An actuary estimating next year’s losses in a certain line of insurance will typically take the losses from the past few years and use them to forecast next year’s results. Frequently the amount of data available is so small that it would be inappropriate to base next years rates purely on that data. On the other hand, it is not appropriate to ignore recent data. One compromise is to take a weighted average of, say, last year’s rate and the rate indicated by the data. These weights are called “credibilities”. This introductory talk will illustrate how these credibilities can be derived and justified.