Disclaimer - Please discredit this if I am incorrect, but I do not think I am.
The out of the box 'bounce rate' metric, which is calculated as 'bounces / entries' does not work when used with the product string. the reason is that 'entries' does not work with the product string, but bounces do. after some discussion with client care I was told the following as it relates to the entries metric.
From Help Section
Entries represents the number of times a given value is captured as the first value in a visit. Entries can occur only once per visit. However, it is not necessarily the first hit if the variable is not defined.
From discussions with client care
the product string can contain multiple products. if the entry server call contains multiple products, only the first product in the string will get credit for the entry. all other products in the string will not have an entry associated with it.
We often drive people to landing pages that contain multiple products on the page, thus we set a product string with multiple products. So when we aggregate our products we end up with bounce rates way over 100% because bounces end up higher than entries, something that should never be the case.
My idea is as follows:
1-Can we make the entries metric work for the product string? this would change the definition of entries, but i do not think it is clearly definied in any documentation I have found.
2- if we cannot do the above, can we create a new entry metric related to the product string alone? this would allow us to create a new bounce rate metric for products.
A couple of workarounds and their issues:
A short term work around I came up with to calculate bounce rate for the product variable is to divide bounces by single page vistis. this will work but it is not perfect for the following reason: we have instances where an event, containing the product string is the first server call of the visit. this would cause that product to not have a 'single page visit' associated wtih it.
Note - page name does not work so well for me because we have a site that has over 10 million products, so we very quickly run into uniques exceeded issue. we have the same issue with the produt variable but we have been allowed to increase this limit into the millions.