This world map has to be wrong!

The right hex-map of the world is based on a mercator-projection. This means, it is misleading in accordance to the area each land or continent is occupying. This also means, the hexes shown in this map are not all 72-miles hexes. I could try to explain this in a thousand words, but this has already been done by somebody else and so I would just like to point you to this video:

If I had to explain...

Mathematical Carthography isn´t my favorite subject (though it seems I learn a lot of it in recent times), but if you insist, I will try to explain how I see the problem with the maps. But first let me point you to a lace where it is described in more detail:

https://en.wikipedia.org/wiki/Map_projection#Equal-area

Imho there are two major problems:

1. The 2D-maps where I put the hexes on as an overlay are already "wrong" as you can´t project a globe on a 2d-face without distorting at least one of the following:
the areas, the angles or the distances (or whatever else I forgot).

So what you would have to do is to first place your hexes on the globe and THAN make a map from the globe (including the hexes) by projecting it on a 2D-face.

But if you would do so, not only would the world itself be distorted but also your hexes would look very "funny" afterwards (no 60° angles, not the same size, no straight walls for example) and most people wouldn´t recognize them anymore as common "hexes". I would like to do this anyways, just for to see the result, but that leads us directly to problem two:

2. I simply have no tools to first place the hexes on the globe and afterwards to project them together with the globe on a 2d-face (Someone else might have them though and is highly encouraged to do so).

What I can do (and actually did in my hex-map of the world) is putting nicely shaped, all equal hexes on a distorted map.
These hexes look like all equal hexes, but the land-area included in them is far from it.

What I could try is taking another map that was produced with a equal-area-projection and put the hexes over this map. Still the map under the hexes would be distorted, but you could probably assume, that the areas of the land "in between" each hex-walls has roughly spoken the same area. This might come in handy, if you have players who want to create their own dominions and you want to give all of them the same area for their dominion, let´s say 3 hexes. But strictly spoken, when your player for example would head west on this maps they wouldn´t head west on the globe...

I might try to work on a second alternative projected map in some time, which will probably be an equal-area projection, as I myself feel frustated, that this mercator map isn´t displaying correct area-proportions. But this will probably take some time. Meanwhile have a look at  the very interesting map on the right, which was created with an equal-area-projection!

Mercator Projection

Hex-map of the world. Please keep in mind, that the hexes in this map aren´t all 72-miles hexes, as this map is based on a mercator-projection! Click on the map to download the high-res-version of it (roughly 20000x10000px and 15MB)

Area-Equal Projection

In contrast to the above map this is a map where the areas of the land-masses are displayed correctly. You might notice, that for example Africa looks much bigger than before! I have not made a hex-map of this world-map, but I might choose to in future.
Click on the map to download a high-res-version of this map.
Copyright by Strebe.
Source and license: wikipedia