We looked at SAML and it didn't seem to be a good fit for our use case. It is overly complex for our needs.
Instead we built a very small subset of what SAML allows, that is very easy to understand and allows our partners to use lightweight JWT libraries with simple APIs instead of trying to figure out how to get a complex SAML implementation to work with our flow.
We didn't re-invent anything. We used an existing, simpler standard for one of it's intended use cases. Our implentation is < 100 lines of code (not including the JWT library which implements the standard).
Edit:
The relevant SAML flow is this:
http://docs.oasis-open.org/security/saml/Post2.0/sstc-saml-t...
But good luck finding good documentation on it.