[Halfdeck]

The difference appears to be in the degree these factors affect the outcome.

Exactly, Peter. I didn't say "domain authority doesn't matter"; I said it's overrated.

Domain authority is the high ranking of web pages of a domain on the basis of that domain having a high number of inbound links.

John, so in your opinion, the difference between "domain authority" and "authority site" is topical dependency. A strong domain has a potential of ranking high for every query under the sun, while an "authority site" refers to a site that's considered authoritative in a given niche.

Google doesn't make that distinction. An authority site is a domain with many pages with high authority scores. Domain authority is the combined authority scores of all pages belonging to a domain.

Authority score calculation pre-hilltop is query/topic independent (PageRank-based ranking). That's slightly problematic, as the Hilltop paper notes:

PageRank [Page et al 98] is an algorithm to rank pages based on assumption b.* It computes a query-independent authority score for every page on the Web and uses this score to rank the result set. Since PageRank is query-independent it cannot by itself distinguish between pages that are authoritative in general and pages that are authoritative on the query topic. In particular a web-site that is authoritative in general may contain a page that matches a certain query but is not an authority on the topic of the query.

* assumption (b): authoritative pages tend to point to other authoritative pages.

Authority score calculation post-hilltop is topic/query-dependent. Hilltop, for example, refines results based on PageRank but the refinement is based only on links from relevant, "expert" sources (btw, I'm not assuming or suggesting Google is actually using Hilltop).

Matt Cutts' reference to hub-like scores and authorities, which is probably a reference to the paper "Authoritative Sources in a Hyperlinked Environment" (you can find the reference by Googling "googleguy hub authority") suggests Google calculates authority scores at least in part based on topic/query.

In response to a query, we first compute a list of the most relevant experts on the query topic. Then, we identify relevant links within the selected set of experts, and follow them to identify target web pages. The targets are then ranked according to the number and relevance of non-affiliated experts that point to them. Thus, the score of a target page reflects the collective opinion of the best independent experts on the query topic.

Now people put alot of emphasis on "relevance" when talking down links / PageRank / authority score. But they discount the abundance problem:

The number of pages that could reasonably be returned as relevant is far too large for a human user to digest. To provide effective search methods under these conditions, one needs a way to filter, from among a huge collection of relevant pages, a small set of the most "authoritative" or "definitive" ones.

- Authoritative Sources in a Hyperlinked Environment