It multiplies each ball by the x amount! I apologize for forgetting to write the tooltip. In the below comment I talked about the plans for these upgrades, but they need a lot more design still. Thank you for playing to that point and getting as far as you did!
Also I really appreciate the positive feedback. I agree -- I know this game won't be for everyone, but we've tried a bunch of different things now, and this system with the tiered stages does feel like the best way forward for this particular game.
And I need that clean slate feeling too. We added the "hold to click" so that re-buying things wouldn't be so painful. And added the keeping money, that helped a lot XD