American football is the most complex and strategic of all popular sports.

You make some very good arguments with many valid points. Yes football is a very complicated sport but I do not think it is the most complicated. I will make an attempt to rebut your statements and use examples of other sports to show that they have more complexity. First off as no clear definition was first described I am assuming that the complexity in the sport, for which we are arguing, can come from many different angles and variables. Those variables include individual player, team work, coaching, and even scouting. As you stated the definition of complexity can include, but is not limited to, a variety of factors. I will explain how just because something has a variety of factors does not make it complex. Although football does have a lot of positions and roles that need to be filled in order for the team to function this does not mean it is complex. I think I can even use your own argument against you in that there many roles. The players each have there own role and they don't even have to switch on defense. A lot of the roles are based on repetition. (wide receiver running a route they have ran hundreds of times or a running back running through a hole.) This makes it easier to play the game in that your role is a lot more simple when all you have to know are a few things and the others are irrelevant. This makes the game easier to play, coach, and manage. Drafting players is not as complicated when there are not as many factors that need to be decided on. Coaching players is also not as difficult as you don't need to teach one person too many things. In rugby most players need to be able to fill certain roles when necessary and make the proper reaction. Every single player in rugby needs to play offense and can immediately need to react to the situation to play defense without stopping to take a drink break. Not only do they need to make a swift reaction but they need to know how to work together as a team on both sides without stopping or slowing down to draw up a play. In soccer, hockey, and basketball the players all need to be able to play both offense and defense while continually playing and working as a team with limited communication. The point guard in basketball must be able to play both defense and run an offense calling plays when needed and reacting quickly to situations. The point guard can't just throw the ball away and try again in another 40 seconds. I would like to use a metaphor that might come across as absurd but I am just trying to get my point across. Now lets say you take 2 average not extremely educated high school kids and give them a team of average people. (Quantity not important) You give student A 20 tasks to complete but they are all things like cleaning, yard work, painting, etc... You give Student B 1 task. His only task that he can use his team in what ever way he wants is to solve a large Rubik's cube. All I intended to do with this example is show you that just because there are more roles and factors involved does not prove that something is more complicated. I'm sure most people would agree that the 1 task of solving a Rubik's cube is more complicated than the 20 tasks for student A. While I can't argue that there is another sport with more plays or rules I can point out the a player only has to remember their job in that specific play and often that job can be repeatable. Very good argument using scoring. I don't think I can name another sport that has as many scoring options as football does and you are right it does add to the complexity of the game but I do not think it is an important deciding factor.