You don't need to be a mathematician to quantify the problems and improvements in user interfaces. Often the most compelling metrics are simple to compute and require no more than arithmetic and basic algebra.
When thinking back about an experience (a voyage or an Amazon purchase, for example) are we truly capable of accurate mental replay? After all, we can only recall what we encoded into memory. If an experience was great, will we remember it as such? And if we remember an experience as a positive one, did we truly experience it as such at the time?
Sometimes it necessary to "kill your darlings" in a design project and go back to identify the true purpose of the solution. It's easy to fall in love with a design suggestion because of subjective factors and forget about the origin. Here is a great article with a proposed approach in order to change focus from solution to problem again. /Hans