Jolly Roger - your info has been filed for a later date. I know it's juicy but is far over my head at this stage.
Maybe I can point you in the right direction…

With a paper map, the scale represents the ratio of an object on the map to the same object in the real world. This is expressed in the form 1:24,000 which (in our Imperial System) means a one inch long road on the map would be 24,000 inches long in the real world (2,000 feet). Maps at 1:24,000 scale are called "24k maps" here in the US, which is a standard the USGS started using during the early 20th Century (based on what I've seen in the USGS archives).
But the whole concept of "scale" has gotten more complicated with computer devices that display images on a screen instead of a printed page. You need to consider the screen size and how many dots it displays per inch. As a mapmaker, it's virtually impossible for you to know what size screen a user might have. My iPhone has the same number of pixels on a 5.5 inch screen as my 46 inch television for example. There's no easy solution for this, and I suspect it will only get worse since hardware is evolving and screens are getting more pixels, while software isn't really keeping up with this.
Now if you look at the zoom scale list I posted, that shows the equivalent paper map scale, for example level 15 is about 1:18,000 (18k) which would be the closest to the USGS 24k standard. This is what I am currently using for my smartphone topo maps maximum scale.
Now each "click" in zoom levels doubles the map scale, so level 16 would be about 1:9,000. Map files start getting very large when you get into this scale, and it is far more detailed than any paper maps that would have been created for any large area, such as a state or province.
Remember, document size and file size are squared functions, because they represent area - when you double the scale, you quadruple the file size. So if your level 13 zoom scale map is 10MB, then a level 14 map of that same area will 40MB, level 15 will be 160MB and level 16 will be 640MB. When you combine these into a map for a smartphone, you add all of the included zoom levels to get the total file size.