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I think Chen Tang was referring to Western Han dynasty when he said one Chinese soldier can handle five non-Chinese soldiers, but during his time, he said because the non-Chinese states have learnt technologies from China, thus improved their fighting quality, but one Chinese soldier can still handle three non-Chinese soldiers.

Mobility is essential factor in winning steppe warfare. Wudi tried first to ambush the Xiongnu by luring them to border-town Mayi, but sense its a trap, Xiongnu horsemen simply run away. If one cant even catch up with the enemy, how could one actually fight them?

An example is the conquest of Kharazm by the Mongols. No doubt Chingizkhan was a brilliant leader, still, the Kharazmian had a fatal defensive measure which doomed them to destruction. They are said to have 300k standing army, but when the Mongols came the Kharazmian forces were scatterred to defend every Kharazmian cities. Elder Prince Jalandin actually suggested that Kharazm should gather up its force, since Mongols are coming far from the steppe, before they could get a rest from their long journey, use Kharazmian army's superior numbers to make a decisive fight.

But instead his suggestion was rejected by the Kharazmian Sha. This means Mongols could take out the Kharazmian cities one by one without the risk of confronting with a superior enemy force in numbers. Chingizkhan marssacred the defenders whoever had inflict heavy casuaties on his men was due to the fact the Mongols were less in numbers. Jalandin's judgement was right,its probably better than sitting there and waiting for the Mongols taking their cities out one by one.A similar strategy was also executed by the Jurchens at the battle of Yehuling, but due to unable generals they didnt co-ordinate well, and its disaster for the Jin.

The reason that Jalan din was rejected was due to court fight among the Kharazmians. The Queen mother to the Sha was of Qincha descend, many of the Kharazmian lords are also from Qincha, they didnt want to Jalandin, whos mother is of Turkic descend to be the heir, which could threatening Qincha nobilities power in Kharazm. Accepting Jalandin's suggestion would also mean granting him the authority to command entire Kharazmian military, and if hes victorious against the Mongols, he would definitely be ascended to the Kharazmian throne which Qincha nobles wouldnt like to see. So internal rivalries and treachery among Kharazmians contributed somewhat to their destruction.

Not surprisingly, the first serious nomadic invasion in Chinese history, when the Western Zhou capital was sacked by "barbarian" which ended the Western Zhou was also partly due to Zhou treacherous officials collaborating with the "barbarian" invaders. As was with the Southern Song, if the founder of Southern Song was not worried about any possible return of captured Northern Song monarchs by the Jurchens(perhaps like that of Ming emperor who was captured by the Mongols but eventually returned), he probably wouldnt had gave up central China so easily, no wonder LiQingZhao wrote  the famous literature to condemn the government's retreart to the South.

But if the central government is strong enough, even Xiongnu under Muodu which then was at its height could not conquer China.

Its interesting to think, that Muodu had the Chinese emperor Liubang and Chinese main force encircled, but rather than destroying them and enter China to establish his own regime like later the Wuhu("five barbarians") did, Muodu let them go.