On a related side note, it's important to note that the difference equipment made on the battle field. Oftentimes, the "Champions" would have access to better equipment and armor, something that I have noticed isn't taken into account in the modern media and video games. Armor works, that's why they wore it.

Here is an interesting video on it, you may have seen it before: https://www.youtube.com/watch?v=5hlIUrd7d1Q&feature=youtu.be

Insert standard introduction saying that specific cases vary from century to century in different places

In my area of expertise, military doctrine dictated that mounted knights would charge at each other on one or both flanks while the infantry engaged. After one or more successive charges, whichever cavalry broke through first would proceed to encircle the enemy infantry from behind, which rather than engage in one-on-one duels like in Hollywood likes to show, resembled masses of soldiers shoving each other. The impact of big men on big horses on the rear of flank of a tight mass of people was more often than not more than enough to shatter the enemy's morale, and the vast majority of losses would be sustained when mounted cavalry mowed down fleeing enemies.

The most excellent example of this occurred on the 29th of May 1167, between Mount Porzio the castle of Tusculum. Emperor Barbarossa, descended into Italy for the fourth time to enforce his rule over the Italian communes (and possibly replace pesky Pope Alexander III), while engaged in the siege of Ancona sent Rainald of Dassel, Archbishop of Cologne, southwest to siege Civitavecchia with a small force of about 700 Brabantine mercenaries and 800 knights. Soon after, the mob of Rome, instigated by the Frangipani family, set out with a force of nearly 30'000 poorly armed citizens against the Theophylaci family, who's imperial-leaning tendencies had already forced them to flee Rome for the safety of their castle of Tusculum (Oddo Frangipani, having seen the chance to crush a rival family, seized it). Although he was outnumbered 20:1, Rainald of Dassel turned his army around and marched for Tusculum. Was he daft? Was he mad? No. He knew he had cavalry superiority. The ensuing battle saw what Sicard of Cremona called "The greatest army which Rome had sent into the field in centuries" engaged from the front by the Brabantines, while a detachment of cavalry quickly overcame the Roman cavalry and fell upon the rear. The Roman army soon routed as another wing of cavalry fell upon their right flank. Rainald chased them all the way back to Rome, where the Pope and Oddo Frangipani locked themselves inside the Colosseum (which was still intact and fortified at the time) while Rainald sent word to the Emperor that the city of Rome was his (the Counts of Tusculum, who catalyzed the victory, only delayed their continued slip into obscurity, never even returning to Rome).

So why were mounted knights so important? It has a little to do with Armor and weapons; a knight would come from a family that could afford good equipment, and most knights drew income from their land, allowing them to employ servants, attendants, and pack animals, meaning they would arrive on the battlefield rested. It also had to do with free time; a knight that draws income from rents doesn't need to work and has more time to devote to learning how to use a sword and lance. The impact of big men on big horses is also pretty frightening in and of itself.

Knights weren't always superior to infantry. In the Battle of Legnano which ended Barbarossa's fifth and final descent in Italy, the army of the united Lombard cities, knowing they had inferior cavalry but numeric superiority, dismounted and fought as Infantry. They were quickly surrounded, but were able to organize themselves into a compact round mass of spears (also called a schiltron), which successive cavalry charges were unable to break.

Sergeants could be interesting for you given your question. In a noble household, servants that were charged with defending their lord were called Sergeants, and would have access to better armor, training and weapons than your average conscript. However, in times of war, in most armies there were 7-12 conscripts for every two sergeants, who would be dispersed amongst the conscripts and shove against their shoulders in order to keep them standing compactly in a line (and making it more difficult for them to turn and run). Not exactly the noble heroes single-handedly turning the tide of battle that you'd expect.

edit:typos