In applying for jobs or making it far in the interview process, how much weight does a personal referral hold?

Would hiring managers hold a strong introduction/referral higher than a solid candidate?

Is a referral the deciding factor between two candidates that are equally qualified, equally liked (during interviews), etc?

For a highly competitive opening at a popular company, is the referral the best chance to land the job?

Are referrals measured differently during there lower ‘margin of error’ (as long as the referrer spoke highly of the candidate to their connection)?