To be fair I feel like I've outlined them quite clearly above.
I thought we undersold and overbought. I thought the recruitment was poor and as I've said before I'd like a smarter man than me to look at the historical results of sides who've sold their best striker for thirty years, sides who've had wholesale changes and sides who have been trying to take a step up in level with such fierce competition. A cursory glance at milans season so far doesn't dissuade me that these are all factors.
That would be the Milan who have 12 points from 6 games in the league and are top of their Europa group with a 5 point gap to 3rd, would it?
This caught my interest on a good day though, so I've spent a bit of time having a look at how your points total and goal difference varies with both number of players brought in and for those that lost an important attacker. The big caveat is that the search methodology used to collate examples would never pass peer review for publication.
There are also many limitations to this kind of analysis, which is why it's not really done. How do you rigorously account for confounding factors? Is the amount actually spent important when assessing this, probably but when heavy inflation is involved there's not a simple way to account for that. I've limited this to summer transfer windows and the first 6 games of the season through laziness; you'd hope that factors like fixture difficulty and transfers late in the transfer window will average out, but it's not easy to test for that. This data is over a number of different leagues, how does average league strength affect the results? How
All that said, here's a load of useless stats!
In this dataset, 23 teams signed 6 or more players (average of
in the transfer window, with 12 of these teams losing at least one star attacking player. The median finishing position the season before was 7th and after 6 games, the average number of points was 10.8 with a goal difference of +3.08. There was no relationship between number of players signed and points total, but there was a weak correlation (r = -0.37 for the maths nerds) between number of players signed and goal difference, with teams that signed more players having a slightly worse goal difference.
Here's a graph showing all that crap...
So, we might be a bit below average, but 4 other teams have picked up 7 points or less in this small group of teams. Brendan Rodgers was sacked in 2014/15 with Liverpool on 7 points, going on to finish 6th; the next season Koeman's Southampton had 6 points from the first 6 games, but went on to finish 6th. Sevilla went on to finish 5th and 7th after their poor starts.
For wider context, after 6 games, the average team will have picked up 8.3 points after 6 games. So given the games we've played, we're not really that far behind in terms of points given our fixtures.
The other main question is how other teams have done after losing a key attacker. The average number of points for a team that's not established in the top 4 and has lost a key attacker (n=12) is 9.5 with a goal difference of around 2. There's a stronger relationship between goal difference and number of players signed (r = -0.56; -0.70 if you exclude us this season).
As I said before, there are many limiting factors to any kind of analysis along these lines. Even then, it probably does indicate that we should be more considerate of the situation.
I can't really say it's changed my mind on Koeman though personally. It's more about the process than the results for me.
(Oh, and if anybody wants to look at the teams I included in all this, the spreadsheet is here: https://drive.google.com/open?id=0B0ZHi3fNbv1TTUNPdk0zTmtMbWM