A progress curve and its formula to describe how productivity improves for law departments

An equation known as a progress curve “describes how productivity improves in a range of human activities from manufacturing to cancer surgery.” Having read that brief enticement in the Economist, April 2, 2011 at 76, I tried, probably unsuccessfully, to apply the equation to law departments.

The formidable equation Tn =T1n-b quantifies a learning curve. Tn is the number of days between the nth event and the next event. Try this to wrap your mind around the formula. Think of the number of days between the fifth bankruptcy proof of claim a paralegal completes and the 30th one. How much has the paralegal improved during that period?

The power b is calculated from the relationship between the logarithms of the event number, n, and the period of elapsed time. Perhaps the 30th proof of claim came on the 400th day after the fifth one. The logarithms of the 30th event (1.47) and 400 days (2.6) are used to compute the superscript power, which when divided by log2 gives the negative number (See my post of March 11, 2009: learning curve with 9 references.).

Since I have probably not explained the equation and its application correctly or fully, despite trawling on the Internet, take this as a work-in-process post.