What to the last four Stanley Cup Winners have in common?

LAK 2014, CHI 2013, LAK 2012, BOS 2011 had one statistical advantage. Name it. It's not goal differential and it's not special teams.

Hint: Steve Simmons doesn't think it exists.
Update: Its Shot attempts (rolling average) over their most recent 20/30 game splits. Teams that are in the top 3 walk away with hardware (PIT and SJS are in the top 3).
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