If this is the injuries he is dealing with after basically five weeks, just imagine what a full season could generate for him.
Yes, injuries are somewhat random (unless his team is loaded full of injury prone players), and of course some teams in some seasons will have a larger amount of injuries to deal with.
But there is a significant difference between random bad luck, and a repeat of the 2014 Texas Rangers, and his team is looking like it's going to shatter that level of injuries. I can't even try to convince myself this amount of injuries (length and severity) is anything close to normal, random bad luck. Not in a five week time frame.
I found a column about the Rangers of 2014, and as of the 31st of August, 2014, that team had 14 players on the DL (9 on the 60 day DL) and had used 59 different players in a game that season (with one month to go). That 59 players used tied a record seen three other times. With a month (and roster expansion) to go in the season.
Texas Rangers MLB Record for Most Players | Beyond The Spread if anyone is interested in reading this.