One of Bill James' maxims is that hitting is a skill that cannot be learned once a player has already made it it to the major leagues. He has penned numerous essays over the years showing that even in the instances when it looks like a player learned to hit after making it to The Show, it was really a matter of some set of circumstances (moving to a more favorable ballpark, etc.) that led to the statistical improvement. Hitting coaches can help improve certain segments of a batter's game -- but if the player can't hit the curveball before he gets to the pros, all the coaching in the world cannot help him correct that issue.
Pro football has a few areas that probably fall under that "uncorrectable" category: quarterback accuracy and a receiver's pass-catching ability are the first that come to mind, but the one that might be the most potentially damaging to a team is a quarterback's risk-taking mentality.
Take the case of Brett Favre. He had a long history of making insanely dangerous throws but decided to rein that in during his first season with the Minnesota Vikings. This effort helped him to tie for the lowest interception percentage in the league last season, but he still couldn't help throwing an incredibly risky pass in the NFC Championship Game that ended up costing the Vikings a chance at going to the Super Bowl. The risk-taking mentality was too ingrained for him to make a total change.
Jay Cutler has a similar history in that he has always thrown caution to the wind and passes to the other team, but his play so far this year has been stellar. He has tossed only one interception in two games and his 121.2 passer rating is tops in the league.
That performance leads to this question: Is this one of those rare times when a quarterback truly makes a change in his risk-taking philosophy, or is this just a mirage that will vaporize under pressure the way Favre's did? The tape and metrics from the Bears' first two contests offer differing opinions.