The "Mercenaries" map has a score system for tournaments needs. The score is calculated in the following way:

In the course of the game, player is rewarded points for completing (in some cases, advancing) quests. Usually 10-20 points. Great achievements like killing Master Phoenix or finding the Grail are rewarded more (30-50 points). 
Player also gets points (around 5) for visiting certain important places. 
After the game is completed, players is rewarded 2 points for each point of renown (maximum renown is 100) and 10 points for each hero level. 
Next, player gets reward for completing "challenges": 
- "Prodigal" - Never recieve "your money bug is full" message: +50 points 
- "True neutral"- Always keep alignment close to neutral (no more then 15% shift to either side is allowed): +150 
- "Homeless" - Complete the game without capturing the Fortress: +100 
- "Champion" - Be champion of Light or Darkness when the game is completed: +75 
- "Fallen from grace" - Gain AND lose BOTH holy and unholy auras: +100 
- "Secret operative" - Complete the game with less than 50 renown (extremely difficult, you can not complete ANY quests except for main line, and must avoid killing heroes, as they grant 1-3 points of renown, and must avoid leveling up, as each level up grants you 1 renown): +250 
Then player recieves a bonus if he completes the game within 300 days - 2 points for each day before day 300 (so, day 299 grants 2 points, day 298 - 4 points, day 250 - 100 points, etc). 
Finally, if played on hard difficulty, get 33% bonus to total score, and if played on hero difficulty, get 50% bonus to total score. 

After it's all computed (including difficulty modifiers), player gets a penalty of 1 point for each day after day 300. 

Minimum score is 1.