World Cup: Advancing out of the Group Stage

About this project: After the USA was drawn into the "Group of death" (with Germany, Portgual, and Ghana), I wondered how many points it would take to get out of the group stage.

The way the group stage works is: four teams, each plays each other one time, wins are worth 3 points, draws are worth 1 point. The top two teams advance.

To simplify things I just assumed every game had an equal probability of drawing or either team winning. For tiebreakers, I assumed a uniform distribution of who gets to go on. So, without further adieu:

# points% to advance% advance without tiebreaker
00.00%0.00%
10.00%0.00%
21.23%0.00%
37.87%2.78%
454.32%25.93%
598.77%96.30%
697.53%92.59%
7100.00%100.00%
8--
9100.00%100.00%

graph of probabilty of advancing versus points

Observations:

Source files: