Answered December 31st, 2019

The New England Patriots have the most fourth-down attempts - fourth-down conversions by a team in a game, with 5 versus the Broncos on October 8, 1995.

most 4th down attempts minus 4th down conversions in a game by a team
Interpreted as:
most 4th down attempts minus 4th down conversions in a regular-season game by a team

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