Maybe in other sports this happens, but I seriously doubt QB's engage in that. First of all, taking a sack is not pleasant. In the extreme it can take you out of the game, or land you on the IR (injured reserve). Drew Bledsoe was replaced by Tom Brady after such a sack, and was never the star he had been before. Second, the number of sacks a QB takes is a statistic in itself. Third, the top stats for a QB are in this order: touchdowns, interceptions, passing yards, and completion percentage. If a QB takes a sack to avoid an interception, I'm 100% happy with that. If he takes a sack so that his completion percentage is higher by 0.01%, I would not be, but then the completion percentage is reported at the 0.1% level of precision. There is simply too much physical pain in taking a sack for a QB to trade that for an imperceptible gain in a pretty unimportant stat.
some QBs like aaron rodgers will take a sack instead of throwing the ball away.
rodgers had a 50 sack season twice in his career and has a sack career of 6.96. this is reflected on his interception rate (which is the best in the nfl). he just prefers to take a sack to attempt a pass that could be intercepted -- and everybody looks at those int/td numbers and don't look a lot at sack numbers (because sacks are usually not the qb fault).
