Q:

Reducing web app documentation

Does anyone know of any good research showing the benefits of designing for better usability and less documentation?  We all know that good usability should require little if any documentation.   However, having the research to back it up helps when making the case to those that make the decisions.  

A:

I believe the metric (qualitative or quantitative) that might be appropriate in your case is Learnability. 
From Usability 101: Introduction to Usability, by Jakob Nielson:

Learnability: How easy is it for users to accomplish basic tasks the first time they encounter the design? 

Measuring Usability has an article on How to Measure Learnability, which discusses how one might quantify learnability.  The article goes into a fair amount of detail on what learnability is and the importance of it, as well. 
A high degree of learnability would imply a reduced reliance on documentation by the user.  It does not, however, replace the need for documentation - especially as the product becomes more complex.  Significant resources should still be applied to creating good and useful documentation!