I love Babcock. Definitely have confidence in him if not simply for his winning pedigree, and the trust that the likes of Shanahan, Dubas, etc, seem to have in him. He's made questionable decisions with the lineup pretty much every season with the Leafs, and his tactics have made me raise my eyebrows. But he has also shown willingness to change and adapt, which I really love. Last season he moved in younger guys like Johnsson, Kapanen, and Dermott, and reduced the roles of guys who weren't cutting it, like Martin & Komarov.
However, I would say that the main reason the team underperforms on some nights can often be attributed to his tactics. I do think that Toronto is having a fine season, and a lot of the Babcock hate is a knee-jerk reaction to losses and bad games. However, I also think that there are ways to optimize the skills of our current player personnel, and Babcock isn't grabbing as many of them as he should. Some things, like the stretch pass, our poor defensive zone coverage, or just line combinations and ice-time, seem like pretty obvious changes to make that would make the team more consistently lethal.
For me to regain full confidence in Babcock, I would need to see him outcoach Cassidy, and have the Leafs soundly beat Boston in Round 1. I'm not talking about chasing linematchups, I'm talking about adjusting our tactics so that the Bruins cannot stop our offense from rolling over them in waves. No more easy to snuff out stretch passes and poor neutral zone play. Come up with an effective breakout, d-zone structure. Come up with line combinations that don't make it easy for Boston to target certain positions (ie. right-side defense). Get creative, throw Muzzin & Rielly together, or Dermott & Rielly, something that will get the puck out of our zone, and into Boston's. Then I will have hope for Babcock to bring this team to a Cup.