[yawetag]

Originally Posted by Rich Ives

You said:

or where the umpire believes he would have reached absent the obstruction.

and the use of "or" means you pick one of the options and ignore the other - thus you could throw out the "minimum one base" part and pick the "base he would have reached" part

so on a pickoff attempt at first, given those words, one could think you award first.

This.