I'm reading Subramanian et. al's (2005) original GSEA [paper][1]. In the paper, the authors mention the following:

> We noticed that the use of
> weighted steps could cause the distribution of observed ES scores to
> be asymmetric in cases where many more genes are correlated with one
> of the two phenotypes. We therefore estimate the significance levels
> by considering separately the positively and negatively scoring gene
> sets

I understand what they're saying, but I simply don't understand why it's a problem. Basically, they're saying that in some cases, most genes in the list we're testing could appear mostly at the top or bottom of the list. But I don't understand why having asymmetric distributions is a problem. What is the issue here? 

EDIT: Here are some example GSEA plots I found via a web search with such gene sets. Where is the problem?
[![enter image description here][2]][2]

One thing I don't get though is why this problem would be introduced through "weighting" of the steps. I feel like it would also be a problem without weighting. The way it is phrased in the paper seems to suggest that it's the weighting that causes an issue.


  [1]: https://www.pnas.org/doi/10.1073/pnas.0506580102
  [2]: https://i.sstatic.net/qJdzT.jpg