This PDF has some great I for about the HPS lamp. Including how to achieve the greatest efficiency. According to it, color corrected HPS retrofit lamps with a CRI of 50-60 and efficiencies of 105-130 lm/W were developed, which is great efficiency for a higher CRI HPS lamp.

https://www.govinfo.gov/content/pkg/GOVPUB-C13-2ca9f727d8799b3e0ab0c8890b41fcef/pdf/GOVPUB-C13-2ca9f727d8799b3e0ab0c8890b41fcef.pdf

This is amazing, I am only a third of the way through and I am definitely going to finish reading it. Excellent find

Thanks! This article does have a lot information, just look at the attached equations!

Yeah I saw those equations, I don't know what half those symbols mean lol. I definitely learned from that.