Every successful team has a process they follow. That allows them to not only add talented lunatics but get the most out of them. See Moss, Randy and Johnson, Chad with the Patriots.
Are they more likely to turn it over in the last minute of the half? Do points in the last minute of the half count extra? If not then they should absolutely never throw it from their own 8. Probably not until they cross the opponent 40 just to be safe.