Not what you would expect from me, huh?
But it's true.
I want your players to be selfish - not in life or as people - but at least while running the Read & React. And you should too.
Here's a quote that puts words to why that assertion makes you uncomfortable.
“There is a tension, peculiar to basketball, between the interests of the team and the interests of the individual. The game continually tempts the people who play it to do things that are not in the interest of the group. On the baseball field, it would be hard for a player to sacrifice his team’s interest for his own. Baseball is an individual sport masquerading as a team one: by doing what’s best for himself, the player nearly always also does what is best for his team. “There is no way to selfishly get across home plate,” as Morey puts it. “If instead of there being a lineup, I could muscle my way to the plate and hit every single time and damage the efficiency of the team — that would be the analogy. Manny Ramirez can’t take at-bats away from David Ortiz.” from an article on Shane Battier
If you understand the tension in the above excerpt, you’ll understand some of the reasons behind the structure of the Read & React Offense. Wherever I could do it, I built the actions of the players on the baseball premise above.