Explaining Math in Academic Papers

In any academic paper dealing at least in part with math, the authors have to make a choice how much explanation to actually give the math.

It can range from pretty much no explanation:

Given a foobar of 12, a ackbar of 57, and general frobnosticating parameter of 9, the resulting nyan level will be 8.

To belaboring the obvious

The first three people went into the city. Later, four more people went into the city. This meant that seven people had gone into the city which is derived by adding the first three people to the next four people. We add because people are individual units and moving them to a new location neither combines or divides those units.

How does one decide the appropriate level of explanation? Is there any sort of standard that can be appealed to decide when something is clear enough?

The actual background for this question is that I've looked at a paper for a colleague. It is in a non-mathematical subject but does engage in some mathematical reasoning. I think the paper doesn't explain enough, but my colleague disagrees. I have to work at figuring out what calculations were done in the paper and the justification for many of the inferences he draws. That indicates to me that the explanation is insufficient, but is there a less subjective standard I can appeal to?