Roma team is in a very bad situation this season. Roma has won only 3 matches out of 12 matches. Last season Roma was able to stay in the top 6 of the points table. However, this season Roma will probably not be able to stay in the top 10 of the table. This team has weaknesses in both defense and attack.
Firing Mourinho was a big mistake for Roma. Roma management should have given Mourinho big funds. And given the opportunity to add talented players to the squad. Then Mourinho would have been able to strengthen Roma team. But Roma management found it easier to fire Mourinho than to give big funds. And that is why Roma's performance this season is very bad.
Roma can improve with their new coach Ranieri because he is an experienced coach so he is able to help them. However, Roma already lost many points so far while in this season, there are many clubs with good performances like Atalanta, Fiorentina, Lazio and we have to count top teams like Napoli, Juventus and Inter Milan and perhaps AC Milan too.
Fixing issues from now, is very hard for Roma to catch above clubs and perhaps they will have to forget top four and reduce their finish target to top six in order to join UEFA Europa League next season. It will be a disappointed ending position for Roma after spending a lot of money in summer transfer season for De Rossi. I agree with you that sacking Jose Mourinho in the last season and refusing to give the coach money for transfers, is very bad strategic mistake from Roma.