If you are looking for a rule of thumb, there is no right way to go about determining the average life expectancy for a pirate during the 1680-1740. One thing to consider is that while some got caught and hanged, others bribed authorities or received pardons and managed to live the rest of their lives out without being outlaws.
The careers of pirates, be it ended voluntarily or through being caught, could vary greatly. Anne Bonny and Mary Read's careers as pirates lasted only 2 months. Blackbeard's lasted from sometime in late 1716 to November of 1718, so around 2 years. John Cockram started in small boats in 1713 and took the pardon in 1718, so around 5 years or so. Four guys in a boat in 1727 took a schooner and robbed two sloops and were then caught by locals in North Carolina over the course of about a week or two. They were tried in Williamsburg. This stuff jumps around significantly.