Probability is neat. Brian Burke, the wizard behind the Advanced NFL Stats studies, strikes again. If you don't know the drill by now (follow the link!), you probably voted "13-14" on the poll yesterday. Also, you should stay away from sharp objects.
Using conditional probabilities based on first quarter game data, Burke shows that holding is actually an advantageous strategy more often than you'd think. The math involved is pretty straightforward, so go read. This boils down to game theory that can't possibly be used in a game situation as the odds of holding detection are not known aquantity. Holding detection involves all sorts of factors, like the egregiousness of the hold and the visibility of the interaction to the corresponding referee. Still, it makes an interesting case study. If you assume that getting beat results in a sack even 30% of the time, it's only worth holding if you the ref will blow the whistle 25% of the time or less. Bump p(sack | beat) up to 50% and you'd still have to hope the ref swallows his whistle on all but 40% of holds. Now assume your quarterback enjoys holding the ball and DeMarcus Ware is currently on his way by you (let's be honest, you aren't stopping Ware). Take him down.