I notice sometimes that a player that is playing particularly poorly will often later suffer some sort of injury. I am not sure whether this is random or whether I am picking up a pattern that suggests it is built into the game. It would certainly track real life where a pitcher, for example, has several terrible starts, then is later placed on the DL for some sort of elbow or shoulder injury.

Any thoughts?

I have noticed and wondered the same thing.  But I somehow doubt that this is something that's programmed into the game.

We all notice when a player is way underperforming his ratings.   And we look for a reason.   I think that's what this is.