Before they decided to sack Nagelsmann I'm sure they had considered what happened to Bayern Munich, including losing their playing style because they were handled by a new coach where there would definitely be differences from his coaching style, one of the forms of play. However, his dismissal was said to be very hasty, especially with the appearance of Bayern Munich, which can still compete very tightly as you said.
This is a new chapter for Bayern Munich this season, I just hope they don't decline with their new coach.
Talking about Bayrrn style of play, It is not going to be different. the only thing I will commend is the individual improvement which in hand will promote the team's performance.
The players will want to show their best to the new coach so as to have first team shirts in his square. Tuchel is a German coach, he is a good coach and I'm sure bayern Munich's management have seen what they need in him else they wouldn't go for him.
Yes, it's true he is a coach from Germany, of course he understands how to play for German League clubs. Maybe in this case he will benefit because he will be able to communicate more easily at Bayern Munich. We know that Thomas Tuchel was not given many opportunities at Chelsea, he felt the same way when he was sacked by Chelsea. Now he is in charge of another big club, Bayern Munich. He has to show that he is a great coach, I won't talk about it in the Bundesliga, but I hope he can do well in the Champions League.
Maybe Tuchel would really be better for Bayern Munich in every way. But I still think that attitude against Nagelsmann was unfair. They could have at least waited for the end of the season before making such important decision.
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I agree with Pulsar77 about the timing. Mid-season isn't the best time to switch the management and players will require some time to get used to the new coach strategy. What might be good, is the international break. The advantage of having a week before the next game rather than 1-2 days is important. There is also 2 weeks to prepare the team before facing City in Champions League.
Otherwise, Bayern players are professionals and I assume they will get used on him fast.
It seems unfair to Nagelsmann, and the same thing is felt by Thomas Tuchel, because Tuchel must also be able to realize expectations in a short time of preparation, yes he must quickly understand this club as a whole so he can implement the best of his strategy. This has already happened, we can only see if this is the right decision made by Bayern Munich or vice versa. Obviously it won't be easy, but we'll see them in the next few days.