Learning the value and price of MLB free agents

After the Yankees recent and reasonable contracts handed out to CC Sabathia and AJ Burnett, the media and fans have exploded with disgust. The big argument is that the Yankees are stupidly spending this money on pitchers and overpaying. This is false and I presume people do not know that, since they do not know how to value free agents.

Currently, there is a stat that does just that- WAR. WAR literally stands for Wins Above Replacement. A Replacement player is your typical AAA/AAAA player. A team of replacement players would easily set the record for most losses in a season. As Tangotiger wrote, WAR is, "he talent level for which you would pay the minimum salary on the open market, or for which you can obtain at minimal cost in a trade."

For positional players, the replacement level is set at -2.25 per 162 games, below the league average. However, since the AL is a tougher league than the NL, the AL replacement level is -2.5 and the NL replacement level is -2.

Along with league adjustments, there are positional adjustments. This is done to make sure an average defender at one position, lets say LF, is not equal to an average defensive SS. The adjustments are as follows:

+1.0 wins C
+0.5 SS/CF
+0.0 2B/3B
-0.5 LF/RF/PH
-1.0 1B
-1.5 DH

Starting pitchers and relievers have different baselines, since pitchers are expected to perform better out of the pen. The replacement level for starters is .380 win% and .470 win% for relievers. Again, there is a league adjustment; AL starters and relievers are .370% and .460% while NL starters and relievers are .390% and .480%. Closers have a replacement level of .570%. If a closer gets any wins above that level, it is multiplied by his Leverage Index.

The formula for calculating WAR for positional players takes into account league, position, PA, wOBA, and defense. The formula for starters and relievers includes ERA and IP. Right now, 1 WAR = $4.84 million. So a player with a 2 WAR on today's open market is worth about $10 million per year. The free agent value, this year $4.84 million, increases about 10% each season. Last year it was $4.4 million.

So lets test this out on some free agents or former free agents. First, we'll do Mark Teixeira. Marcel projects Teixeira to have a .386 wOBA. Subtract that from a projected league average- I am using .340. Use that answer (.46) and divide by 1.15. Times that answer by projected PA (in this case, 600). Now divide that by 10.5. Now add in 2.5 for the league adjustment, but subtract 1 for the positional adjustment. Adding in .84 for defense (Runs defensive metric/10.5) and Mark Teixeira's WAR is about 4.5. Multiply that by the free agent value of 4.84 and you will see Mark is worth about $22 million per year. An 8/176 deal is around fair price for him. (The .338 is whatever the league average wOBA is, which is EXACTLY equal to whatever the league average OBP is; 1.15 is the relationship between wOBA and runs; 700 is the number of PA per 162 games; 10.5 is the relationship between runs and wins- Tangotiger)

Now, lets do CC Sabathia. After plugging in projections on my WAR calculator (if you want one, just ask), Sabathia has about a 5.1 WAR. So he is worth about $25-$26 million on the open market and is worth an additional amount of money to the Yankees. They are paying him $23 million per year.

Finally, lets do AJ Burnett. After accounting for a risk of injury and not throwing 200 innings annually, his WAR is around 3.5. That makes him worth $16.94 per year. The Yankees are paying him fair value. If Burnett stays healthy and can pitch effectively for 200+ innings, the Yankees could even have a bargain on their hands. Of course, this and the CC contract can blow up on their faces because of injury.

If anyone wants an exact formula for batters, just ask me. And there- now you can tell if a team is spending too much on a player or not. You are welcome.