I like doing my own data digging on playing styles to see what different managers have to offer. Yes, xG is nice, but there are other things too I think which show a manager's style and tactical thinking. If the brief really is possession-based attacking football, then it should be something that shows up in their body of work. So I went and looked up a few different things for different managers to get an idea of what they look like, and then see how they compared across Europe's Top 5 Leagues (so, England, France, Spain, Germany, and Italy, totaling 98 teams), to get a rough idea of everyone in a single group. All data is from FBref. I included one guy not mentioned by anyone who might be a good fit, and I included Nagelsmann to see why he was so highly rated.
So, first off, the classic xG. I wanted to see it as a constant rate, so it's per 90, but I also wanted to see both for and against (xG/90 and xGA/90). A guy with a good difference could be a mediocre attacking team but brilliant defensively, or vice versa. I'm also including Shots/90 to get an idea of which guys coach teams to do more active attacking, or leaky sieve defending. We're Spurs, and we want people to be on the front foot all game long, but good teams don't give up a lot of shots in return.
Potter xG/90 1.43 (33rd) xGA/90 0.98 (13th) S/90 12.82 (28th) SA/90 8.76 (9th)
Galtier xG/90 1.33 (44th) xGA/90 0.70 (1st) S/90 12.94 (27th) SA/90 8.77 (11th)
Fonseca xG/90 1.84 (13th) xGA/90 1.31 (48th) S/90 13.79 (18th) SA/90 10.15 (24th)
Lopetegui xG/90 1.36 (40th) xGA/90 0.91 (6th) S/90 12.00 (38th) SA/90 8.76 (10th)
Kovacs xG/90 1.80 (14th) xGA/90 0.91 (7th) S/90 12.49 (31st) SA/90 8.60 (7th)
Nagelsmann xG/90 1.90 (10th) xGA/90 0.81 (3rd) S/90 15.68 (4th) SA/90 7.26 (2nd)
So, Potter combines an top 1/3 in Europe attack to a roughly top 10 defence, with Galtier's attack taking about as many shots as Potter's team, but from worse places, and he combines that with an in some respects, best in Europe defence. Fonseca's team attacks better, but also gives up more shots, and those happen to be quite good shots. Lopetegui is in the same region as Potter and Galtier in defence, but takes fewer, crappier shots. Kovacs manages roughly the same shots as Potter, but of much better quality, while being maybe slightly ahead on defence. Nagelsmann combines a lot of good shots with giving up very few, crappy shots.
In terms of possession, I wanted to know how much of the ball they had (%), but I also want to know who is passing into the final third more. That's just a stylistic thing, but the Spurs way is heavy on the possession, and heavy on the pass and move FORWARD. So, I wanted to know who was making the most progressive passes forward per 90. I also wanted to know who was the most active in the final third, so I wanted to see who had the most touches in the final third. And finally, we know we want a pressing team, so which team had more successful pressures per 90.
Potter Possession 51.5 (40th) ProgPass/90 34.5 (40th) F1/3T/90 171.3 (22nd) Press 43.1 (33rd )
Galtier Possession 54.1 (24th) ProgPass/90 41.9 (11th) F1/3T/90 174.6 (18th) Press 42.3 (37th)
Fonseca Possession 52.3 (35th) ProgPass/90 36.6 (27th) F1/3T/90 156.5 (36th) Press 41.0 (50th)
Lopetegui Possession 61.7 (5th) ProgPass/90 35.3 (37th) F1/3T/90 169.8 (23rd) Press 39.8 (66th)
Kovacs Possession 56.1 (17th) ProgPass/90 42.2 (9th) F1/3T/90 169.3 (24th) Press 46.6 (14th)
Nagelsmann Possession 59.9 (11th) ProgPass/90 48.8 (8th) F1/3T/90 201.5(10th) Press 51.3 (3rd)
So, Nagelsmann has more possession, plays the ball forward more, has his team doing more in the final third, and pressing more than anyone else. So, the stylistic gold star goes to him. Galtier's Lille passes the ball forward much more often than Potter's Brighton, with slightly higher possession, but Potter's team is doing stuff more often in the final third than Lille, and is pressing more. Fonseca's team is in-between Potter and Galtier on posession and forward passing, but does significantly less in the final third, and presses less as well. Lopetegui's Seville has a LOT more of the ball, but passes it forward and uses it in the final third only as much as Potter's Brighton, and presses massively less. Wenger's infamous sterile possession? Kovacs has more possession than Potter or Galtier, passes it forward as much as Galtier, but works with it in the final third as much as Potter, and presses significantly more.
So, your mileage may vary, and opinions will differ. I think Kovacs is interesting as an unmentioned guy, but if Monaco are seeking to replace him with Galtier, then if he is available he could be a very interesting choice, who seems to tick the same boxes that Nagelsmann or Potter do. Fonseca and Lopetegui look interesting, but flawed. Lopetegui's team looking much less proactive than we'd like, and Fonseca perhaps having too much of the Bobby Martinez about him (as in, we'd get put the sword by a good team too often).
Potter is interesting for me in that despite working with Brighton's resources, he is getting a team to play like a "big team." Stylistically, they very much play like what we want a European giant to do, and it seems like bar a complete inability for their forwards to even hit the broadside of a barn, they would be impressively far up the table and he would be getting a lot more attention.
Even if some egos in our squad might be put off, I think those players might be leaving anyway. If they're willing to give it a go, I think Potter stands out as a very good match. If they aren't then we need to make sure we have someone quite ruthless as a forward to make use of what he would get the team to do.
But don't sleep on Niko Kovacs. He might be a great dark horse idea.