I wrote an answer at morning, but got erased. I'm going to sum it up.
First: Lance is a d12, one-handed weapon that needs a horse. I have a horse. Average damage 6.5.
Second: I have an 18 in Strength, so +4, and Dueling, so +2 (+6 to each attack). With multiattack, my base attacks are 25 damage.
Third: Shield Master grants you a shove as a bonus action. And that shove has +10 (Athletics expertise via Prodigy). A troll or large creature usually is on par with me on strenght, but I have expertise on Athletics (+6), "negating" their Advantage (not exactly, but I have a minimum of 12 on the Athletics check, and an average of 21, their average is 19 with advantage). Thus, I gain advantage on most attacks. That grants me a critical hit at least 1 every 5 rounds, or 0.65 damage on each attack on average. Almost like a Champion. So, my basic damage is 26.3 (extra attack, dueling, strength and lance)
Fourth: The lance has Reach property and the horse has 60 speed, and their action is usually spent on Dash, so I have lots of mobility. I end having a lot of OAs in minion fights. Requires a lot of position micromanagement, but it is very very useful. One trick is for the horse to Ready an Action to take the Dash whenever the enemies move.
Fifth: Maneuvers like Menacing Attack also frighten the creatures, besides giving me 4.5 extra damage. A frightened creature often runs away without disengaging. Another OA for 14.15 extra damage and disadvantage on ability checks and attacks for the enemy.
Sixth: Action Surge grants me 2 extra attacks once per short rest. Another 26.3 damage.
Seventh: Intelligence and terrain. Although I'm not shy to charge, we usually as a group prepare our battlefield or at least look for the most advantageous location and position. Shoving against stakes, caltrops, rocks, pits, cliffs, streams or fire grants you a lot of mileage. Also, I'm not compelled to spend resources where they aren't needed, thus avoiding overkills. At 6th level, we end fighting a lot of hobgoblins, orcs, yuan ti, etc. Against them I don't need to use all my resources. Furthermore, I end up killing a hobgoblin per strike with lots of mobility, or 2-3 per round without spending any resources. Micromanagement is key. We also fight trolls. Trolls are difficult to fight, but I Thoros of Myr my way against them with alchemic fire (I have a lot of swords and at least 3 lances on my horse to burn).
Final: I'm not hampered by cover, distance (120 feet per round on horseback, and 10 of reach is a lot), and prone enemies benefit me, whereas hamper a ranged creature. Also, OAs are a melee thing only.
Of course, I'm very much Short Rest dependant to have the "maximum" damage, but 26.3 damage is my average once my resources are depleted. And I tend to change horses a lot (they have a tendency to die). I'm not always on the best position (sometimes I have to use swords instead of lances, and very few times the creatures are two sizes larger than me). More than a few times I end brawling barefisted, but they are corner cases. The cat monk is also very useful and we have lots of synergy and mobility together (he pushes/pulls a lot with his Aang powers). But fights don't tend to last more than 5 rounds, and I have a lot of stopping power. Think about any nova that I make: I end making an average of 84.75 damage* in a single round (the first), and then 26.3. when my resources are spent. 111,05 damage in two rounds. Counting only 1 OA. At 6th level.
I'm not joking. I've sustained the math during gameplay, and that tend to be the numbers. The GM usually toss us very strong creatures, such as trolls with 18 AC, and I'm the only one that sustains damage and hits almost every attack. With advantage, I rarely fumble (yes, I know there is no fumbles in 5e, but you undestand: autofail with a 1). I preserve Inspiration to grant key advantage (for example, for shoves against large creatures). And I play it right (my character is alcoholic as its flaw, and I usually play that right, without exaggerating nor downplaying it: I tend to get drunk on guard duty, or behave very aggresively whenever I run out of wine, usually granting me disadvantage on a few checks).
*I'm not doubling the Superiority Dice, but I should, as I tend to use SD when I have a critical hit. So that would add 4.5 extra damage. Micromanage resources is key to a cunning fighter.