Have you seen OTL? Without logistics and running into the heavily fortified and easily defensible terrain of East Prussia numbers of meaningless. See the East Prussian campaign of 1945 for instance. Plus in 1914 the Germans had a serious firepower advantage, forts, and FAR superior internal lines of communication, which allowed them a stunning strategic mobility the Russians fell victim to. When you read up how the campaign went in 1914 its pretty much impossible for the Russians to win unless they wait to mobilize, move very slowly, and get the 9th or 10th army mobilized to assist with an advance further west. In August/September 1914 you're not going to beat the German 8th army on home turf in East Prussia.
Von Prittwitz panicked over some skirmishes early on and was replaced for very good reason; still right before his was removed he regained his nerve and was coming up with the OTL Tannenberg plan. Still his phone call to von Moltke cost him his job for good reason, there was no reason whatsoever to abandon East Prussia, a moron could defend it very easily, especially given the logistics issues that the huge masses of Russian troops caused when your logistics branch wasn't yet mobilized. As it was in the East of East Prussia where Gumbinnen happened that was the only place where the Russians actually had suffiicient supply to fight and once the Germans pulled back they were out of supply effectively and could not move through the forts in the way, while 8th army redeployed against 2nd army.