Sorry I should have explained better my bad.
Ok. So the heat map demonstrates that the game's values for steel (by country) do a pretty good job lining up (correlating) with the iron ore and steel production data from contemporary US and UK sources.
Did I get that right?
Paradox accurately portrayed steel production (iron ore production) circa 1936.
Good on them!
(now Podcat, don't go messing it up and skewing the historical accuracy in response to certain nation's supporters chanting the Billy Idol refrain, "more! more! more!" Rebel Yell, 1983)
I will explain now without going into to much mathematical details.
Basically this. a 1 means there is a perfect correlation between the two variables in question. If one variable is higher the other also get higher according to a certain proportion. In a situation y=2*x or y=x, there is a perfect correlation between x and y if one variable is higher the other is also higher and always in a certain proportion either y is always 2 times bigger then x or in the example of y=x they are always the same.
This is why the units of steel of the game has a correlation of 1 with units of steel of the game because the values are all the same. This is also why I did not include the percentages of steel units they correlate via a certain proportion (aka percentage) with the absolute number of steel units in the game, since the percentage is derived from the absolute number of steel units that particular country has. This would thus learn us nothing extra from making that correlation.
Lower values mean there is a correlation but it is not perfect, If one variable increases in value the other also increases. but unlike the y=2*x example the proportion is not always the same e.g. if x =4 and y = 8 and when x = 13 y= 16. The variables show a very similar trend you cannot really encapsulate it with neatly in a simple equation that is always adhered to like in the perfect correlation. The closer this value gets to 0 the worse the correlation get.
A value of 0 means there is no correlation, a value of -1 would mean an perfect anti correlation that could be illustrated with y = -x if y is negative x is positive and the other way around. However this is not relevant to the heat map since there is no negative/anti correlation in the heat map.
And yes the game's steel values do a very good job lining up/correlating with the iron ore/steel production from the sources you have used in your excel file. Of course there is room for improvement. But as stated in the thread it could be that game play took precedence over getting all the numbers right.
All in all I would say they did a good job in trying to do justice to the numbers while also keeping the game balance in mind.