Richard, the courts or courtyards were sometimes given names or sometimes numbers. Both appear on maps and in addresses, like the census. The courts ceased to be part of the official address sometime in the early 20C. I'm not sure when though.
There is a thread on the numbering of houses with Mikejee's informed comment:
https://birminghamhistory.co.uk/for...cks-courts-and-houses-and-street-names.53233/
So with back-to-back houses each house would have two numbers so 3/244 would be read as house number 3 in the terrace at the back of house 244 in the street. (To use Eric Gibson's example in that thread.)
The names of courts can cease to be used and more regular numbering introduced within a decade or two. Working out who lived where and in which court or terrace can be very difficult.
In the National Trust Back-to-Backs Chris Upton's book Living Back to Back is very useful. His research formed the narrative in the leaflets and information boards there. Court 15 has various houses connected together.
http://www.birminghamconservationtrust.org/our-projects/bct-finished/back-to-backs/
The present address of Back-to-Backs is 55-63 Hurst Street/50-54 Inge Street as it is on a corner plot.
If I've blundered in my explanation then do correct me anyone. I knew Ladywood which did not have named or numbered 'courts' at least in the early 1960s, but back to backs in terraces.
Derek