"Authorship only plays a role with the “in-depth-articles” feature, and otherwise has no effect on ranking in web-search at all. I think it’s a great thing to set up, but I wouldn’t assume that it has any effect on normal rankings at all. We use over 200 factors in our crawling, indexing, and ranking, and we regularly make changes to our algorithms, so there are many potential reasons why a site might go up or down in rankings. My recommendation is not to focus too much on your competitors, but rather to work on making your site the by far absolute best of its kind — focus on your users, don’t focus on your competitors’ sites."

John Mueller, Google