According to the American Academy of Pediatrics, clinical trials have demonstrated that varicella vaccine is 70% to 90% effective for preventing varicella and more than 95% effective for preventing severe varicella.[18]
I was looking into how some people don't become 'immune' to chicken pox from the vaccine, and wondered how that gave them less symptoms. Unless, the vaccine prompted their body to create some immune response, but not great enough to prevent the disease all together. I then thought, there must be some people who don't respond at all to the vaccine, even if it is given correctly, and wondered about the frequency of this.

Not sure if this quote is addressing these two factors, and (disclaimer) it has only come from wiki, but if it is correct - perhaps 1 in 20 (95%) are minimal or non responders to the vaccine and 1 in 7-9 respond to the vaccine to some extent.