Frequently, I receive a comment or e-mail that brings up the dollar-value estimates at Fangraphs.com. Fangraphs is a fine site with lots of interesting numbers, but I don’t think the dollar-value estimates listed on the site (or any simple wins-to-dollars conversion) properly value players. Here’s why.
1) The derived estimates are based on the assumption that there is a constant linear relationship between wins and dollars. This assumption is incorrect: there are clear increasing returns to winning. This is the revenue function I estimated for my book, converted to wins instead of runs.
2) By dividing the total value of free-agent contracts (Y) by total “wins” added by the signed free agents (X), this method assumes the y-intercept (b) is 0, which biases the estimates. Y = mX + b, when you assume b is zero when it’s not, bad things happen to slope m. The graph below from the popular econometrics textbook Understanding Econometrics: A Practical Guide by A.H. Studenmund demonstrates why this assumption biases the estimates.
Due to the thinness of the free-agent market and the potential for market mistakes, I prefer a fundamental-value approach to valuing players as opposed to a market-valuation approach. However, if I want to use the free-agent market to value talent, I prefer Anthony Krautmann’s “free-market returns” approach, which can be implemented in ways to avoid the problems mentioned above.
In Chapter 4 of my book, I explain why I prefer the Gerald Scully inspired approach to the free market returns approach. This is not to say that market prices are not useful for valuing free agents. In my book explain where free market returns helped me shape my estimates. Also, here is a working paper in which I discuss the pros and cons of the Scully and Krautmann methods.