When it comes to predicting the next seasons results, the simplest method is to simply assume things will stay largely the same. It's the best starting point for a prediction, the 'base rate', to use bayesian terminology, from which to anchor predictions.
To get a little more complicated, an even more accurate predictor of future performance is a measure called Total Shots Ratio. Basically, how many shots a team takes versus how many they allow. The reason why TSR is effective is because it's essentially a measure of how much a team controls games - the more control you have, the more shots you will take and the less shots you allow. More accurately, TSR correlates fairly well to points gained - it's not the best correlation, which is goals, but it's still a very reliable indicator
But then why not just use goal difference? Regression to the mean. Put simply, TSR has the lowest regression to the mean of all statistical indicators. Regression to the mean, for the uninitiated, can be considered as how much a statistic relies on skill versus how much it relies on luck. The more regression, the more luck is involved and the less predictable a statistic. TSR has the lowest regression to the mean, at 31.2%. Goals has a 42.4% regression and Points a 47.8% regression over consecutive seasons.
So the best indicator for basing a future prediction is the TSR of teams from the previous season. To add just a little more complexity, we can also add in Shots on target ratio, which has a regression of 32.1% and is of course a good indicator of shot quality that teams create and allow others to create. Finally:
TSR+Shots on Target Ratio=
Arsenal: 0.557
Chelsea: 0.643
Everton: 0.547
Liverpool: 0.606
Man City: 0.657
Man U: 0.546
Tottenham: 0.563
To then turn that into Expected Points:
Man City: 79.1
Chelsea: 76.8
Liverpool: 70.4
Tottenham: 63
Arsenal: 62
Everton: 60.3
Man U: 60.1
Now, a few notes:
1. in real terms things get more stretched and less close since points are obviously awarded by integers; you can't get 1.85 points
2. No doubt everyone will pick out Tottenham and yell "Lol Tottenham r shit. Didn't u watch last season. Stats = Craps" First of all, Tottenham did finish 5th, on 69 points, which would have been enough for 4th place in many preceding seasons. Additionally a few other stat measures which I won't get into went badly for them but could explain better why they have this rating.
From these positions, we can then add our qualitative observations to slide expected points up or down. From a purely statistical perspective, United are 8th (I didn't bother including Southampton) favourite, but only marginally with little difference between them and Arsenal or Tottenham. However Arsenal have done fairly well with their transfers so far, so adding in my qualitative observations I would not expect them to overhaul the expected gap. The difference to the top 3 teams is likely far too large to overcome.
