The 'classic' defense against archers in every western army from Classical Greece to Medieval spearmen, great swordsmen and mounted knights, was to charge them. If they stood fast, they got massacred by more heavily-armed and armored enemies, if they ran away they usually kept running and never came back. T his in a nutshell is why missile troops on foot were never a battle-winning force in European warfare until gunpowder. The "English Longbow" was actually a military system, not just a weapon, and despite winning three great battles they still lost the 100 Years War: if they didn't have stakes in front of them and dismounted knights beside them, they had to run just like every oher European archer when charged by mounted troops.
The crossbow was invented in China some time in the 6th century BCE, and in Syracuse, Sicily in 400 BCE. It became the primary weapon of a large part of every Chinese infantry force; it was virtually ignored by every field army in Europe until 1500 years later.
What was the difference?
In China they also developed Volley Firing by Rank: in which a deep formation of 8 - 10 ranks of crossbows would fire the first rank, that rank would file to the rear, the next rank would fire and file back, etc. The first rank would be reloaded before the last rank fired, so they could keep up continuous heavy fire as long as the ammunition held out. In Europe, Volley Fire was not invented until it was applied to muskets at the end of the 16th century CE (By which time the Chinese, Japanese and probably the Koreans had already adopted volley firing for their own handguns).
That meant, simply, that Chinese massed crossbows could potentially stop an infantry charge with massed firepower, while no European force could mass enough fire to do the same.
That also meant, by the way, that the first handguns in Europe were 'Hook Guns' or Hackbusse, designed to be braced against the parapet of a fortification and fired in defense - from the top of a nice stone wall where the tar get could not get to you with any kind of charge. It was only a century or so later that Arquebusses ventured onto the battlefield, and then quickly protect ed by blocks of pikes, halberds, swordsmen and other heavily-armed melee troops.
So, realistically, it takes special training, organization and technique to allow muscle-powered missile troops to remain on the battlefield for any length of time. That's no fun at all for the gamer who just spent X turns producing Archers, Slingers, and their ilk only to see them run for their lives after one shot.
So, forget about 'Historical Accuracy' in this instance. To keep archers from being almost completely useless outside of fortifications, they have to be given excessive effect and the ability to be protected by other units in front of them. The only difference I suggest would be to reduce their normal Melee factors to keep them honest: archers hit by regular melee troops with melee weapons (spears, swords, shields) have almost always turned into disappearing runners or Speed Bumps, and that should still be true in the game.