What is the Power Law Formula for standards-based grading?

An internet search for “Power Law Formula” results in hundreds of listings in a wide variety of fields including astronomy, meteorology, and engineering. In his highly regarded book TRANSFORMING CLASSROOM GRADING, Robert J. Marzano describes the use of this formula for standards-based grading. The math behind the power law formula is quite complex (see below), but all that’s necessary for its use is that you know what it does, how to interpret its scores, and when best to use it.
In essence, the power law formula predicts what the student’s next score will be based on scores already present. It can be thought of as a mathematical calculation that answers the question: “If the student were assessed right now on a skill, at what level would the student likely perform?” Since a student’s grade on a standard is meant to be an indication of skill at a certain moment in time, the power law formula can be used to calculate standard grades.
To gain an understanding of how the power law works, let’s look at sets of student scores and Easy Grade Pro’s power law calculation of each set. To keep things simple, let’s say there are four assessments and four students and each student has earned the same scores 1.00, 2.00, 3.00 and 4.00, but in a different order. If we were to simply average the four scores, all students would receive a 2.50. However, with the power law, we’ll get different values because the power law puts more weight on recent assessments. Let’s take a look:
Assessment #1
(least weight) Assessment #2 Assessment #3 Assessment #4
(greatest weight) Power Law Score Interpretation
Student #1 1.00 2.00 3.00 4.00 4.00 The scores show continuous improvement. The student will likely demonstrate mastery on the next assessment.
Student #2 1.00 3.00 2.00 4.00 3.66 The scores show irregular improvement. The student will likely demonstrate high but not complete mastery on the next assessment.
Student #3 2.00 4.00 1.00 3.00 2.16 The scores show very uneven performance. The student will likely demonstrate a mid-level of achievement on the next assessment.
Student #4 4.00 3.00 2.00 1.00 1.28 The scores show continuous decline. The student will likely demonstrate a low level of achievement on the next assessment.

As you can see, the power law formula can result in more meaningful values than averaging. Should it then always be used? No! The power law formula is best used on narrowly defined standards (i.e. Subtraction of mixed numbers with borrowing). Avoid its use with broadly written standards that consist of multiple skills – the results will be less meaningful