The Ugly Index: Part III

Math, the gory details

The task of manipulating the math remains.

For the sake of illustration let us consider a length-of-commute between home and place of employment.  A worker might consider a commute of more than 60 minutes to be excessive, but they also might consider a commute of less than 10 minutes to also be undesirable because they might count on their inbound commute as time needed to put on their "game face" and outbound commute as time needed to provide separation between work and home.  That would make the two endpoints 10 minutes and 60 minutes.

The generalized formula is:

((The average of the upper and lower limit) - value observed for candidate)^2/(The average of the upper and lower limit)^2

In our example of the commute, a the average of the longest and shortest commute is 35 minutes.  A commute of ten minutes and sixty minutes both have an ugliness of 1.0.  A commute of zero minutes has an ugliness of about two.  An ugliness of ninety minutes and two hours have ugliness of approximately five and eleven respectively.

One sided limits

A valid question regards how to treat "one sided"  limits.  An example of this might be the yield of a process or a crop.  More yield is always better.

A solution is to "trick" the math.  This can be in a couple of different ways. One can force the math by using the top yielding selection  as the mid-point for the parabola or one can use a cubic equation.  Both methods have advantages and disadvantages. 

The Ugly stacks up quickly after you pass the lower limit for yield.  This stacking up overwhelms stakeholder attempts to game the outcome by loading a number of highly correlated variables into the selection process or by highly weighting any one variable.

Tabular data:

Cultivar	Yield	Ugly
Drake	6.13	0.13
Rupert	5.77	0.32
Davidson	5.27	0.72
Sparrow	5.01	1.00
Kwik Krop	0.81	11.72
Dubois	0.64	12.40

This example uses data from HERE.

At this point the reader is observing that this is a tremendous amount of additional work when one could just pick some points off the chart and dismiss the other alternatives.

The reason for all of the work is to translate the data (measured value) into a universal units that can be added together to produce a single selection index.  By mapping variables like disease resistance, ripening season, flavor and yield into Ugly, they can be added together and then sorted by overall ugliness.

Beauty is as fleeting as the dew before the morning sun.  Ugly accumulates.  -Derivative of Jones's Motto