The real no. 1 is always the player with the best accomplishments over that particular year. Of course sometimes that can still be highly subjective, for instance with 2003 when many people disagree over whether Roddick, Federer or Ferrero had the best year.
However with 1977 it was clearly Vilas.
While I still think that Connors was the third best player that year behind Vilas and Borg, I still think he had an excellent year given that he won 2 titles and reached 2 more finals at the 4 biggest tournaments he entered.
He had a much better year than similarly questionable year end no.1 players Mac in 1982 or Sampras in 1998 (despite winning Wimbledon) I would say.