I owe the web analytics community an apology.  I was doing some analysis yesterday that made me realize that my Omniture formulas for the hard bounce rate and the soft bounce rate didn't match my definitions.  So here are my corrected formulas:

• Soft Bounce Rate:  ( [exits] - [single access] ) / ( [visits] - [single access] )
  
• Hard Bounce Rate:  [single access] / [entries]

Originally, I had the soft bounce rate as ( [exites] - [single accesss] ) / [visits], then I realized that the definition requires the denominator to be only the multi-page visits.  In light of this, the formula can now be stated as the number of exits that were not part of single page visits divided by the number of visits that were not single page visits.  Here we are trying to answer the question, "Of visitors who have visited at least one other page before this one, what percentage end their visit on this page?"

I also incorrectly had visits in the denominator for the hard bounce rate, when it should be entries.  So the formula in plain english is calculating the number of single page visits divided by the number of entries through that page.  Here we are trying to answer the question, "Of visitors who start on this page, what percentage don't visit any other pages?".

One caveat I have thought of is when a visitor visits a page, refreshes the page, then leaves.  It is advised that you consider the refresh rate when contemplating the soft bounce rate as it will add to the soft bounce rate when you would probably consider that a hard bounce.  Although, not every refresh is a two page visit.