I don't think it is entirely random how injuries happen in this game. Boyscout gave a really nice detailed advice, very good method.

Basically, my opinion only: Don't train guys too hard, make sure they will all have ~90% in the next match they play in (keeping in mind how many matches you have, the bench for the first will need to be at 90 for your second match..) Make sure their skills don't out pace their physical/mental by an extreme amount. Have the best facilities you can. Don't use hard tackling or attacking but for when you feel it's your only chance in a match. Same for arrows. Sell guys that keep getting injured... and don't play a guy you have just got in the next match. This is what I have been doing, and I rarely have more than a couple guys sitting injured in each of my team(s), including my 35T team.