An Example of Credibility and Shifting Risk Parameters

In this paper, the won-lost record of baseball teams will be used to examine and illustrate credibility concepts. This illustrative example is analogous to the use of experience rating in insurance. It provides supplementary reading material for students who are studying credibility theory. This example illustrates a situation where the phenomenon of shifting parameters over time has a very significant impact. The effects of this phenomenon are examined. Three different criteria that can be used to select the optimal credibility are examined: least squares, limited fluctuation and Meyers/Dorweiler. In applications, one or more of these three criteria should be useful. It is shown that the mean squared error can be written as a second order polynomial in the credibilities with the coefficients of this polynomial written in terms of the covariance structure of the data. It is then shown that linear equation(s) can be solved for the least squares credibilities in terms of the covariance structure.