As long as Madrid can keep all their players injury free like last season, I'm confident they can focus on winning multiple titles, just like they did last season. Madrid won the UCL and La Liga when all the players consistently contributed and maintained their fitness levels. This season, it seems Alonso understands Madrid's weaknesses and won't repeat Ancelotti's mistakes, with the desire to bring Madrid back to its strongest form.
It is not in the hands of the management or the manager to keep the players from from injuries as you know injuries happen unexpectedly but if they escape having injuries it's just luck. Last season Real Madrid didn't win any trophy I think you are mistaken their performance in the previous seasons but this season under a new young manager Real Madrid will be aiming to win trophies like the champions League and La Liga which I think they will focus more on this season.
Well, players injuries depend on their rational behavior and training session. Some manger used a difficult task at training session and due to which sometimes player feels fatigue and as results they got injured. Hard drills at training session can cause a muscle stretch injuries mostly. Instead of hard training drills manager need to give some motivational quotes to the team players. At the time of Zidane all of real madrid have never feel any long term injuries rather than bale and the reason behind it was easy training session and motivation. Under the management of Angelotti many players has injured because he only prefers head training session over motivation.
Now I do believe Alonso will try to copy zindane structure to get back real Madrid on track to make history once again.