ntaatgen
Posts: 52
Registered: February 2005

Are adventures balanced? Ask statistics!

Sat, 30 December 2006 06:31


Updated 1/1/2007
I posted the following balance analysis on the boardgamegeek, but thought it might be useful to post here as well:
Using the reported wins and loses on the Days of Wonder site, it is possible to calculate whether scenarios are likely to be balanced. What I did was use the binominal function to calculate the 95% confidence interval. That is, for each adventure I will give a range of percentages, and it there is a 95% probability that the true win percentage is in that range.
For example:
1. Agincourt: 85 wins out of 135 for the standard banners means that the 95% confidence interval is 55%71%. This means the true probability of winning for the French is somewhere in between 55%71%, with 5% probability that is is outside this range. This means that Agincourt is probably not fair, because 50% is not within the confidence interval.
Here are the others. The confidence interval is always the probability that the standard bearers win, and the numbers are based on the information on the DOW site on 1 January. I will make an update when the numbers increase at some point to improve the reliability (assuming people are interested).
2. First Chevauchee 39 out of 72, 43%65%
3. Burgos 25 out of 37, 51%80%
4. Deeper in Castille 16 out of 21, 55%89%
5. Wizards and Lore 14 out of 33, 27%59%
6. A complex web 22 out of 32, 51%82%
7. Crisis in Avignon 6 out 13, 23%71%
8. A Burgundian Chevauchee 4 out of 16, 10%49%
9. Free companies on war footing 9 out of 19, 27%68%
10. Assaulting the Tourelles 9 out of 14, 39%84%
As you can see, there are quite some adventures that are not balanced given the current reports. It is of course unlikely that the probability of winning is exact 50%, so hopefully the intervals can inform you how reasonable the odds are (and they will become more precise with more data).
[Updated on: Tue, 02 January 2007 02:15]

