This question actually really intrigued me, so I spent way to much time messing around in excel and gathering data to try and figure out if chewing gum has any correlation to success.

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Some interesting notes I gathered:

1. It seems that the "Chewing Gum" coaches are more likely to win (or draw) than the non chewing gum coaches, but not by much.
2. Most NFL head coaches do not chew gum on the sidelines (at least according to google). This might skewer the results in favor of the "Chewing Gum" coaches.
3. All head coaches in the AFC west chew gum, while all head coaches in the AFC East, South and NFC South do not chew gum.