We ("we" being u/FlavivsAetivs and u/zeeblecroid and I) discussed the lethality of arrow wounds in https://www.reddit.com/r/AskHistorians/comments/9r1oed/how_were_archers_used_in_ancient_and_medieval/

A crude summary is that if the arrow penetrates the thoracic or abdominal cavity, or penetrates the skull, you will die, either immediately or later from infection, and if the arrow hits an arm or leg, and you don't die of loss of blood from a major artery being hit, you will probably survive (19th century rates of death from infection for such wounds were 5-10%),