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I did a search on the player finder on pfr, and there have been 142 separate 4000+ yard passing seasons by quarterbacks since 1960. You can see it here:
http://www.pro-football-reference.com/play-index/psl_finder.cgi?request=1&match=single&year_min=1960&year_max=2016&season_start=1&season_end=-1&age_min=0&age_max=0&pos=qb&c1stat=pass_yds&c1comp=gt&c1val=4000&c2stat=choose&c2comp=gt&c3stat=choose&c3comp=gt&c4stat=choose&c4comp=gt&c5comp=choose&c5gtlt=lt&c6mult=1.0&c6comp=choose&order_by=pass_yds&draft=0&draft_year_min=1936&draft_year_max=2016&draft_slot_min=1&draft_slot_max=500&draft_pick_in_round=pick_overall&conference=any&draft_pos=qb&draft_pos=rb&draft_pos=wr&draft_pos=te&draft_pos=e&draft_pos=t&draft_pos=g&draft_pos=c&draft_pos=ol&draft_pos=dt&draft_pos=de&draft_pos=dl&draft_pos=ilb&draft_pos=olb&draft_pos=lb&draft_pos=cb&draft_pos=s&draft_pos=db&draft_pos=k&draft_pos=p
To see how unlucky (or just plain shitty) the Bears quarterback situation has been over the last 50+ years, you can roughly calculate the odds of any given (non-expansion) team not having any 4000+ yard passing seasons since 1960 by taking .97[SUP]142[/SUP], which equals approximately 1.3%.
Same odds as the Bulls winning the draft lottery for Rose right?
So you're saying a Bears QB breaks the 4,000 yard mark this season?!