The S&P 500 Is the World’s Largest Momentum Strategy

>You would assume that half of all stocks would outperform a market index while the other half would underperform.

Why would you assume that? The probability space isn't even symmetrical. Stocks can't drop more than 100%. Not to mention that prices tend to grind upwards, but crash downwards, whereby mathematically the only way it works out is if you have a skewed distribution. Even the most naive investor would have a hard time justifying a "mean = median" assumption.