I think most would clearly consider Borg as the best player in 1977. Of course we are looking at the top ranking instead, which is not exactly the same thing, but the two are also related. I do think head to head is important as well when the records are this close in terms of pure accomplishment for the year. It's not the only thing to be considered, but it is important to factor in. Now, how much of a factor it is can be debated. Regardless, with Connors, Borg split their two big matches, but Borg's Wimbledon win trumps the Masters loss and he did go 2-1, with wins on grass and clay. You have Borg going 3-0 versus Vilas, including his Masters win. So, if you count the Connors win as significant because it was at a big tourney, you have to also concede that Borg beat Vilas at a big tourney. Borg beat Vilas on both clay and carpet. I think Borg #1, with Vilas at #2, and Connors at #3 would be my order.