Question
Has anyone ever investigated weather game dynamics in certain sports ever experiences a percolation-type transition with catching probability as the driver?
Details
I recently started playing Ultimate Frisbee, at the beginner level, and I noticed something interesting which could also apply to other sports (Rugby, American Football, Basketball etc). Games which involve a free field, scoring "goals" at one end of it, and, last but not least, catching something thrown by players of your team where it will go to the other team if you fail to catch it.
As a beginner, by far the most common error you make is failing to catch the frisbee. So, every team can be labeled by "the probability a frisbee thrown by a player will be caught by another player of the same team", and the main driver for this probability is capacity to catch (Of course capacity to throw is also important here, but I think capacity to catch improves monotonically while capacity to throw quickly reaches a plateau).
Now, in our beginners games we typically let the frisbee drop MANY times between each goal, so the game stops continuously with the frisbee going to the other team. Players run for short periods of time, accellerate and decelerate a lot, and direction changes discontinuously. I watched a more advanced game, and lo and behold it went on much more smoothly. An experienced friend confirmed that for experienced players many goals pass before the frisbee is dropped. As a result, the game involves pretty much uninterrupted (but smoother) running between goals, with the probability of the team which has the ball from the start actually scoring the goal being very high (as a result a typical experienced game has a small score difference).
Now, here is a question: The field is two dimensional, and you can imagine the pass of the ball as a "link" between players, which form a disordered network. A link which is "on" when the pass is successful and "off" if it fails. Could it be that this dynamics approximates a percolation type transition? Of course this is a finite system, but it would make sense that there would be a "sharp cross-over" between two regimes, a "beginner game" analogous to the non-percolating phase (where the typical number of passes is "1") and an "experienced game" analogous to the percolating phase (where the typical number of passes is >>1).
Every characteristic of the game (mean accelleration, number of stops, point difference, mean distance traveled by players) would then vary sharply between the two regimes. The strenght of the transition would be proportional to the extent in which the capability to "keep the frisbee/ball" can be parametrized by a single number (I expect such phase transition not to exist, or to be very weak in football (Soccer for Americans :) ), since there keeping the ball cannot be reduced to "one action". But in Ultimate Frisbee or Rugby or Basketball it might).
I wonder if this was ever investigated before (googling indicates no).
I imagine it would be pretty easy to investigate, both empirically (game stats) and with a Montecarlo (just simulate players moving around, throwing balls at each other and accept/reject with a probability).
If a sharp transition exists, awareness of it could in principle help training, since the gameplays, strategies, and even player fitness requirements will vary quite a bit between the two phases. My expertise in this comes from a slightly different enviroenment than sports :), https://inspirehep.net/record/893765?ln=en
