Do sharp arrow heads really matter?

Obviously sharp arrow heads cut better; but when they are shot at fabric armour does it really matter? I thought it didn't - Duh!?

Just as important what effect will sharp arrow heads have on the composite armour of gambeson (fabric) and (chain) maille in combination?

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Lockdown longbow film 1    • CRAZY idea... War bow archers - turn away now  
Lockdown longbow film 2    • Lockdown Longbow - Now I have WAR ARROWS!  

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"Do greased shafts penetrate deeper?"    • Does a greased shaft penetrate deeper?  
"Distance and speed loss"    • Shields; Distance and speed loss  

David Jones wrote two really useful and interesting papers on the subject here
https://www.academia.edu/5520314/Arro...
https://www.academia.edu/7691143/Arro...