In the Battle of Pharsalus, Caesar's infantry won by throwing their spears at the horsemen's faces.
So how come in Battle of Zama and many other battles, including the battle where Khalid ibn al-Walid captured Syria from Byzantine the infantry didn't just use the same tactic?
Also what advantage does being mounted carry against infantry? You can thrust lances? That's all?
As Wladimir noted, the precise "vs" analysis is impossible since it depends heavily on what kind of armor, weapons, tactics, training and commanders both infantry and cavalry have, as well as economics of society (which heavily influences these things for the cavalry which is a lot more expensive to equip/train, especially heavy cavalry).
Also, it's difficult to discuss "cavalry" in general - light vs. heavy was two different beasts tactically. I will try to give some general advantages below, with the understanding that a LOT of those can and have been negated by the infantry with proper responses in tactics/weapons, or heck, a whole lot more infantry.
"Also what advantage does being mounted carry against infantry?"
Advantages are:
Strategic advantage: marching speed.
Logistics
Horse mounted warrior has greater carrying capacity, reducing the requirement for logistics train.
In certain climates, horses can be used for environmental protection (barrier against sand/snow storm, warmth).
Horses can be used as food if worse comes to worst. Mongols again (drinking horse milk, drinking horse blood, or worse to worst, eating a horse)
Higher position of the fighter
Allows you to thrust down (stronger hit, steadier position since you can lean forward during the hit).
Your opponent needs to raise weapon/shield higher to parry - tires their arms
Carrying capacity of the mount in combat
Allows you to carry heavier weapon (e.g. lance) - this adds to next advantage (mass), and is an advantage on its own since a heavier weapon can be made sturdier/better.
Allows to carry longer weapon, increasing your range.
Allows to carry heavier/stronger armor. See anything from Persian heavy cavalry of the late Roman empire time to mounted knights in medieval times.
Allows to carry MORE weapons. Both different ones (lance, sword, bow/arrows, whatnot, later on firearms); and replacement throwing ones (e.g. 10 javelins), more arrows.
Greater mass of the attacker (horse+rider+armor+weapons).
This increases both your momentum, and kinetic energy (see below).
General psychological advantage. People can be scared if massive things gallop at you.
Speed. This allows you to:
Put more kinetic energy into your weapon attack (extra bonus from earlier mentioned extra mass).
This applies both to handheld weapons, AND especially range weapons (e.g. javelins) since those don't have the drawback of Newton's 3rd law of motion from your own strike, nor added risk of hitting opponents' pike/sword harder.
Use the horse as weapon. Galloping horse/rider can simply trample you, or horse can hoof you. Heck, simply being hit by a horse is a Bad Thing.
Use the horse to physically break the lines of the opponent due to momentum.
Extra tactical maneuverability (see below)
Tactical maneuverability.
Allows to attack from any direction you choose, before infantry formation can re-form. Flank and rear attacks.
Get quickly within range of ranged weapon then get out before they can shoot back. See battle of Carrhae or Mongols.
Once slower-reloading firearms appeared, a variation on the last was 16th century caracole tactics (in this case the advantage is that you get in range, shoot, and get away to reload your wheellock).
Quickly get in range of attack on slow firing artillery (best example would be Gustavus Adolphus at Breitenfield).
Pursue the enemy in case of victory and to escape enemy in case of defeat. Defeated cavalry has a chance to escape the battlefield and later regroup. Defeated infantry (if the winner has cavalry) will be caught and captured/slaughtered.
There are no magic recipes to win a war. Caesar's tactic was new and surprising, it demoralized the attackers who were certain of their superiority. But this only works once - once that tactic was known it was no longer effective. Note that this wasn't the only reason that Pompey got defeated, it is probably even more important that Pompey's behavior was passive, he essentially gave up the initiative in this battle to Caesar.
The general question amounts to "which is stronger, cavalry or infantry?" This question makes little sense - as usually, it depends on a number of factors (tactics, unit numbers, positions etc.). Cavalry is faster than infantry but typically limited in numbers, it is very strong in an attack but useless in a defense. So all armies used both infantry and cavalry and the success of the battle largely depended of whether the advantages of both could be used in an optimal way.
The infantry-cavalry balance has changed a lot over time. And back and forth.
In primitive warfare, the addition of a large animal gave the advantage to the cavalry. This changed during the times of the Greeks and Romans, who invented the phalanx and legion INFANTRY formations that had no cavalry counterparts.
By "stabilizing" riders in horses, the invention of the stirrup (fourth century A.D.) gave the advantage (using hand weapons) back to cavalry, which could now quickly form into large, heavy armored formations that even Roman infantry couldn't counter. It wasn't until the wide use of missile weapons (long bow, muskets, early rifles) that infantry could again fight on more or less equal terms again. The invention of "repeating" weapons put the advantage back decisively in favor of infantry (a cavalryman would manage a horse and a lance, but not a horse and a rifle simultaneously).
