The
Shield is pretty much a piece of ubiquitous equipment for European warriors from prehistory until the 13th century. The Romans, Greeks, Vikings, Carolingians, Franks, Saxons, Celts, Dacians, Normans, Arabs, Assyrians, etc all have their close combat infantry armed with shields.
With historic sources shield penetration is kind of split between shields succeeding and shields failing. Generally it seems shields succeeded more than they failed. You look at 15th century art depicting the hundred years war for example showing troops with shields who have arrows half sticking through them with the soldiers behind them continuing to fight unharmed.
In the Viking sagas the consensus seems to be that a shield will parry an incoming arrow more often then not, for example here is a description of a battle between Archers and Spearmen in Anglo Saxon England.
'The Battle of Maldon' -
'And yet no warrior could injure another, except by the flight of a feathered arrow.'
'Bowstrings were busy, shield parried point.'
'The hostage helped them with all his might - his name was Æscferth, the son of Ecglaf; he came of a brave family in Northumbria. He did not flinch in the battle-play but shot his arrows as fast as he could. Sometimes he hit a shield, sometimes he pierced a man, again and again he inflicted wounds for as long as he could hold a bow in his hands.
And,
'just as the warlike bowman in the midst of battle is hemmed in by a dense formation of enemy legions, then, when his bow is tensed by his powerful hands and arms and arrows are drawn from the quiver,... the throng, swollen with the arrogance of pride, their shieldwall having been shattered, turn their backs and flee headlong.'
These can be found here,
http://www.regia.org/warfare/SaxonArchery.htm
on the other hand,
Njals saga,
Sigurd Hog-Head was in the lead, with a thin round shield in one hand and a hunting-spear in the other. Gunnar sighted him and shot an arrow at him; Sigurd raised his shield when he saw the arrow curving high, but the arrow went right through the shield, pierced his eye, and came out at the back of his neck”
Thinking about it I can remember two separate campaigns where a later medieval force went up against an older European force using what would be considered outdated equipment, knives javelins, and shields. One is covered in Froissart, which covers an English engagement against the Irish:
“The Irish had laid an ambush and when we came up to it they sprang out at us and began to hurl their javelins, while the archers on our side shot back at them. The Irish could not stand their fire, for their armour is very simple, and they retreated”.
I remember a later French that described Irish mercenaries as being equipped with javelins, long knives, and shields. Although no shields were mentioned in this account I would not discount the possibility that they were equipped with shields. I also have a vague memory of reading a description of the Teutonic Knights crossbowmen exchanging bolts with and driving off Slavic warriors armed with javalins and shields. There was also a story describing a man who armed the some Slavic peoples with crossbows and taught them how to use them in order to resist the Teutons. This is all just food for thought really.
Here is a complaint by Vegatus describing the vunerability of Roman soldiers without armour but with shields:
In consequence of this, our troops in their engagements with the Goths were often overwhelmed with their showers of arrows.
In any case, as far as history is concerned, sometimes arrows penetrated shields and sometimes they didn’t. It might be fun to see how angles effect shield penetration as this might explain some of the irregularity. There are 16th century sources for targeteers that recommend holding the shield out in a manner where the edge of the shield is pointing to the center of your opponent’s chest. I’m not saying that this was intended as a defense against missiles, just that it doesn’t look like many people held their shields straight out necessarily. Tilting the wood say 30 or 45 degrees off angle might (or might not) give interesting results. It should increase the actual thickness of the material when it is being penetrated and would lend towards more deflection as during penetration one half the arrow head will be hitting more material then the other.