This is a lot of words to say a very simple thing: if you measure a stock picker's performance on a binary scale (did they outperform the market, yes or no?) th

This is a lot of words to say a very simple thing: if you measure a stock picker's performance on a binary scale (did they outperform the market, yes or no?) then you'll get different results from if you measured them on a scale that includes how much they under or outperformed the market by. It just so happens that for the stock market the former yields a result that makes the stock pickers look worse than the latter. The original paper, as far as I can tell, is saying nothing more brilliant than that for stock picking results, the median is lower than the mean. Hence, the "average" (aka median) stock picker underperforms an index (which is, after all, the mean).