Nope, nope, nope that's not how statistics works. Median != Mean

Also volatility matters, like a lot.

Median is obviously not mean. I never mentioned median anywhere. Where is the median of market return relevant here?

Yes, volatility matters and is why people generally prefer to get the lower volatility average market return. But that’s not very relevant to many peoples claims on here that SP500 outperforms most capital, which is obviously incorrect.

Not OP but I think the 50% of cases above or below only applies if you refer to the median (https://en.wikipedia.org/wiki/Median). If you refer to the average, or mean, the distribution could be different.

But I’ve never mentioned median. I’m stating that by definition, 50% of $ outperforms SP500. Sure that could be skewed, with a median underperforming, where in the extreme 1 participant has $20T outperforming and the other 1,000 collectively have $20T underperforming. But on average your $ has a 50/50 chance of under or over performing total market (and thus basically SP500) by throwing darts at a board.

But you mentioned average (mean). You can have the same average but different median, and only if you would talk about median it would be guaranteed that 50% of the cases are above and 50% under.

In the case you mentioned, with an average, there might be extreme outliers that make the average different from the median, thus rendering the assertion that 50% of the cases are above the average and 50% under false.

Thanks. I couldn't not bring myself to explain what a median is.

Which definition do you mean? SPX is a cap-weighted index, but that's very different from "50% of capital outperforms the index".

No point dropping such a useless comment without elaborating. This is effectively gatekeeping and I wouldn't be surprised if it's against HN guidelines