By my reckoning City should be top and are currently furthest off the points you would expect them to have from the first 4 fixtures:
Liverpool on 10 points - 3 wins and 1 draw would have been likely.
I would, with the form of recent seasons, expected 1 win, 2 draws and 1 loss, so 5 points. I hoped for 2 wins, 1 draw and 1 loss, so 7 points, if they could continue the form since January. So the start is a very pleasant surprise.
Arsenal on 9 points - 3 wins and 1 draw would have been likely so probably should have had 10
I would have expected 2 wins, 1 draw and 1 loss , so 7 points the same as Liverpool because they have become slow starters.
Spurs on 9 points - 3 wins and 1 draw would have been likely so probably should have had 10
Spurs have kept the same manager and spent significantly, so I would have expected 3 wins, and 1 loss , so 9 points
United on 7 points - 2 wins and 2 draws would have been likely so probably should have 8
Why you expected the Champions to not start as well as city baffles me.
Yes, they have a new manager, and a difficult start, (on paper) but they were so far ahead last year. I would have expected 3 wins, 1 draw, so 10 points
Chelsea on 7 points - 3 wins and 1 draw would have been likely so probably should have 10
With Moaninho coming back I expected to give the team a confidence boost as he does with all his teams. I would have expected 3 wins, 1 draw, so 10 points
Man City on 7 points - 4 wins would have been likely so probably should have 12
I don't see how you could have expected 4 wins from a team who finished so far behind Utd.
Yes, they have spent a lot again, but they also have a new manager in the mix and points to make up. I would have expected 2 wins, 2 draws, so 8 points
5th fixture is a likely 3 points for Liverpool, Arsenal, Spurs and Chelsea and probably 1 point for United and City