Maille Construction in Renaissance
Europe
Another weakness of maille armor is its
vulnerability to thrusts from pointed weapons,
arrows, and crossbow bolts, which could easily split butted rings. Riveted rings of course
were significantly more resistant but could still be pierced if the projectile hit with
sufficient force. (Note: Modern day tests made by various reenactment groups have
demonstrated that a bow fired arrow will punch holes through maille constructed of
butted steel rings while maille made with riveted steel rings will resist the same arrow.)
This seems like an attempt at an accurate test and although the test is imperfect I hope you find it informative:
Conclusion: Good maille is very effective against arrows and is extremely difficult, if not impossible, to cut with a sword. However, it is no match for heavy polearms such as the poleaxe, and swords with very acute points can at the very least draw blood without much effort. A good thrust from such a sword can kill.
The part which begins with, "This part of the tests focuses on a combination of maille armor over a padded gambeson" has photos to show the difference between very good compared with mediocre riveted mail.
The "very effective", which he says is the conclusion, is relative: his best (for the arrows) test result was:
70lbs, 15 feet: 2 out of three arrows pierced the maille/gambeson and imbedded themselves in the pell. The third arrow broke two links but bounced off, stopped by the gambeson underneath.
Youtube videos may only be demonstrating the ineffectiveness of modern, butted mail.
In particular, Pratchett may have been wrong when he wrote, "a series of loosely connected holes". Instead it's a tightly-connected weave of riveted rings, supplemented by multi-layer cloth padding underneath and/or on top; apparently, cloth armour resists arrows:
Bow Against 10x Jack
I did not test the bow vs. the thicker jacks, because the 10 layer jack stopped the 70lb compound bow at 20 feet 3 out of 3 times. I believe that a sharp arrow such as a medieval broadhead (which would have no chance of defeating maille) would be able to penetrate a jack, but the arrows I had just bounced off.
[...]
Where the jack rally shines is against arrows. Even a 10 layer jack stopped my arrows cold, and I believe medieval bodkins wouldn’t fare any better. These tests have gone a long way towards convincing me that the jack was used primarily as a defense against arrows.