The formula the NFL uses to determine compensatory picks - draft picks slotted at the end of each round starting from the third and extending to the seventh is both complicated and hidden.
The basic gist of it is teams are rewarded compensatory picks in the draft after the season they lose a player to free agency. The level of that pick depends on several factors, including salary, playing time and postseason honors of the player leaving, and the value of any player the team signs in free agency.
While it's not purely apples-to-apples, if Team A signs one player to a one-year deal for $1 million, and loses a player who signs the same contract elsewhere, they wouldn't likely receive compensation.
The player has to have entered the free agent market due to an expired contract, not a release.
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