An NFL roster is a zero-sum game, thanks to the salary cap. Paying one player more means you have to pay another player less. To offset larger premium contracts, each team is trying to get as much value as it can out of its veteran contracts.
Below I've analyzed the rosters of all 32 NFL teams based on present value, future value and percent of the salary cap tied up to try to select the most valuable contract on each roster. And these aren't necessarily the cheapest contracts on each team -- one player on the list signed one of the largest contracts in sports -- but rather a calculation of how much value the team is getting for the amount it is paying.