SERP analytics shows boost
The SERP status over the past few months of activating HTTPS on this site provides a clear message of SERP improvement.
Using the Google Search Console as the easiest SERP position checker available it shows that, at least for now, the shift to HTTPS can for a site provide an easy optimization of SERP rank.
With the same content a quite old page jumped in rank, and with hosting services providing free certificates and easy activation going HTTPS is a no brainer.
As an example Let's Encrypt offers free certificates which provides an easy path forward.