If the rate you're getting is that bad, hten think about just buying the shards from the store.
If you are using the 200 crystal refeshes, then using both cost 400 crystals for 240 energy or 15 battles. At a drop rate of 33% that is 5 shards from 400 crystals, the same price as in the store.
It is a gamble you may get more than 5 shards from the refreshes, but if you're constantly getting less then take the less risky route and buy them.
If you are using the 400 crystal per refresh, and not buying them then you are just throwing away crystals.