They went to London in 2015 on a mission to become the first team to win successive World Cups and that time they won it decisively, confirming their class as the leading exponents of their game and the most consistently successful team in any sport.
Now they are in Tokyo looking for a "three-peat". The goal does not have the same urgency. For the team, it is probably not their prime motivation. They will be focused not on repeating past successes but on meeting their present challenge. They are facing a tournament that appears tougher than those of 2011 or 2015.
Several of the old rivals are looking better than they have been for a while, none more so than the one they face in their opening match tomorrow night, South Africa. But England, Ireland and Australia have also recently shown they can beat the All Blacks on a good day.
In the knock-out stages it will only take one of them to have one good day and New Zealand could be disappointed. That is what makes tournaments such compelling sporting events. A rugby tournament is even more unpredictable than most because the
sport is so difficult to referee.
No referee wants to award a penalty that decides the result of a match but it can happen. Coaches and players react professionally when it happens. Fans should do the same. The game is fast, collisions can be confusing, people can see the same incident differently.
Everyone who cares for the game of rugby will want it to be seen at its best in Japan, where it has been established now for many years but has not begun to match the growth in popularity of the round ball over a similar period.
The All Blacks try to play fast, attacking rugby but not all of their rivals do the same. Close marking can enable defending teams to gain territory without the ball. It is dull but effective. If the All Blacks can destroy that style of rugby at this World Cup it will be for the good of the game.