"Doug Harvey was primarily responsible for the Habs +68 goal differential in 1961. The Habs goal differential immediately jumped to +93 after Harvey left in 1962, but again, Harvey was the primary reason why they were good enough to be +68 in 1961."
"Doug Harvey controlled play entirely as a Hab, but then went to the Rangers and immediately lost that capability, which is why he was a minus player and his new team had a losing record and went nowhere. But still he was the biggest reason for the Habs success."
I'll address these two points because I think they're fair and interesting questions. (The other three points, I think, are misrepresentations).
It's not accurate to say that Harvey didn't help improve the Rangers. The year before he arrived, the Rangers allowed 248 goals (38 more than the league average), and in Harvey's first year that dropped to 207 (4 fewer than the league average). The crucial fact here is, aside from Harvey, the Rangers' rosters were otherwise pretty similar (HOF goalie Gump Worsley played 59 and 60 games those two years). Star scorer Bathgate was his usual consistent self (77 points and 84 points). Low-end HOF defenseman Harry Howell played 70 and 66 games those two years. The biggest change from 1961 to 1962 (aside from Harvey's arrival) was that the Rangers lost Hall of Fame defenseman Bill Gadsby (though he was past his prime by that point).
In other words - in front of the same goaltending, and after losing an (aging) HOF defenseman, Harvey helped the Ranger reduce their goals against by 42 goals relative to the league average, in one year, with a 70 game schedule. They jumped ten points in the standings and made the playoffs for the first time in four years. Is all of that due to Harvey? No; but it's the most obvious change on an otherwise stable roster. And the people who witnessed this season agreed - Harvey was runner-up for the Hart trophy.
I agree Harvey didn't have a great plus/minus on the Rangers, but nobody here has been using plus/minus as an argument in his favour. (Incredibly, he was only on the ice for 9 more ES goals against in his first year in New York - the reason his plus/minus dropped is because the Rangers were a much weaker team offensively than the Habs).
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As to the question about why the Canadiens allowed fewer goals right after Harvey left - they allowed 22 fewer goals than the league average in 1961, and 45 fewer than the league average in 1962 (a swing of 23 goals). Again, we need to look at the roster changes rather than attribute everything to one player.
In 1961, Plante had the worst season of his career to date. He had torn cartiledge in his knee and he was even sent down to the minors mid-season (I think it was an EPHL team). In 1961 (Harvey's last year on the Habs), Plante posted a 90.4% save percentage (easily the worst mark in his career at that point - he averaged 92.2% over the past five season). And he spent nearly half the season in the minors, forcing the Habs to start Charlie Hodge (a competent goalie, but not a HOF'er).
Plante recovered in 1962. He played literally every minute of the season. And his save percentage (92.3%) was almost exactly what it had been in the five years leading up to his injury (1956 to 1960). Plante won the Hart trophy that year.
Can this be used to argue that the Habs didn't need Harvey, since a healthy Plante had a great season without him? Sure - but nobody has taken the position that Plante "needed" Harvey to be successful. The 1950's Habs were such a strong team that they probably would have won several Stanley Cups even if you removed any one of their top players (just like how the Oilers won a Cup without Gretzky, and two without Coffey).
The other significant change is the Habs top forwards, in general, were much less productive in 1962 than in 1961. Geoffrion dropped from 95 points to 59. Moore dropped from 69 to 41 points in the same number of games. Beliveau had 90 points, then dropped to 41 points in 43 games. Beliveau was obviously injured, but Geoffrion and Moore struggled in their first year without Harvey. Hard to say if that's a coincidence or not.
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This has turned into a much longer post than I intended. But the point I'm trying to make is Harvey immediately helped his new team reduce their goals against significantly (with no other significant changes in the roster). And although the Habs improved as well, that's due to Plante having an all-time great comeback season, and the premise implicitly blames the Habs' unusually high goals against in 1961 on Harvey, rather than Plante being injured.