Roman Abramovich is probably the most impatient man of all time. From my knowledge of the Russian billionaire, his main goal with Chelsea was to win the Champions League. What did Roberto Di Matteo do? He brought his team to the Champions League final, where they won. He also won the FA Cup. That's two trophies for a manager who wasn't even in charge at the start of the season.
Along with the success he brought to the club last year, he brought in some fantastic players over the summer transfer window. Whether that was Ambramovich or Di Matteo, a player would be reluctant to join a club if he doesn't think the manager can do the job. Hazard, Oscar and Moses are all exciting young players, the type of players Chelsea haven't had for years.
Unfortunately for Di Matteo, he hit a slump in his managerial career, which in all honesty, was bound to happen sooner or later. However, Chelsea currently sit third in the Premier League, not far behind the Manchester Clubs, and although their Champions League ambitions were hit by a 3-0 thumping by Juventus, they can still qualify, with a bit of luck.