last season before the play offs and during the play offs, I had the same problem like you. I think it was even a little worse. during my semis 3 of my starters were injured.
anyways at that time I had a level 6 doctor, short before Play Offs I even bought a level 8 doctor, cause of that many injuries.
at the end of Play offs one manager of my league told me he just got his first injury. he just finshed his second season, still sticking with Max paine (level 1 doctor). At that point I was a little frustrated from the work of my doctors, so I decided to buy a level 3 doctor, cause why pay more for a level 8 doctor if he is not helping preventing injuries at all.
Havent had any injuries since then....