It's an interesting post. I have focussed on the first 14 games as Ancelotti has had 14 league games, so not sure where or why the 24 games figure has emerged from?
On Allardyce, we were a a bad team when he came in. We have been defeated heavily that season on about 5 or 6 occasions, often to sides like Southampton. We were a long way off being competitive in a lot of games. Under Allardyce, particularly at home we started winning the games we ought to win. He is quite good at that. He will see a poor group of players, low on confidence and develop a game plan that allows them to be competitive. I don't think there can be any doubt he can and does do this. Thats his party trick. The issue he has is he is very dislikeable, and he can't do anything other than this.
As for Carlo his record after 18 league games is far better than Koeman and Silva's were. I also think, mid season, hovering by the bottom 3, he inherited a situation that was probably equally perilious and has navigated it well.
There has been disappointments, but the fact we count our disappointments as bad defending in a narrow defeat at Arsenal, and a woeful performance at Chelsea is quite demonstrative of how well he has done.
After 15 games we were in the bottom 3. We were bottom of the league for 2nd half performances. We had not come from behind to win a game in 18 months. There were lots of things wrong about the team, but also lots of real negatives too. Post Silva, mainly under him we have been showing top 4/5 form. It's a significant turnaround. I happen to think we are probably better than we showed under Silva, and have rode our luck a bit under Carlo, and maximised outputs and that probably sums up Carlo to Silva. The performance levels probably haven't changed much, but getting over the line has been much better. A lot of that is avoiding playing a system that ill suits the team.