Imagine you have 8 people searching as axis, 2 people searching as allies. Finally, matchmaking puts two if them into a game. If one new axis an one new allied player starts searching (which would be a 50/50 split for the newcomers), you still stay at 80% axis.
A constant 80% searching axis does not neccessarily equal 80% wanting to play as axis at first, in fact you can't derive anything from these numbers alone (especially not your statement of "80% want to play axis first").
Hum
8-2=6+1=7
2-2=0+1=1
1/7x100=14%, 100-14=86%, no 80%.
edit: To make it clear: you can't derive what people want to play from these numbers (no % of player preferring axis over allies everytime), you can only derive how many people actually play a faction (what I already did in this thread).
I don't try to state anything, number are already there. The problem is coming from your method. Here we have 2 distinct populations and not just one as you state.
1)People that are actually playing a game
2)People willing to play a game
Our interest cover people willing to play a game.
We always have 100% of people looking a game.
We have X% of this population looking for a game as Axis
We have X% of this population looking for a game as Ally
Many analyses from many players state that between 70-80% of the population is more interested to launch the game as Axis than Allied on a regular basis.
Some people made some statement about the reason like the sensation of playing the bad boys. In fact They maybe right or not, it doesn't matter, the average is there, 70-80% of people willing to play COH2 in multiplayer ranking mode want to do it as Axis in first instance.
Why do I say first instance? Because as many here mentioned before, looking for a game as Ally is a matter of second before being matched. So there are no 2nd instance for an ally 1st picker, or your are really fast in changing your mind and your faction or you made a mistake selecting an Allied faction but in fact since it also happens on the other side, the % or error is negligible.
On the opposite side when you are looking for a game as Axis, you have plenty of time to change your mind before being matched, not only because you selected Axis by mistake but because people don't want to wait 5 minutes before being matched.
So the population willing to play a game isn't that stubborn, people wants to play a game first. And from then, as Axis in 1st instance , which is not every time possible. So people just switches faction and get matched faster.
From that point, they then leave the group of people looking for a game to the group of people playing the game.
Are all Allied players in that group wanting to play Allied in 1st instance, my conclusion is no with a negligible % of error.
Are all Axis players in that group wanting to play Axis in 1st instance, my conclusion is yes with here again a negligible % of error.