I think Total War games look very consistent about archery casualty rates (at least the historical ones). They can be powerful, but are unlikely to heavily damage a heavy infantry unit by themselves. Historically (in the West, at least), missiles thrown by skirmishers were extremely effective against massed light infantry (you are likely to hit something soft), and very ineffective against heavy infantry (mostly if they had good armor and/or shields). However, massed archers, while rare, were really effective when employed in the Middle Ages.
I know nothing of Chinese military history, though.