I was reading a blog post by someone comparing an NFL quarterback from the 1960's and 1970's to one from this era, stating how the one back in the older era was overrated and worse in many ways than one from today. A basis of this, was in his opinion, that the older QB had a completion percentage of 50.1 as compared to 55.7 of today's QB and the interceptions thrown were higher as well for the older QB than the current player.
But to accurately say that the older players was worse, you really need to compare his numbers to the other QB in the league, the average and standard deviation come into play. I know for a fact that completion percentage in the past era was much worse than the current era. Players may be better today offensively with the complex schemes, but I know the defense isn't allowed as much freedom in today's game. For whatever the reason, have to compare statistically.
Suppose the league average completion percentage in the 1960's and 1970's was 50 percent, therefore the older QB was right on the average.
But today, a 55 percent completion percentage may be way below a league average of, say 60 percent. So in essence the older QB did better compared to the rest of the league even though his actual percentage was lower.
The same holds true for other statistical categories.