In some ways polo is a whole different (metaphorical) ball game from a cavalry charge because it’s a (literal) ball game. The point of bumping is to get an advantageous position in relation to the ball and/or deny that position to opponents, whereas in a battle the object is to kill, disable or intimidate the enemy. I can’t see this kind of bumping giving the advantage claimed by the historians I’m arguing against. But polo is more analogous to the close combat that followed a charge if neither side ran away and they didn’t just pass through each other. The cavalry could spend some time fighting as individuals or small groups using swords and pistols, and I think John Keegan compared it to an aerial dogfight. In that situation pushing enemies out of the way with your horse can help to get you out of danger or into a good position to attack someone else. Contemporary descriptions of English Civil War combat do mention horses pushing against each other during the melee.

I played for five years in college, and slamming your horse into another horse is a necessary part of strategy. It’s not perfectly analogous, since, due to safety regulations, you are supposed to “bump” or “ride off” only laterally, meeting the other horse shoulder-to-shoulder while traveling in the same direction and at approximately equal angles and speeds.

Still, horses do run into each other, on accident or at the urging of their rider, in other configurations. This happens often enough that most of the rules of (intercollegiate, at least) polo are aimed at preventing “t-bone” type collisions, by stipulating that a player can’t cross in front of other players if it would be dangerous to do so. T-boning itself is a major foul.

I haven’t seen horses run into each other head-on, but that doesn’t mean it doesn’t happen.

For arena (indoor) polo, we also train horses to run directly towards the wall, pulling them up short and making sure they stay perpendicular to the wall as they halt. This is so they don’t duck out at the last minute and cause a collision with another horse moving towards the wall. The well-trained ponies would absolutely run straight into the wall if you didn’t pull them up (though it would also be a foul to let your horse do that in a game).

That being said, I’m not sure it negates your argument, as such collisions with the wall or non-legal collisions with other horses generally result in at least minor injuries to the horse, and the risk increases as the speed does. I just thought it might be worth looking into, in addition to racing and other horse collisions.

This isn’t the best video, but there are some cringe-worthy collisions here: http://www.youtube.com/watch?v=W7q5G_r_q7U&feature=related. See especially the one around 0:35, where one horse crashes into the hindquarters of another.

http://www.youtube.com/watch?v=5-p64RHqi38

With lances (both in jousting and combat) the speed and weight of the horse put the necessary force behind the lance, but the force was concentrated into a very small area by the point of the lance, which could put sufficient stress on enemy armour/bodies without being too dangerous to the man using the lance. Lances were designed to absorb some of the shock by bending and breaking – more so in jousting, but this also happened in battles. Pro and anti lance theorists in the 16th century both seem to have assumed that the lance would break in the first charge. I think that rather than maximizing the shock of impact, lancers would have to control their approach very carefully to get just the right amount of force behind the lance.

In the late 16th/early 17th century the heavy lance was abandoned. According to Clifford Rogers this was because improvements in metallurgy meant that plate armour could only be pierced by firearms. I assume that if lances could have been made to exert the necessary force (eg by increasing the speed of attack) it would have been too dangerous to the user.

In the English Civil War cavalry often charged into close combat with each other, but I haven’t found any evidence that this involved collisions of walls of horses, or that anyone at the time thought this was a good idea. When cavalry charged each other without lances in this and later periods, the usual outcomes were that one side would run away before contact was made, both sides would pass through each other, or they would stop and engage in hand to hand combat. It’s likely that with so many horses and so much stress there would have been some accidental collisions, but I can’t find direct evidence of them.

In the 18th and 19th centuries the theory of shock (ie crashing your horses into the enemy) was very widespread but there’s little reliable evidence of it happening in practice. I can say for certain that if it could be done it wouldn’t give any advantage, because Newton’s third law says that the force of a collision is equal for both bodies (calculating the magnitude of the force is surprisingly tricky but it’s always guaranteed to be equal on both sides). I suspect that the theory persisted because no-one could actually do a shock charge and therefore never found out what would happen if they did. I also suspect that the theory was based on some kind of folk memory of heavy lancers, but the weird thing is that it went underground in the 17th century.

Attacking the enemy at speed could have had the benefits of intimidating the enemy into running away, increasing the confidence of your own cavalry, and spending less time under enemy fire, but it’s not clear whether these were the real reasons for charges or just side effects of charges undertaken for other (spurious) reasons.

Cavalry vs infantry is a bit different. When infantry used pikes it was virtually impossible for cavalry to do anything to them. This led to Reiters using pistols, which were effective against unsupported pikemen, but the “caracole” tactic is often assumed (probably wrongly) to have been used against cavalry as well. After the pike was abandoned it was still difficult for cavalry to do anything to infantry, but it only took a collision of one horse to throw an infantry formation into confusion. Therefore we can’t rule out cavalry deciding to try and sacrifice one or two horses to break an infantry square, but this was still hard to achieve as horses don’t like running into things.

Which makes sense, at that speed a sudden swerve isn’t going to work well, especially if the track is at all wet.