The New Moneyball: Paying Players Lots of Money?

Yu Darvish

An assumption I have made in the past may not exactly be completely accurate.  I was thinking last week about Yu Darvish and how much he would be worth on the open market.  I casually increased price per win because I think the economy is rebounding (arguable) and that scarcity causes elite players to be paid at a higher rate.  The first assumption is one that is beyond me.  If I was in tune enough to properly predict the market, I would probably own my own team by now.  The second assumption I can test in a slightly less casual way.

I decided to compare cost per win of free agents in general against cost per win of elite free agents.  I calculated average cost per win by back calculating fWAR and the value attributed to it.  I then produced a weighted average for the performance of elite free agents over the three years prior to free agency.  Elite players were defined as players who have received contracts in excess of 100MM in the free market from 2007 until now.  Here is the list:

2007 (average 4.09 MM / Win; elite 5.86 MM / Win)
Carlos Lee - 6/100MM (5.85 MM / Win; +43%)
Barry Zito - 7/126MM (6.97 MM / Win; +70%)
Alfonso Soriano - 8/138MM (4.77 MM / Win; +17%)

2008 (average 4.47 MM / Win)
Alex Rodriguez - 10/275MM (3.5 MM / Win; -22%)

2009 (average 4.42 MM / Win; elite 3.62 MM / Win)
Mark Teixeira - 8/180MM (3.99 MM / Win; -10%)
CC Sabathia - 7/161MM (3.25MM / Win; -27%)

2010 (4.10 MM / Win)
Matt Holliday - 7/120MM (2.79 MM / Win; -32%)

2011 (average 4.53 MM / Win; elite 3.39 MM / Win)
Cliff Lee - 5/120MM (3.43 MM / Win; -24%)
Carl Crawford - 7/142MM (3.25 MM / Win; -28%)
Jayson Werth - 7/127MM (3.5 MM / Win; -23%)

Based on this data and a quick overview of the years before 2007, it appears that prior to 2008 that elite players were paid about 30-40% above market rate for wins.  From 2008 and onward, elite players are now paid 24% less than market rate for wins.

Are elite players undervalued?
I don't think so.  I think what this list might show is that the thinking change for a large number of teams around 2007-2008.  Revenue streams were drying up which limited the number of teams able to spend top dollar for players, but also, I think, there is a greater understanding of player aging.

How does this affect the project value I threw out for Yu Darvish?
If his pitching the past three years translates as a 3.50 ERA over 200 IP / year, he is worth about 4.4 WAR per year.  With a 24% decrease in cost per win, we are looking at him being worth 75MM over five years if he was a free agent.  If you believe in the prediction from the translation model (2.97 ERA), then you are looking at a five year worth of 102MM with the elite reduction applied.