I'm not sure if you're thinking of the same thing. Ransom and hostage-taking are treated as distinct topics within medieval historiography (ie. the study of history) and the words themselves are not synonyms in lay usage either. Hostages are, in the medieval period, typically taken to assure future good behaviour (more practically to punish bad behaviour) and a fairly frequent feature of high inter-state medieval politics (ie. at the end of a war). Ransom equally pragmatic but less: it's an alternative to being killed which relies on your personal reputation, both fiscal and moral, to be able to make good on the merciful deed. As I have not read Pinker, and thus I am not aware of his wider thesis on hostage-taking in Mesoamerica, I am rather unwilling to offer a comparative example especially where I do not think that the comparison is a good or balanced one. So I will give you what figures we can reliably put together for the number of dead at Agincourt, and explain the underlying mechanics of ransom and warfare in the early fifteenth-century.

That caveat aside let's get to the meat of the matter. Figures of the dead from Agincourt are obscured by the nature of the sources to hand. Thomas Walsingham gives a figure of 3069 knights or esquires who died on the French side, which he explicitly states does not include the 'common' people who would not have been counted by the heralds. Antonio Morosini, a Venetian writing to the city of Paris five days after the battle, quoted a figure of ten and twelve thousand (although he does not state whether this is including the 'common' folk and erroneously states that twenty-six named barons had been slain and another thirteenth had been taken prisoner). While the precise number of French dead is perhaps irrevocably lost the comparison with the English is stark. A reconstruction of the figures which does not include those who would later die from their wounds is, at a top end estimate, not likely much more than 112. Of these almost exactly two-thirds were archers. On the French side the dead were so numerous that even the heralds, who recorded only those entitled to bear coats-of-arms, simply couldn't keep up.

Agincourt is a good exemplar of medieval prisoner-taking and ransom and less so of hostage-taking. The chivalric ideal and its more seedy undercurrents were represented by the large numbers of noble prisoners taken which, in turn, endangered the smaller English force (c.10,000 including all ranks) once it looked like the tide of battle might turn against them. Henry V, supposedly upon hearing of a reinforcing French army, ordered the massacre of the French prisoners who had surrendered to his soldiers. Their throats were cut and the reinforcing army never arrived. Later historians and commentators have attempted to use the killings as a stick with which to bash Henry. None of his contemporaries did. It was a sad but understandable mistake and one which had conformed to the expectations of warfare in the period.

The French had fought under the Oriflamme it was a symbol that the traditions of chivalric culture would not be honoured by the French - ie. no prisoners would be taken - and was one of the many reasons why contemporary commentators did not condemn Henry V for the eventual massacre of the French prisoners. It should be noted that these prisoners would not be of 'low' birth anyway. At Agincourt the duke of Brabant, Antoine de Bourgogne, was killed while masquerading as a result of hiding his identity (probably with the intention of securing a lower price for ransom). Those who would not profit the captors would be killed or left for dead.

The chivalric class, which had extended beyond those dubbed as knights to include the loosely defined 'men-at-arms' by the fourteenth- and fifteenth-centuries, could expect a reciprocal extension of certain ideals and customs in warfare such as ransom - whereby an individual could surrender himself into the protection of his captor and either on license (ie. they were released for an agreed future fee) or held until a fee was agreed with their kin or lord (where the boundaries are more blurry with regard to hostage-taking). The origins of this system can be traced back to what is called the Frankish diaspora (essentially the spread of proto-French warrior aristocrats across Europe taking not only their military technology and customs but creating a massive web of interpersonal bonds which would remain in place even while fighting one another under various lords and rulers. In a period where blood feuds (or at least the spectre of such feuds) loomed large in the mind, the ability to not have to kill your opponent was valued highly. It made sense not to kill those whose kith (friends) and kin could feasibly retaliate. The rise and popularity of the tournament in the twelfth-century created not only a point where large numbers of similarly-minded individuals could test their prowess and win honour, but could test these principles and loyalty to their vows. Finally, and made most obvious by the tournament, was the economic incentive. Ransoms were far more valuable than dead nobles and knights (in most cases).

There was little or no such incentive to preserve the life of those who could not pay a ransom. The modern concept of the merciful knight has intruded from the historiographical conflation of the Peace of God movement and the Romanticisation of chivalry in the eighteenth- and nineteenth-centuries. Mercy was extended usually to your peers and the rest may as well go hang. We should never forget the economic incentive well captured by one contemporary French chronicler:

After this bloody battle, the king of England and the nobles of his army bought from their men, and also from working men and the lower folk, the most important lords of France so that they could put them to ransom and gain great sums of money. The English put to ransom all the others, even those who were lying on the ground amongst the dead and who were still breathing and givig sign of life.

Chronique de Religieu de Saint-Denys, ed. L.-F. Bellageut, 6 vols, Paris, 1839-52 (reprint Paris, 1994), v, p.568. Trans. Anne Curry, The Battle of Agincourt. Sources and Interpretations, (Woodbridge, 2000), p.108.

Agincourt is notorious because it supposedly contravened these ideals which the warrior aristocracy had placed upon themselves. This ire, like that directed towards Richard I after the massacre at Ayyadieh (1191), was not a contemporary one. In the context of the points mentioned above Henry's actions were completely understandable and justifiable (although Henry was not made to during his lifetime). Likewise many of the other battles of the Hundred Years War played out in similar circumstances, although this would be the last battle the French fought in the shadow of the Oriflamme. It is held up as a brutal battle because it was the nobility who suffered, as they had at Poitiers and Crecy in the fourteenth-century.

There are other aspects which I should probably expand upon but I'll have to leave it at this point for now. A final comment is that this entire system relied on trust. Trust that you could allow someone to return to their kith and kin and pay the agreed ransom and not seek immediate revenge. Trust that if someone gave you their word it could be respected. This cut both ways - if you were a notoriously faithless individual then good luck getting any person to take you prisoner when there were more profitable individuals to seize.

For more detailed examinations see:

Ambuhl, R., 'A fair share of the profits? The ransoms of Agincourt (1415)', Nottingham Medieval Studies, 50 (2006), pp.129-150.

Barker, J., Agincourt: Henry V and the Battle That Made England, (London and New York, 2005).

Taylor, C.D., Chivalry and the Ideals of Knighthood during The Hundred Years War in France, (Cambridge, 2013).