Why are you doing a 1/6 calc to get 16.7%? Because there is 1 goalie and 5 skaters on the ice? That's just one shift though....there are another 13 skaters on the bench waiting for their shifts. I'd suggest you shouldn't really look at 2 goalies as the population because can't look at starters and backups the same, but you could say the same about 4 line players vs. 1 line players I guess. So, generally a team is going to start a game with 2 goalies and 18 skaters. So 2/18 = 11.1%....but 14.4% of the members of the HHOF are goalies by your calc. To me, that doesn't suggest under representation.....it's not the simple, but that's the starting point I always consider.
This is basically saying that the most underrepresented group in the HHOF is shitty players. It’s… not
wrong.
But I don’t think it’s a meaningful way to think about “representation” in this context. The number of players sitting on the bench is immaterial to the question of who the best players are.
Say we lived in an alternate timeline where NHL teams had only 2 lines/pairings and were allowed to carry 3 backup goalies. When it came time to pick awards, would goalies be “better represented”? No, we’d still be picking one guy for the Vezina and two for All Star positions, same as now. Likewise, the HHOF would still be choosing from a pool where the ratio of first-line skaters to #1 goalies is 5:1, same as now. The bench players and backup goalies are just a big pile of ineligibles — the representation of
positions on the ice remains constant.
That’s why, all else being neutral, there should be a 3:2:1 relationship between top forwards:defensemen:goalies. If that’s not happening, then something is not neutral in the selection process.