Q. How do you determine if it is “In the 1970s bad things happened” or “In the 1970s, bad things happened”? Comma or no comma? Why?
A. You can determine it by consulting a style manual like CMOS. You can go to the table of contents and look for the chapter on punctuation (chapter 6), then scan down the list of topics until you find a section on commas. Within that section you can look for the paragraph that addresses your issue: 6.36, “Commas with introductory adverbial phrases.” There you can read that “an introductory adverbial phrase is often set off by a comma but need not be unless misreading is likely. Shorter adverbial phrases are less likely to merit a comma than longer ones.” You can decide that your phrase does not need to be set off by a comma. Why? Because misreading without the comma is unlikely.