Friday, November 09, 2012

Application Trajectories

For any tuition-driven college, the run up to the arrival of the fall incoming class can be an exciting time. There are ways to lessen that excitement, and one of the simplest is to track the S-curves associated with key enrollment indices. An example is shown below.

In this (made-up) example, historical accepted applications by application data are show as they accumulated from some initial week. It's a good exercise to find two or three years of data to see how stable this curve is:

1. Get a table of all accepted applicants, showing the date of their acceptance.
2. Use Excel's weeknum(x) function, or something similar, to convert the dates into weeks, and normalize so that that 1 = first week, etc. This first week doesn't have to correspond to the actual recruiting season. You just need a fixed point of comparison.
3. Accumulate these as a growing sum to create the S-curve by week.
4. Plot multiple years side-by-side.
5. If this is successful, the curves will be pretty close to multiples of one another. That is, they will have the same shape but perhaps different amplitudes. You can normalize these by dividing by the total, so that the sum is 1 at the right of the S. This is your distribution curve. You may want to average the last two.

Once you have a historical distribution curve, you can multiply it by your admit goal to get the trajectory you hope to see during the current cycle. The graph above illustrates the case where the current numbers are on track to meet the goal. If the current numbers drift off the curve, you'll have lots of warning, and can plan for it.

Note that this probably works with deposits and other indicators too. I've only ever used it with accepted applicants.