When to Ban from minecraft

So you'll probably hear on my next episode of minecraft that we had to ban someone. 

I'm curious what you think it takes to ban someone from a server or what others who are reading this might have been banned for that seemed unfair.

Basically the man wasn't participating with the rest of the group as was the point of this co-op minecraft scenario we where running.  He explored large chunks of the map against the server host advicement because it makes the server more difficult to backup.  He did this to loot all the chests nearby.  he went into the twilight area alone without recording and killed the fortress. 

All of that is just kinda jerkish but not bannable in my opinion.  The one that did him in i think was when he kept trying to use a mod that currently crashes the server several times, each time being warned not to use it.

Admin said that we can do better for our server which I believe but made me wonder what it would take before I ban someone from a server myself.