself most of the time.
The third site you mention may fall into that category. The pages may not have a specific topic and there may be no advertisers. You say it's partly about sports so let's use an example. If you write about David Price's new contract with Boston, the topic is - to a human - about David Price. Adwords/Adsense may even determine that. But no advertiser bids on "david price". However, "price" may trigger other lateral thinking. You would hope that Google knows this is baseball-related and serve such ads but don't bet on it.
If you want to monetize with Adsense, do so. I don't think you'd have better luck with other ad networks. What you could try is the suggestions above and also, approach advertisers directly. If I sell baseball jerseys, I'd want to find the best sites/pages to advertise on such as my hypothetical David Price page you have. Yes, I know, lots of work but a win for both of you and Google too.