Even when infantry (mostly) had the advantage, cavalry had the advantage of speed and position. U.S. civil war generals considered cavalry mostly a form of "transportation," and often fought dismounted, with one man out of four holding horses for three other men. This was a disadvantage that sometimes, but not always outweighed the advantage of greater speed.
Cavalry could also get behind infantry, thereby fighting at an advantage. This was the case at Zama, where the cavalry won. On the other hand, the (Roman) infantry at Pharsalus was facing a FRONTAL cavalry attack--at a time when infantry had the advantage in such situations.
Even after the invention of the stirrup, which gave cavalry a shock power it had not had before, and before the invention of gunpowder, infantry in phalanx could sometimes defeat heavy cavalry on favorable ground or other conditions. Examples are the Flemish infantry in the battle of Coutrai and the Scottish schiltron developed by Wallace and used to devastating effect by Robert the Bruce. The most outstanding example of medieval infantry superiority, however, was that of the Swiss halberdiers, who dominated the battlefield against their Austrian and Burgundian enemies for nearly 200 years.
In Battle of Zama Hannibal had the army of greenhorns. Veterans were dead already. It needs a great amount of previous experience to stand against a horse that is galloping against you and even to throw something at the rider. BTW, in that battle, cavalry acted rather as a lock, as in Cannes on the Carthago side.
It would be difficult to throw a Macedonian sarissa somewhere. :-)
All arguments of DWK are interesting. But there is no need in many arguments. We need only one, the key one. Times change. In different times different reasons were the key one. Often the key reason in wars were against the cavalry. Infantry is more stable. You can never train horses as you can train people, and even the most trained horse could be easily frightened. It is almost impossible to make the horse go against sharp points or against something that looks like a wall. Or, on the contrary, to stop a horse in time then a pit if ahead.
Logistics arguments are good, but they work no for cavalry only, but also for infantry, transported by horses and fighting on foot. (dragoons)
The answer is - different classes participate in cavalry and in infantry. They have different reasons to fight, different experience, different quality of arms and armor and everything changes according to the concrete situation. Times change. 100 years ago mass armies won. Now the prof army wins.
By the time of the Napoleonic wars the odds seem to be on the side of the infantry and their rifles.
Although cavalry were effective against a marching column and were lethal against a retreating army, once the infantry could form squares on a battlefield they were pretty much safe. IIRC none of the British squares at waterloo were penetrated by French cavalry and concentrated organised rifle fire from a square could stop a cavalry charge.
When you consider transporting and feeding a horse in a campaign they probably cost the equivalent of a squad of a dozen infantry so overall probably a net loss
it is hard to categorise specific units as better than others. As for the diagram above, the general consensus was that heavy infantry had an advantage over light infantry (if they could close the distance)
Warfare isn't rock paper scissors where light cavalry always dominates heavy infantry, or heavy cavalry always decimates light infantry. In fact you can find historical examples of any type of cavalry defeating any type of infantry and vice versa.
The Romans (often considered to have a military disadvantage to the mobile Parthian cavalry) repeatedly dominated the battlefield against Persian mounted archers. likewise the french foot archers scored crushing defeats against french knightly cavalry. many battles, even in antiquity (when infantry was considered superior) were decided by fateful cavalry manoeuvres.
it is also important to note that the stirrup wasn't some grand design that made cavalry unstoppable. i can guarantee you if medieval heavy cavalry charged a Macedonian phalanx they would be torn apart. One massive reason for the rise of cavalry was the decline of infantry. The Roman legions were softened through the years and longer unstoppable. Likewise Persian cataracts proved just how decisive a heavy cavalry charge could prove. But even the mighty Sassanids were repeatedly defeated by Roman infantry. even in the middle ages where cavalry was considered superior it had many useless applications. Cavalry was never suited for rough terrain quite like disciplined infantry was. (this is part of the reasons the Romans were so successful against their Parthian rivals...excluding Carrhae) Another thing cavalry was terrible at was taking fortifications. Even the mongols had their difficulties until supported by Chinese allied infantry. any one dimensional army, even one of mounted archers, is effectively doomed. there is no single correct approach to warfare and the best way to approach war is with a combined arms military composition to achieve total battlefield success. This involves exploiting an enemies weakness with one tactic to make it vulnerable to another. The Byzantines were masters at this type of warfare, surviving for over 800 years.
Hope this helps.
See combat diagram here: Combat Diagram From The Art Of War In The Western World by Archer Jones
