They don't seem to do anything, check you tube on subject, tests have been done where players didn't get exo's until they're Toc buff finished, same happened to me, and when I did get an exo to drop it gave me a duplicate, so it seems Toc are bugged,they seem to remove all chance of exo drops when used, save your shards don't buy them, spread the word guardians, peace be with you all