You are comparing real life.... to a computer game. 
Umm... no... I'm comparing a game some people play outdoors, to a game other people play indoors. They're both games.
The point about each team having the same number of players is a good one, and yes, that does make it a bad analogy in that way. But I wasn't trying to suggest that it's wrong to switch teams, just that loyalty to a team is not the same thing as loyalty to the
symbol of the team. Nobody is loyal to a certain color t-shirt or a guy in a lion (or turtle or whatever) suit any more than anyone is "loyal to a chess piece". They're loyal to the team.