### What is Decaying Average?

The Decaying Average formula is a calculation method that places more weight on recently scored materials, allowing for a better measure of growth by rewarding students for how far they’ve come without punishing them for where they started.

Decaying average displays an objective score that is most indicative of a student's current mastery level. Using the word “decay” is actually counter-intuitive, as this calculation method assumes and reflects growth over time.

The Decaying Average formula considers scores, or observations, over time and recognizes that a recent score is more representative of the student's current mastery level and thus puts more weight on that score. This is different than a straight average that counts the student's first work and most recent work as equally important.

**Note:**The most recent observation is determined by the timestamp of the most recent original score, not the most recent score modification. For example, if an instructor changes a student's score after having already graded it, the mastery calculation for any aligned objectives would only reflect that modification as the most recent observation if the original score was the most recent.

### How does it work?

Decaying average uses a variable called the decay rate to determine the relative weight of the student’s more recent scores versus earlier scores.

In the Mastery Settings of your course **Mastery** page, instructors have the option to enter their own decay rate when using the Decaying Average formula. The default value for the decay rate in Schoology is 75%.

**Note:**As of July 1, 2018, Decaying Average is the default calculation method for student mastery reporting in newly-created Schoology courses.

Let’s say you evaluate mastery in your course on a four-point scale, and you use the default decay rate of 75% with the Decaying Average calculation. You have aligned five assignments to Learning Objective A. Over the period of the course, the student received the following scores on these assignments in chronological order: 2, 1, 3, 4, 3. Note that the observations are ordered based on when they were first graded.

- Mastery Score on Objective A after first observation: 2 * 100% = 2
- Mastery Score on Objective A after second observation: (2 * 25%) + (1 * 75%) = 1.25
- Mastery Score on Objective A after third observation:(1.25 * 25%) + ( 3 * 75%) = 2.56
- Mastery Score on Objective A after fourth observation: (2.56 * 25%) + (4*75%) = 3.64
- Mastery Score on Objective A after fifth observation: ( 3.64 * 25%) + (3 * 75%) = 3.16

→ Final score for Objective A = 3.16

As you can see, this method gives weight to the most recent observation, while gradually allowing for increased “forgiveness” of early scores over time.

Please note that this is an example that uses whole numbers for the sake of simplicity. When implemented, the Schoology algorithm uses a raw score of points received divided by total possible points for each observation:

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