Every year, the NFL awards 32 extra draft picks, spread over rounds three through seven. These picks are divided among the 32 NFL franchises based on the previous offseason's free agency transactions. Essentially, if a team loses more quality free agents than it signs, they could stand to gain compensatory picks.
The league uses a formula to caluculate the picks to be awarded, though it is a highly guarded secret exactly how the formual works. There are places that try to predict the compensatory picks to be awarded, and in which round, and some are pretty good. Over The Cap has a pretty detailed breakdown of how they expect the picks to work out.
The things that are known about how the system works is that, if a team signs more free agents than it loses, they will not receive a pick. Unrestricted free agents are the only players who are considered in the formula, not "street" free agents. This is one of the few times when there has to be a deliniation between the two: unrestricted free agents are players who had their contract run out at the end of the previous league year, street free agents are players who are cut by their previous team or players who were restricted free agents that the team does not tender.
Several other things go into the formula, including size of contracts signed and Pro Bowl or All-Pro selections. When it is all weighed out, the results are then ordered from highest ranking lost free agent to lowest, with picks given to the top 32. That means, a team can receive multiple compensatory picks, if they lost several free agents, or a team can receive none if they signed several free agents.
The Miami Dolphins last received a compensatory draft pick in 2013, when they were awarded two. The team lost three qualifying free agents in the 2012 offseason (Will Allen, Chad Henne, Kendall Langford) and signed one (Richard Marshall). The Dolphins were awarded the 33rd pick of Round 5 (166 overall) and the 44th pick of Round 7 (250 overall).
Miami did not receive any compensatory picks for the 2014 Draft, following the spending spree of the 2013 offseason. They did help the Baltimore Ravens (Dannell Ellerbe), New York Jets (Dustin Keller), and Pittsburgh Steelers (Mike Wallace) add picks. The Dolphins lost running back Reggie Bush (Detroit Lions) and left tackle Jake Long (St. Louis Rams) that offseason, but signed more players than they lost, preventing compendatory picks from being awarded.
What can Miami expect this week? Probably another year without picking up a compensatory pick. Miami again signed more players than they lost in the offseason. The team added Branden Albert, Earl Mitchell, Shelley Smith, Cortland Finnegan, Jason Fox, and Knowshon Moreno during free agency, while losing Chris Clemons, John Jerry, Paul Soliai, Nolan Carroll, and Vaughn Martin.
Looking ahead to the 2016 compensatory picks process, the Dolphins have added Ndamukong Suh, Jordan Cameron, Brice McCain, and J.D. Walton this offseason, while losing Jonathan Freeny, Brandon Gibson, Jared Odrick, and Jimmy Wilson. Charles Clay is an interesting one, because the Dolphins had the opportunity to match the Buffalo Bills' offer, which could make him ineligible for the compensatory picks formula, but that is not clear at this point.
Across the league this week, 32 additional draft picks will be handed out. Just don't expect the Dolphins to pick up any of them.