As a quant myself, we don't try to predict the market, at least not the way that people normally talk about predicting, and we certainly don't move the market in our favor.
At least what my firm does, is we look at the current state of the market at any given time point, and test whether the current state of the market satisfies our model of an efficient market. If it does, then there's no action to take, if it doesn't then we determine what kind of violation is present and jump in to close the gap.
So a very trivial example would be to take two ETFs, like QQQ and TQQQ. As a simplification a model of an efficient market would have at any moment in the day the change in price of TQQQ = 3x the change in price of QQQ.
We then observe the actual state of the market and if the actual change in price of TQQQ matches our model, then there's nothing to do. If it doesn't, then either TQQQ is under priced or it's overpriced or QQQ is underpriced or it's overpriced (or our model is just wrong or some outlier). Depending out what the condition is we buy x dollars worth of TQQQ and sell 3x worth of QQQ or do the opposite.
There's no real prediction here, we simply have a model of what an efficient market looks like, we scan the market for violations of that model, and then we perform an action to bring the market back to an efficient state.
The model I presented above is incredibly simple and just for illustrative purposes, but in a nutshell, that's our job. We have literally hundreds of models for an efficient market and for every model we have algos that test whether the market satisfies our model, and when the market deviates from our model the algo produces a signal which other algos act.