Also here is the ultimate defining truth about what I think you are talking about:
https://en.wikipedia.org/wiki/World_War_II_casualties
How well do Britain and the U.S. rank in "involvement"?
Well, places 17th and 18th. Some other interesting data they include in that chart is the total prewar population and deaths as % of the prewar population, which I think should be used as reference to foot such comparisons. This is my basis to demonstrably and measurably show that freedom lovers have been 10 times more genocidal than nazis.
It is definitely not the same to say that 507,000 to 807,000 Greeks died than 450,900 British people or 419,400 gringos, because the UK's pre war population was more than 6 times and the U.S. more than 14 times greater than Griechenland.
I think those charts should separate the European from the Asian part of WW2 not only because of geographic reasons, but the political causes and consequences are different to some extent as well. The causes, "reasons" why Japan started the war can't be compared to Germany's.