I think @Lyrian had a good observation here about the articulated rates of Shards from the Seasonal Caches:
We know this team is not that clever when it comes to diversifying calculations about things so I agree its safe to assume that these percentages are likely the same percentages used in determining random shard drops from chests (this same distribution seems to be apparent in the story rewards but not so much in the use of Marks in purchasing shards which seem to have a more even distribution). Given the paucity of higher level evolve materials and the relative importance of upgrading weapons over say, Minions or Spells, the lack of weapon shards is a huge problem. Yet another thing that we didn’t know for sure until we stumbled across some evidence that confirmed the very issue we have been complaining about for months and months.