[jason1990]

Interesting. I have no idea. But I see no reason to think that E|X|^4 would be more stable. In fact, a "naive" argument suggests it should be less stable. After all, SD is less stable than winrate from player to player, so perhaps stability decreases as we look at higher moments.

Also, I think it would be difficult to test the stability of E|X|^4. We would have to compare its "true" value for many different players. But to get a "true" value for any particular player, they would have to have a large personal database. So all we could really test is the stability of E|X|^4 among players with large databases. And my guess is that "large" here would mean something larger than the database of the typical player who would want to make use of this statistic.