With these rankings, I try to give a rough idea of the offer I'd be comfortable making to each player, assuming I were the general manager of a contending team (or would-be contending team) and operating at or above the median payroll level.
Estimating the actual dollar value of a player to any specific team is nearly impossible, because we don't know what the marginal revenue product of a win is for each club, and that number can change for a team from season to season, or even within a season, if it's much better or worse than expected.
My numbers are not predictions, and they often will fall short of actual market values. That is due to the "winner's curse" phenomenon, in which the winner of an auction for a good of uncertain value is the bidder whose internal estimates of that value are the highest (and thus perhaps too optimistic), and because teams with large payrolls can and often do pay more for a win in the free-agent market.
I've also noted which players have received a $15.3 million qualifying offer. If a player receives one and signs elsewhere, the signing team will lose a draft pick, and having a qualifying offer "attached" can really hurt the value of non-elite free agents.
Now, on to the rankings.