150 rings can be ordered and divvied out by the owner as they see fit.
I think I heard that the Rams had over 70 different players on the active roster this year at some point due to injuries, trades, etc.
They have over 20 coaches in various capacities...
The Rams front office is hundreds deep technically when taking all staff into play by evidence of this list...
Los Angeles Rams Front Office Roster: Official team site with news, videos, photos, schedule and front office staff bios
www.therams.com
If you assume the obvious players who deserve one and all of the coaches will get one. Add in the top tier front office staff and that probably leaves less than 50 to distribute per the owners discretion and a lot of those would probably go to family, business associates, and other bullshit like that. I think players like Djax and young are on the outside looking in. One person who probably does deserve one like someone mentioned in another thread is Brad Holmes. He had a huge hand in getting the core of this team drafted.