Barring a few places in the erstwhile USSR, for which communism and its fall had a major role to play, countries with a predominantly white population, collectively called "The West" are the most economically (and socially?) well to do ones in the modern world.
Going back a few centuries, it was the Europeans that populated the "new world". Why not people of other regions? Because Europeans had the most resources to do so? But some medieval Asian countries were rich too. Asian, African and South american countries were the ruled upon, not the rulers. Why were the Europeans the colonists, not these other countries? Even if they weren't, why couldn't they keep the invaders out effectively? These countries actually had a very rich and ancient history, with access to considerable engineering and tech for those times. Trade flourished too, think about the silk route and the extensive reach of the Indian subcontinent. But they still did not/do not thrive as much as the Europeans.
I know race had no part to play in this, but why the coincidence? Was it the climate? the geography? The religion? Invention of the steam engine and the following industrial boom? (But colonisation started before that era)