Direct link. I used full season data, unadjusted for scorer bias, regardless of score and location. Only 5v5 events were counted. Empty net events were excluded.
First, line combinations. He bounced all around.
The Blackhawks are better with Troy Brouwer on the ice.
Strangely, the Hawks' tough-minutes D are better with Brouwer, but their soft-minutes D are worse off. Maybe that's because those soft-minutes defensemen normally play with Sharp, Kane, Stalberg, and Hossa instead of Brouwer. Maybe those soft-minutes D saw tougher competition with Brouwer on the ice.
Every forward except Frolik and Johnson is better off with Brouwer, and even then, Frolik's Delta1 is roughly zero and Johnson has a very small sample with Brouwer (47 events--change one of his events from negative to positive and the Delta1 becomes a small positive number). While Bolland, Pisani, Bickell, and Frolik may have seen easier competition with Brouwer than without, the competition argument likely doesn't hold for the others.
Brouwer looks like an above-average player on an elite team. He should be able to play top-six minutes on the Capitals next season (and hopefully, for years to come).