Looking for Adam's previous work, I found his blog post from a year ago:
AdamJT13.
"As the NFL explains, compensatory picks are awarded to teams that lose more or better compensatory free agents than they acquire. The number of picks a team can receive equals the net loss of compensatory free agents, up to a maximum of four. Compensatory free agents are determined by a secret formula based on salary, playing time and postseason honors. Not every free agent lost or signed is covered by the formula."
A key passage:
"A simple method of determining for which qualifying free agents a team will be compensated is this – for every player signed, cancel out a lost player of similar value. For example, consider a team that loses one qualifying player whose value would bring a third-round comp pick and another qualifying player whose value would bring a sixth-round comp pick but signs a qualifying player whose value would be in the range for a third-round pick. That team would receive a sixth-round comp pick because the signed player would cancel out the loss of the higher-valued player. If the signed player’s value was equal to a fourth-round pick or lower, however, the team would receive a third-round comp pick, because the signed player would cancel out the loss of the lower-valued player."
While we're not going to match Adam's prognosticating skill, we can at least get a head start by listing the free agents lost and free agents signed by the Pats last season, and then assigning approximate values.
How many free agents did the Patriots sign? I worry about this caveat from Adam's blog:
"No team has been awarded a comp pick after signing more qualifying free agents than it lost, no matter how significant the difference in combined value."