I just got my PhD recently and have a postdoctoral position now. I started applying to faculty jobs (tenure track/US/engineering/R1) for this cycle. I know that the whole hiring process is complicated, can/may involve politics, luck etc. and since most applicants don't hear back from search committees, how can I evaluate/compare my application to others (especially those who got interviewed/hired)? I would like to hear opinions from those who have served in search committees or are involved in the hiring process. Any tips or information will be much appreciated.
Unfortunately, there's little you can do on your own. One huge obstacle is letters of recommendation, which play a major role in screening applications. You probably won't know exactly what's in your own letters, and until you've served on a search committee yourself, you certainly won't know what the letters look like for the applicant pool as a whole. This makes it really difficult to gauge how impressive your letters are: you just won't be in a position to estimate whether a given opening might receive three applications with letters comparable to yours, or thirty. This makes an enormous difference for estimating your chances.
Partly you'll have to rely on advice from experienced mentors, who have years of experience seeing how job searches play out. Partly you'll just have to guess, and apply to a slightly broader range of jobs than you hope for, just in case. But you can at least make quantitative comparisons with recently hired people at universities you aspire to. (Number of publications, prestige of journals/conferences, number of citations, etc.) Don't take these numbers too seriously, since they can offer at best a crude impression of your track record, but they will show whether you're in the same ballpark as the successful applicants. If your application looks quantitatively similar, then it may be reassuring. If it doesn't, then that will at least show what you need to emphasize in your application. (E.g., if you have relatively few publications, then you'd better make sure readers are impressed with their quality.)
@Anonymous_Mathematician has some good advice. Another forum that contains useful discussion and advice, including commentary from a range of people who have been on search committees in various academic fields at various types of universities and colleges can be found at The Chronicle.