But, from the point of view of a developer, the thing that I appreciate the most on a fellow sysadmins is to be calm and methodic at all times. Organised. Having a plan and know what to do. Being ready for disasters.
Do we need to update a security patch on every single server? Ok, list of servers, start with server one, finish with the last one, don't let any one fall behind.
A server suddenly catches fire? No problem, remove it from the load balancer, get a fire extinguisher, remove it, order another one, recover from backup.
Is there a problem on production? What could be wrong? Check logs, think a little, then try to fix it. Do postmortem and come with improvements. Try not to be bitten again for the same thing.
In mi opinion, the core of good sysadmin is to minimise risks and errors in the stability of the system. Mistakes can (and will) happen, but the aim is to make them only once. I think it has a big component of learn from battle stories.
Processes and servers can fail, but the whole system should hold up.