They are not capped to anything. If anything, Nordeus description of buidling medical facility to reduce the length of injuries would suggest otherwise.
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Only had 4 injuries up until the 21st league game. Had 5 more in the space of 2 days. I, like some others refuse to heal them now. I'm still undefeated in the league, but I'm sure that will change since my team has no spare defenders left. Go on Nordeus, hit me some more. I've already won my league, so don't give a rat's.