If you want to do something that actually would help me, why don't you try to derive the formula for transforming LMSR prices into their LS-LMSR counterparts. They are both 0 and 1 at their extremes, and at uniform ( 50%-50% in the basic two State case) they are each multiplied by v (from the paper, alpha = v / (n log(n)) ). Last weekend I tried transformations for two hours, trying to cheat and grab it easily using statistics.

Later this week, I will resign myself to do the...algebra...