Randy Carlyle is, IMO, easily the worst defenseman to win the Norris trophy.
Last year I wrote an essay about "Norris trophy shares". Basically, a player who wins a unanimous Norris trophy earned 1.00 points, a player who earns 80% of the maximum votes in a certain years earned 0.80 points, etc. Here are the Norris trophy winners with the fewest career Norris trophy shares:
Player|Shares
Randy Carlyle|0.40
Tom Johnson|0.85
Harry Howell|1.02
Doug Wilson|1.05
Jacques Laperriere|1.39
Here's all the seasons they earned at least 5% of the maximum number of votes:
Carlyle: 1st (1981)
Johnson: 1st (1959), 4th (1956), 5th (1960)
Howell: 1st (1967), 5th (1964), 6th (1966), 9th (1965), 9th (1962)
Wilson: 1st (1982), 3rd (1990), 4th (1983), 4th (1985)
Laperriere: 1st (1966), 2nd (1965), 4th (1964), 4th (1970), 5th (1973), 5th (1968)
Carlyle won the Norris trophy in 1981 (and he did have a great season), but never earned more than 5% of the maximum available votes in any season. Even the next worst Norris trophy winners are far superior in this regard.