I think the attribute that will help a player the most off the ice isn't exactly an expected one. People will focus on the speed and agility attributes to in theory move quicker. Maybe they will focus on strength in order to be stronger. In my opinion, the one that will help the most is defensive read. When you think about it, defensive read encompasses all other attributes. It's great if you can move fast but it doesn't matter if you can't figure out where you are going? It is great if you're stronger than everyone else but what does it matter if you don't know how to use your strength? Defensive read will allow you to look at any situation and figure out instantly what the best option is. You're always be two steps ahead of everyone else and you'll never get in any sort of trouble. You'll be able to read any situation and always know the best option for you.