World games mixed stats...
it seems like there is quite a bru-ha-ha about the involvement of women in the coed game. i remember thinking about this during the world games as i looked at some of goals scored and assist data being reported from the tourney. as i understand it, those games were all played with 4 men and 3 women on the field at all times. this allows us to set some expectations about each gender's involvement in the number of goals.
i made an assumption of randomness, meaning that i expected that any player on the field was equally likely to throw a goal and each receiver was equally likely to receive a goal, which allowed us to group by gender. of course it isn't true that each player has the same likelihood of throwing/receiving a goal, whether the game is same-sex or mixed, but for the purpose of argument let's just go with it. under random conditions we would expect that 4 out of 7 goals would be thrown by men, and that their goals would be evenly split between men and women (because when a guy has the disc, 3 of his receivers are male and 3 are female). 3 out of 7 goals should be thrown by women and two-thirds of their goals should go to men and only one-third should go to women. so for a given goal, the probability of it being:
i think that you'll actually find that the US team was one of the better balanced among the teams in attendance. a quick look at the 3rd place gamesheet shows that the canadian women threw 2 of their 15 goals, with men on the receiving end of all their goals.
i made an assumption of randomness, meaning that i expected that any player on the field was equally likely to throw a goal and each receiver was equally likely to receive a goal, which allowed us to group by gender. of course it isn't true that each player has the same likelihood of throwing/receiving a goal, whether the game is same-sex or mixed, but for the purpose of argument let's just go with it. under random conditions we would expect that 4 out of 7 goals would be thrown by men, and that their goals would be evenly split between men and women (because when a guy has the disc, 3 of his receivers are male and 3 are female). 3 out of 7 goals should be thrown by women and two-thirds of their goals should go to men and only one-third should go to women. so for a given goal, the probability of it being:
- man to man = (4/7) * 0.5 = 0.2857
- man to woman = (4/7) * 0.5 = 0.2857
- woman to man = (3/7) * (2/3) = 0.2857
- woman to woman = (3/7) * (1/3) = 0.1428
- man to man = (8, 9, 7, 8, 7, 7) 46
- man to woman = (1, 2, 1, 2, 3, 1) 10
- woman to man = (2, 2, 4, 4, 3, 5) 20
- woman to woman = (2, 0, 1, 1, 0, 0) 4
i think that you'll actually find that the US team was one of the better balanced among the teams in attendance. a quick look at the 3rd place gamesheet shows that the canadian women threw 2 of their 15 goals, with men on the receiving end of all their goals.