As a bum-ass player myself it's easy for me to imagine an award for this category.  My Award would be the Kunitz Award.  It would be given to a player that had a the worst season relative to the TPE of their linemates.  I'm on Atlanta's first line with Otter who is 2k+ TPE and Zheng who is 1900ish I believe.  It's basically the award for being most carriable.  I barely hit 30 points even with my amazing linemates.  But Atlanta is a playoff team.  This award really demonstrates a players ability to fail regardless of how optimal you make their situation.  Truly encapsulating the bum-ass aspect of the award.  I barely had any 5v5 points so even with these linemates I still needed the other team to be down a guy for me to be effective.  I'm truly a black hole of a player.  I can only hope to not be a complete liability next season even though the situation will be much the same.  Just with my linemates being one season deeper into regressing.