"**Indexing beat half of all invested dollars in the past, I do not expect mathematical laws to change**, so I expect it to beat half of all invested dollars in the future."

Apparently the laws of math did change over just the past few days:

Maybe you want to restate that? **By definition, the average will perform worse than half of all invested dollars and better than half of all invested dollars.**

**Incorrect. You forgot to take into account the dollars also in the index :-P**

To make this easier to visualize, imagine 98% of all invested dollars are in the index with me, with 1% beating it and 1% losing to it. According to your definition I will have performed worse than half of all invested dollars, when in fact I would only have been worse than 1% of all invested dollars.

Oh well...

Yes, the correct statement should have been:

"Indexing beat or matched half of all invested dollars in the past, I do not expect mathematical laws to change, so I expect it to beat or match half of all invested dollars in the future."

Thanks for catching that!