The score is calculated by multiplying each player's medal count by their bracket contribution percentage and adding it to a total score. The alliance is divided into fifths with the top players contributing the most medals and the lower players contributing the least amount of medals.
 
For example: if I have an alliance with 5 members:
  • Amy: 2000 medals
  • Bobby: 1500 Medals
  • Chelle: 1000 Medals
  • David: 750 Medals
  • Eric: 500 Medals
The Alliance Score would be (2000 * 50%) + (1500 * 25%) + (1000 * 12%) + (750 * 10%) + (500 * 3%), or 1585.