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a team that is not patient enough to wait for a satisfactory performance is actually something that is not good either. Because after all, the coach will need time to show all his abilities, and the problem is that Chelsea always wants to see fairly instant results that can make them look good. In my opinion, this is something that is not good for a team, because they will always change coaches when they are not satisfied with the results.
Now there is also no guarantee that when they change coaches they will be even better, because this takes time and it is possible that Chelsea could be worse in the hands of their new coach. Management should give proper opportunities to coaches, especially if the coach shows something good or he can progress well. However, Chelsea did not give that opportunity to a coach who produced results that they thought were unsatisfactory.
Chelsea should be able to put trust in every coach they employ, like Ten Hag at Manchester United and Arsenal with Artata. Not all coaches are able to do a great job in just one first season, even if it is not impossible, it will be really difficult because of the adaptation process.
Pochettino is a coach who can be categorized as a classier coach compared to many other current Premier League team coaches. It's a shame that Chelsea fired him just because he failed in the first season, it seems like they don't appreciate his work in one season. I think Chelsea will be just as bad if this habit continues, they won't be as successful as before.
Every time a coach changes there will definitely be a change in game plan. Pochettino and other coaches will never have the same style of play and strategic decisions. This will make the players adapt again to a new style of play, different portions of training, and even have to adapt to several new players that the coach has brought into the team. It's unreasonable to expect a season of great success instantly, it's very difficult when the team is really bad.