Consistency.
Using 3 or 5 year windows I think the team needs to average near the top (25%?) in a few different categories across these years.
Categories include:
-Regular season standings
-playoff apperances
-Playoff series wins
I think if your averages can be near the top of the league across 3 or 5 year periods in these categories you are a successful team.
Stanley cup is the cherry on top.
edit: This is assuming your team is in a window of contention. Going through a rebuild obviously changes the goals of success
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