CrocoLiga

[berni]

3) Or change the formula, so the median solver gets [the median-rating of the contestants] instead of 1500.

This is an interesting idea. I've done some statistics and calculated the median rating of all participants in the Ü1 over the time. The result was, that this median is somewhat below 1500. This is due to newcomers. So I changed the formula slightly and used for median only participants with more than 300 entries. The result can be seen below:



As one can see: Since middle of 2011 the median is quite stable at 1500.

For comparison the median of the CrocoLiga:

Code:

day 1     day 2     day 3
1 1360.9    1783.07   1793.525
2 1674.76   1872.125  1818.455
3 1652.81   1693.4    1792.685
4 1615.02   1649.95   1679.15
5 1718.19   1735.37   1704.85
6 1716.37   1669.3    1614.96
7 1895.595  1637.915  1750.27
8 1659.28   1637.55   1679.15
9 1852.895  1680.17   1815.9
10 1659.885  1521.19   1624.05
11 1651.58   1693.4    1671.16
12 1757.3    1880.17   1888.49

With one exception the value is clearly above 1500. This proves at least your conjecture.