When the Maple Leafs re-signed Korbinian Holzer, I was not a big fan of the move. The post I wrote at the time outlined my issues with the move that drew upon some other good pieces. I think that they all hold up well. A major concern was that while his performance might improve once he was played down the lineup his mere presence might offer Randy Carlyle the opportunity to make one of patented head-scratching lineup decisions. It was presented as indicative of a flawed decision-making process in the executive suite and that hasn't changed.
To get this out of the way: Jake Gardiner has not been at his best this year. He most certainly can do better whether that's through better deployment or better coaching or simply coming to terms with the expectations on his shoulders, he has to be better and he can be. Holzer, on the other hand, has no such step up. He has shown throughout his NHL career that he isn't up to snuff in a number of ways and @MimicoHero provides a good graphic representation of that futility.
Below is a chart that shows the Leafs' corsi for and against per 60 minutes of 5v5 ice-time. Red bubbles are bad, blue are good and you want your bubble to be closer to the top right hand side as that means that you are on the ice for more corsi events in your favour than against.
Everyone is worse with Holzer
You can look at a number of factors to adjust the numbers whether that is taking into account opposition, linemates (although that's a debatable adjustment), or score but it's pretty evident that at the most basic level that the Leafs do better without Holzer on the ice than they do when he is out there with them. Some players may give up more corsi events against but they make up for it by having more corsi events in their favour. Some examples are stark: David Booth is on for roughly the same amount of corsi events against but sees almost 20 more per 60 minutes without Holzer on the ice. James Van Riemsdyk and Phil Kessel still bleed corsi events against but allow 20 fewer per 60 minutes while taking about 15 more. That's a big swing!
The importance of this chart lies in the value of corsi. Every corsi event represent a shot directed on goal whether it misses the net, is blocked, stopped, or goes in. The more pucks go towards the net, the more opportunities there are for a goal to be scored. Teams that are on the positive side of the ledger tend to do better than those at the negative end. It's been proven over and over in any number of ways. If the Leafs want to improve then they need to dress players that move the puck in the right direction and figure out how to use them to their maximum potential not scratch them. That's just cutting your nose off to spite your face.