I'm doing a science project on why children swarm around a soccer ball as youths, why this changes with age, and is there a mathematical pattern to it. I would like some help as to where to get started with my research. what is the technical term for developing child movement. I can't word it correctly, as you can see. Thanks.
The only mathematical paper that I found regarding soccer is this http://cnls.lanl.gov/~ebn/pubs/sports/html/ that shows that is the most competitive sport. Maybe that is a factor explaining why "children swarm around a soccer ball as youths"
I thikn that flocking behaviour is relevant. You could model soccer players as members of a flock, with flocking rules that change with age. Here are some possible parameters to begin, with some simple thoughts for rules: Attraction to the ball (Very strong with young players. Still strong with older players, but depends on other factors such as who has possession.) Repulsion from team-mates (weak with young players) Attraction/Repulsion from opposition players (depends on who has possession) Modelling ball movement would be tricky. I think that giving it a strong repulsion from players but only at very close range would be enough for a science project. I found a couple of places with flocking simulation software: Craig Reynolds's Boids page with links VisualBots
I suggest you look into game theory. A good starting book would be Two-Person Game Theory. I do not know the author's name (don't know where my copy is) but it is a Dover book. I took a course last year on game theory and multi-player "games" act in many ways just like two-player games. This subject, in my opinion, will help in your observations. I know game theory has changed how I look at "games." You could probably analyze the strategies the children use when "swarming" the ball and dicuss alternative strats and why they do not choose them. This is generally the line between mathematics and psychology with reagards to game theory. So you are going to need to study some psychology, too.
I guess children have trouble evaluating where there are possibilities for the ball to be, that the ball could be passed to a different member and thus the child should cover that position instead of chasing the ball. It could also be that the child don't know his/hers role in it, thus are uncertain about who should cover the opponent team members and as a result give in to the easiest solution which is chasing the ball (while still having the '+' that they are doing what they are supposed to). I don't think there is a mathematical solution to it. Maybe it would look like this though: Definitions: a and b are initial conditions which are then recalculated below. e and f are the ability of the player. a = person from team A has the ball (otherwise is available to pass to) (1, 0) b = person from team B has the ball (otherwise is available to pass to) (1, 0) e = opponent not uncertain (1, 0) f = opponent evaulation power (1, 0) a = (1 - b) * -((e * f)) + 1 b = (1 - a) * -((e * f)) + 1
