Probability that the FIFA has to draw lots to determine the winner of a group at the 2014 World Cup According to section 42.5 of the Regulations of the 2014 World Cup (PDF), the ranking of each team in each group shall be determined as follows:


*

*greatest number of points obtained in all group matches;

*goal difference in all group matches;

*greatest number of goals scored in all group matches.


If two or more teams are equal on the basis of the above three criteria, their rankings shall be determined as follows:


*

*greatest number of points obtained in the group matches between the teams concerned; 

*goal difference resulting from the group matches between the teams concerned; 

*greater number of goals scored in all group matches between the teams concerned; 

*drawing of lots by the FIFA Organising Committee.


We are interested in the probability that the latter happens, namely that the FIFA Organising Committee has to draw lots in order to determine the winner of a group. Note that the order here matters, so for this to happens, we need the first six points to be the same for two teams. 
Some key facts for the group stage:


*

*A group has 4 teams;

*Each team plays 3 games, one against each other team of the group;

*Win gives 3 points, tie gives 1 point and loss, none;

*Goal Difference $(GD)$ $=$ Goal For $(GF)$ - Goal Against $(GA)$.


I only have basic knowledge in probability and am not sure how to tackle this problem. Any help or hints would be appreciated.
 A: As @Tom Cooney says, you would need to fix probabilities for all possible scores in order to calculate the probability of these events happening. This is incredibly hard to do, given the nature of soccer. Which is not to say that lots of people don't try!
What would be much easier is to use historical data to estimate the probability of this happening. The current tournament format has been in place for 5 world cups (1994-2010) and drawing lots has been used a sum total of zero times in that timeframe. So that would imply a long term probability of $\frac 0{40}$ (40 being the number of groups over 5 World Cups).
Obviously the actual probability isn't $0$, but it appears to be pretty low based off of historical data.
In fact, if we go back farther drawing lots has only been used once in World Cup history (I think). 1990. And a team wasn't eliminated based on it, it only determined seeding for the knockout stage.
EDIT: I was right, lots have only been drawn once in the World Cup, but it was in 1990, before the current format. So it wouldn't be accurate to include that in the historical probability calculation.
http://en.wikipedia.org/wiki/History_of_the_FIFA_World_Cup#Group_Stage_Advancement_Format
