So big thanks to everyone who helped with the nerdy challenge. You all saved me a ton of time. In thanks, I'd like to explain the frisbee reasons I was curious.
Mini is an awesome tool for development of individual skills. Unlike 7s, where a young player might touch the disc only 4 or 5 times a practice, Mini affords them a countless touches in a very short period of time. Touches, marking, defending, reading...every essential skill is practiced at game speed in a game like setting at a rate you can't match in a full-sided scrimmage.
I was interested in using it as a tool at the team level. In particular, I wondered if it would be possible to set a possession goal and use mini scores as a way to evaluate this goal. What I mean is, could you record the scores to a whole bunch of mini games and then go back and figure out what the possession rate was? Actually, I knew you could do this work, but I needed the algorithm to figure out the rates. That was the reason for the nerdy challenge.
Using Alpha Chen's probability generator, I cranked out possibilities established expected values and was able to come up with an expected value number for each possession probability. (The spreadsheet is here.) There is a bit of inaccuracy because Alpha Chen's simulator is a Monte Carlo generator and comes up with different values on each run, but from a frisbee standpoint, it doesn't need to be exact.
Here's how it would work: You play mini. Everyone keeps a running total of their score for all their games and how many games they played. (Golden Goal scenarios still 'score' as -1, -2.) When you are done, you add them all up and divide by how many games where played. Compare this number to the chart and voila! You know how you did on possession percentage.
10% = -1.4
20% = -1.2
30% = -1.0
40% = -0.5
50% = 0.1
60% = 0.7
70% = 1.2
80% = 1.4
Last thought. Some of the direction for this thinking came from Anson Dorrance's Vision of a Champion. In particular, Ch 12 and 13.
I think my reasoning is solid, but please, if I messed up, let me know. Thanks!