For what it's worth. I have 6 Doctor & had 1 injury per season with him (3 in total) 2weeks, 1week & 1 week.
Friend of mine same thing, 6 doctor, lost half his team 2 seasons in a row. I convinced him to email a GM about it. They looked & said it's a random factor & not a bug with his team???
Brother plays with a 4 Doctor, has one injury in the last 4 seasons.
I understand that it's random & yes bad luck happens, but this is a controlled environment (database) & who wants to play when these things happen more often? Yes make it true to life but don't let the random factor affect a team more than it needs to. This is played for fun after all.
Right is not a popularity contest!