Markets are not random (I've taken classes on advanced probability).
It would be more accurate to say some things are more or less difficult to predict. And some instrument combinations exhibit more or less empirical variance to modeled distributions.
This leads many participants to limit their participation. Risk controls also weigh into those decisions.
For example, many large trading firms will not take outright index exposure, instead trading the spot/forward or index spread due to the risks being substantially reduced. In the treasury market, the same thing happens where the biggest players are trading the deliverable/forward, roll/forward, and duration spreads.
Quants will talk about 'return distributions' and make useful assumptions about them. These assumptions are required for risk models and this in some ways contributes to the statements about markets being random. Also, the benefit of diversification assumes things about return distributions that could be construed as saying that markets are random.