[stinkytaco]

This is maybe a better explanation:

https://jmanton.wordpress.com/2010/06/05/comments-on-james-s...

It's still math heavy, but there is some explanation. It's hard to explain without the math, since the math if fairly integral to it, that's why it's such an amazing discovery. My understanding is that it's saying that the variables are independent, but the measurement is not. So in the case of the athletes, it's not that home runs predicts touchdowns or goals, but that by using a Stein Estimation we would get a more accurate measure of all three in aggregate. The example used in the article is less interesting, but probably better for understanding:

For example, if i=1,...3 represents the financial cost of claims a multi-national insurance company will incur in the next year in three different countries, the company may be less concerned with estimating the values of the individual means accurately and more concerned with getting an accurate overall estimate.