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Also, the finance side I'd imagine was partially done by the manager. We have Dan Ashworth who (so we're told) is purely responsible for that.
Team selections and tactical methods, I'd like to think that in a truely good set up, would have an equal amount of input from ALL coaches to the decision maker, who is often the manager. In this set up, the head coach is the decider. So, the only difference from before is that he gets to say "yes" to a player ready to be signed and to decide on a way to play football.
By that logic are you saying the only stuff Mourinho does that makes him great is scouting and signing players? Finance doen't really come into it, if you watch any of the fly on the wall documentaries, like the one on QPR, you'll see the manager has very little input into finance.
Obviously the manager's job is more involved then. Mourinho has this reputation because he's good, where ever he's been, and it must extend to more than assigning scouts. If Clarke was so great, why didn't Liverpool do well? You can't say "he was one of the reasons why Chelsea were great, but it wasn't his fault Liverpool were rubbish".
It's a big risk no matter which way people try and paint it. Just hoping things turn out ok because "head coach" and "coach" are similar phrases is crazy.