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I don't understand what quick results AS Roma wants by appointing De Rossi as Mourinho's replacement because clearly, of course De Rossi doesn't have great qualities as Mourinho's replacement. Therefore, by appointing De Rossi as head coach, I think AS Roma has hidden problems with Mourinho, so AS Roma made a quick decision by appointing De Rossi. Thus, the quick result that I understand here is a quick decision to fire Mourinho and a quick decision to appoint De Rossi as his replacement, because De Rossi is also a team legend. Therefore, I think there are no long-term plans regarding the appointment of De Rossi as AS Roma head coach but yes, if for example De Rossi succeeds in improving AS Roma's position then maybe there will be a long-term plan, who knows.
This is where it seems to be a bit contradictory what Roma has done, but it actually makes sense if you think about it. Mourinho couldn't get a winning streak going and Roma was looking for consistent results (like any team does). But Roma was full of surprises all the time and they lost games they shouldn't have lost and most of the time they also didn't perform very well.
But how long could Roma have waited to do something about it? Either immediately as they did, or wait another 10 games and then sack Mourinho and leave the new coach without any chance to change something? That is why they did the change immediately and then they can analyze De Rossi's work by the end of the season and consider to extend his contract or not. There are good incentives for everyone involved to do well now. Mourinho sometimes looked as if he wasn't as interested and passionate anymore.