Just because Crystal Palace can win against Liverpool does not mean that they are improving. They always have the habit of starting well and ending badly. To prove me wrong when the season starts fully, then you will see what they are made of. As for Manchester City, we are going to do something different, and there are other big guns, so it's going to be very hard for Crystal Palace to win even the Premier League; they don't have the strength to pull that off.
We know they won't win the league and that's fact but the thing is, how do you actually define improvement, if you think them winning Liverpool at the end isn't part of improving. This very team against all odds in May beat Manchester City to emerge FA cup champions and just yesterday won Liverpool to still emerge winners of the FA community shield.