During the HYW it was two-thirds. The ratio became 2:1 during the Wars of the Roses as the pool of trained archers got smaller because of casualities.

halberds in particular seem to have been the weapon of choice in close combat in the War of the Roses, for example.
The halberd was primarily a continental weapon. Standard infantry used billhooks, while men-at-arms tended to use pollaxes.
Maces were often considered the best weapons to use in a melee because they were very quick compared to axes. Since they reallied on blunt force they didnt need to pierce armor at all but could still easily break the bones benieth the armor.
Most maces had flanges (those pointed metal strips) along their sides or spikes allowing them to pierce armour. More easily used than a warhammer as it doesn't matter that much what the orientation of the mace is because it had quite a few of those pointy bits.
And how did halberdiers, two-handed swordsmen, and other non-spear infantry fit into the real-life equation of medieval armies?
Halberds/bills/pollaxes are multi-purpose spears. They can be used in a stab attack but also for slash, pierce, blunt (pollaxe) and grappling (halberd/bill) attacks. They were superior to spears when armour gave the soldier enough protection to be able to dismiss the cumbersome shield.