So far in my play I have acquired a single heroic deed from a reward box, for reference my characters are level 5, 8, 25, 11 and 6. Mostly low so I understand I have just been unlucky and my sample pool is very low.
Now, 3 of my friends have all gained considerably more deeds than I have (5-10) and, overall, have lower character levels (and thus have opend less chests.)
The heroic deed missions are, for me, the most fun content in the game, and its a shame to lock it behind a random chance. I enjoy the extra challenge it adds to the maps and fairly repetitive gameplay otherwise
My suggestion, add a fail safe to the reward, for example, if you don’t get a deed after opening 19 boxes your 20th is guaranteed. That way 1 in 20 is the lowest chance to get a deed, but you could still open 10 boxes and get 3 deeds if you get lucky.
You could do the same with red items and cosmetics, but with higher numbers.