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The 01-02 Pens only had 28 wins, 69 points and finished 5th in the Atlantic, missing the playoffs.
02-03 27 wins, 65 points, 5th, no playoffs
03-04 23 wins, 58 points, 5th, no playoffs
05-06 22 wins, 58 points, 5th, no playoffs.
So, did they get a favorable lottery, sure. Did they get draft lucky from “only one bad season” as you assert? Not exactly. They were pretty bad for a few years there. As you said, they nailed the high draft picks also. They hit it out of the park. The GM and front office in those drafts were spot on and the Pens have reaped the benefits ever since. Subsequent GMs since then have made very good trades along the way that have kept the team on track.