Slapping dollar values on a particular player's performance is generally done by multiplying his WAR for the season by about $5M, the current market value teams pay for a single win above replacement.
Yet, an overwhelming amount of Major Leaguers are not operating on contracts obtained through Free Agency. Using the aforementioned methodology certainly has its uses: Without getting into salary inflation, and his decline into the latter years of a long-term deal, Prince Fielder can be expected to be a 5-win player for 2012 and therefore worth $25M.
Just as WAR can't be used in all situations (Even statheads will admit that MVP races shouldn't be entirely defined by WAR, neither should Hall of Fame balloting), and of course, WAR is far from perfect (defensive metrics need a ton of work in general, and are very poor in small samples), neither should this way to calculate a dollar value to a player.
My point is that, the Major Leagues spent $2,786,161,291 on 2011 Opening Day salaries, and used that money to generate a total of 1163.6 WAR (Fangraphs version), or $2,394,432.19 per single win above replacement. I believe this number should be referenced when describing a player's value to a team in dollars, while Free Agent contracts should be evaluated based on the market figure of $5M.
Jose Bautista was therefore worth $19,873,787.18 in 2011, in his last year of arbitration eligibility. This is roughly half of Fangraphs' calculated value of $37.4M, yet represents the true value Bautista would have had to any team.
If you think evaluating players based on this principle is a fair point (or otherwise), please leave a comment!