no, you do not need to talk averages, since your "average" ignores that height is not equally rewarded across all positions.
I provided another analysis which spefically broke down average heights and weights by position. Rely on that if you'd like to your average calculations to be more specific.
unless your average breaks down height by position, your average is worthless.
It does precisely that. I'll provide the link again:
http://wiki.answers.com/Q/What_are_the_average_heights_for_football_players
Here is another:
http://www.pro-football-reference.com/blog/?p=493
This second analysis suggests every single position averages above 6' except for running backs, who average 5'11.
And pointing out current players within the NFL that ARE excelling under 6 feet isn't "anecdotal", its a legitimate data point since we're discussing the NFL's population. It's like saying there are no sports cars in ford's lineup then calling it "anecdotal" when I show you a mustang.
That is not at all equivalent. I am not saying it's impossible for a 4'11'' person to be a great NFL player; just that it is very, very unlikely. A single exception does not disprove this concept -- if I said that it was impossible for a 4'11'' person to be good at NFL player, then yes, that would be a relevant statement. Instead, you would need to show that over a large sample pool, a large percentage of 4'11'' people are likely to be good NFL players; lets set the bar at 10%.
Anecdotes are, by definition, single data points. When doing aggregate statistical analysis, single data points are invalid argumentation.