considering the total 'x' number of recruitment happening in a year, what is the percentage contribution of recruitment happening through linkedin? second question is out of total 'y' applicants applying to the posted jobs on linkedin, what is the success rate? these questions arise because the companies get applicants via a great variety of means (job sites, consultants, their own website ..etc) then they can easily check the profile of candidates on linkedin, if one can get some idea on the above two questions, we can co-relate or understand the necessity as why companies post jobs on linkedin!!
I don't have the numbers per se for Linkedin but I can image that the number of applicants through the network increases everyday. I've recently finished Dan Miller's book "48 Days to The Work You Love" I believe he mentioned something along the lines of 8 out of 100 applicants get hired through online means whether it's Linkedin, Craigslist etc..
Usually once the job hits the general public 9 times out of 10 the position is close to being filled. Companies I believe have to receive a certain amount of applicants before they make a decision. (My guess is to rule out discrimination)
Hope this helps a little.
Think of LinkedIn as a place where you want to be hunted; the world of resumes and job boards as the place where you want to do hunting. By being "attractive" to employers and headhunters you are more likely to be reached out to, to appear to be the desirable "passive job applicant" and have opportunities presented to you, rather than you chase down jobs.