I have dug up some advanced stats on this. This will of course not produce purely defensive zone stats since puck possession is what is mostly measured. But if you count defense as the chance your opponent will get shots or scoring chances while you are on ice, Fenwick and Corsi is a great tool.
Fenwick includes all shots and shots that missed the net but not shots that were blocked.
Corsi includes all shots, shots that missed the net and shots that were blocked.
Both stats take into account the level of your linemates and the level of the opposing players you are on the ice with.
HARD are your defensive ratings (chance opponent will create chances)
HARO is offensive (chance you will create chances)
To get a better sample size I searched Zuccs entire tenure for those who played over 700 minutes total and for the past three seasons he is blowing the rest away by a mile and a half.
A score of 0 is considered the average player.
Fenwick
HARD: 1) Zucc 20.5 2) Stralman 13.8 3) Hagelin 9.8 4) Clowe 9.8 Worst. Pyatt -13.8, Nash -8.2
HARO: 1) Zucc 17.8 2) Clowe 12.8 3) Hagelin 10.6 4) Nash 9.6 (Impressive to have such a gap between defensive and offensive stats) Worst: Powe -16.6, John Moore -13.8
Zucc is #2 in the league in fenwick over past three years just behind Alexandre Picard and just in front of Justin Williams
Corsi (Not surprisingly very similar results)
HARD: 1) Zucc 13.8 2) Stralman 8.3 3) Asham 7.7 4) Clowe 3.9 Worst: Powe -14.6, Pyatt -11.7
HARO: 1) Zucc 16.6 2) Clowe 12.4 3) Hagelin 11.4 4) Nash 7.7 Bickel, Powe J. Moore are worst with -12 to -15
in shorthanded situations you know how the player is performing purely in the defensive zone. Zuccs sample size is very small here but he has been on the ice for 21 minutes in the NHL and the team has yet to concede a goal when he is on the ice in 4vs5.
plus/minus he is #2 on the team tied with Hagelin and behind Kreider both of who were in the AHL or on IR during a big stint of the early season massacres. Those are the only three players with a positive +/-