Here's a scenario

[Jet T]

Here's a scenario:

One site, A has a PR 7, 27000 links to it and returns a top position on Google for a search phrase. Lets say the phrase is blue bananas. The site isn't really about blue bananas but does make some reference to them here and there.

Another site, B has PR 4, 500 links to it and is all about blue bananas. The anchor text linking back to the home page has blue bananas in it, multiple times
for many of the 500 sites.

Has site B any chance of being top with the search phrase blue bananas.

P.s I've no idea who does come top with blue bananas, but this is just an example.

[cbp]

Yes.

CBP

[Duncan Pollock]

I agree with cbp.
Despite all our hand wringing about what Google et al do or don't look for, I'm convinced that, most of all, they're trying to come up with the most relevant results for any given search phrase. Thus if site B is obviously focused on blue bananas more than site A is, commonsense would suggest that it's going to earn a higher placement in the SERPs.
The one problem so many of us have is that there are so very many choices for some of the keywords that people punch into the search box. In these circumstances, there's bound to be some hits and misses in the results (as in "It was extremely difficult to decide which entry should be the winner"). Even then, though, a site that's only indirectly relevant will inevitably (or certainly should) be way, way down in the results.

Duncan

[Jet T]

Thanks. One thing though, if one targets the phrase say blue bananas then hopefully you might get picked up when someone searches for good blue bananas or tasty blue bananas. Or is this not so?

This whole question of relevance is fascinating especially where certain terms of phrases are used and have ambiguous meanings.

One person's relevance is another's 'I didn't want that at all' and Google and other Search Engines have to decide what makes something 'relevant'.

[Duncan Pollock]

Jet T: Well, yes and no -- but you're now asking a different question.
good blue bananas and tasty blue bananas are not quite the same as blue bananas, so it's going to depend on how many (if any) sites are focused on the good or tasty varieties as opposed to (shall we call it?) the plain and simple kind.
There's also the matter (as far as Google is concerned, anyway) of what are called broad, phrase, and exact matches, all of which complicates the way in which good and tasty will or won't "rise above" the plain and simple kind.
However, the underlying principle remains: the more focused a site is on a search word/phrase, the better its position will tend to be.

Duncan

[Jet T]

Thanks for all your help. Duncan, this matter of broad, phrase and exact matching sounds fascinating. Is there anywhere I can read more about this and in detail?

[Duncan Pollock]

Well, you might just as well go to the source, Google itself. Their page at: https://adwords.google.com/select/faq/keywords.html
will tell you as much about it all as anything else manages to do.

Duncan