Going to chime in here: 24 orcs absolutely does = 24 melee attacks per round, because opportunity attacks are Reactions, and you only get 1 per round. Capricia has already mentioned this, but it honestly can't be emphasised enough.
It makes putting your back up against a tree exactly the same as standing in an open field and thereby reduces the exercise to a pure numbers game. Once the Fighter has made his single swipe at a passing creature, any number of them can do a conga right line past him in complete safety. I hate it.
You're correct that I forgot that everyoe and his one-legged puppy has spring attack in 5e, but it's still not as dire as you think.
Anyway, let's do this. With 6 Ability Score Increases under his belt our Fighter can have stats of 20/20/18/13/11/9, so +6 Initiative (4 Dex/2 Remarkable Athlete) with 20 Str and 20 Con, making him statistically likely to win initiative against 18 of the Orcs. We'll have them start in move + attack range of each other, because if you game out a scenario where the two sides begin out of range it becomes a weird cold war of shufflestep spacing and readied actions. If there's a simple way I'm missing for the Fighter to gain advantage with a spaced start, though, I'm happy to look at this again in light of it.
Ok. So we're running with the worst case scenario of a baseline Champion, no feats, no multiclassing, and for some reason no magic weapons.
And we leave the static vacume of the white room and place this fight in the woods above the Rauros falls where Boromir fell.
And since everything else is going wrong we cut the poor guy some slack and start the fight at the optimal distance of 90', with no surprise. The warband of Orcs are marching in a column 4 abreast and 6 deep.
When they see Boromir they double move and use the Orc ability "Aggressive" to close the distance. The head head of the column is in contact with Boromir, the tail is still 30' away. Having triple moved they can't attack. Boromir Chops down the three within reach using his action surge and uses his move to retreat to the best cover he can find, a tree flanked by some shrubs. He is now 30' away from the remaining orc at the head of the column. The tail is 65' away. 21 Orcs, Boromir is at 169 hp.
The orcs use aggressive to move 30 feet closer. The lead orc attacks for 3.45 damage (I'm giving Boromir back his +1 AC Defense Style, we're screwing the guy hard enough without striping away class features.) He tries to move past to clear space for his White Hand buddies and Boromir cuts him down. The remaining 20 Orcs are now in a column 20' wide and 25' long, 10' away from Boromir. The center 2 use 5' of movement to step up and attack then move 25' to the side, avoiding the underbrush. The next two do the same thing, but can only move 20' to the side. The next column attacks and move aside. 9 Orcs have attacked and Boromir is now ringed in by Orcs 10' to 15' away. The remaining 12 Orcs now have to either end their turns next to Boromir or burn movement in difficult terrain, either the underbrush or their fellow orcs. The back rank of 4 can't get an attack in, as they have to burn 65' of movement as some of their buddies will be in the way. Probably we end up with an orc on either side of Boromir and a stack two deep and 3 wide facing him with an odd orc out.
So the Orcs pack 5 deep out to the sides and 3 deep in front.
(As an aside I would never run an encounter with Orcs this way. It's incredibly gamist. Kobolds, or Goblins maybe but Orcs are just too aggressive to use this sort of melee caracole.)
At any rate at the end of the second round 17 Orcs have attacked Boromir for about 58 damage. There are 20 Orcs left and Boromir has about 111 hp left.
During Round 3 the Orcs now have a problem. They need to operate in reverse order with the inside attacking and then moving out through the massed ranks. If you're using individual initiative it can't be done as 5e has no delay action and Readying an action doesn't cover it. By default however you don't use individual initiative for groups of similar creatures and the GM controls flow of action within groups. So the inside 7 orcs attack and move out. I'm not actually going to map it all out, with the aid of agressive, the Orcs can probably bring all of their numbers into one of the 7 spots surrounding Boromir during this rotating scrum. The attacks made from the sides however deal with partial cover. bringing his ac up to 21. So those attacks mean out to 2.25 damage. That's 6 of them, so total damage is 61.8 damage. Boromir uses his second wind and winds up with 64 hp. He also drops two Orcs with his 3 attacks and AoO.
Round 4 the Orcs will probably not drop Boromir. Slightly iffy, he certainly won't last past round 5. He kills another 4 orcs, about. Final tally 1 dead hero, 10 dead orcs.
Ok, it is pretty dire.
Hmm. Yep, that looks about right. Although the only reason the Orcs were so effective was a combination of a gamist combat style and more importantly an ability that allowed them to gain bonus movement. Without that, Boromir could have held them to a running battle where only the front ranks could actually get an attack in each round. Otherwise without the ability to charge the orcs more than 30' away would only be able to close and not attack. Each round Bormoir could simply attack the front rank dropping an Orc or two and retreat 30 feat, taking the AoO with glee. From the description in LotR this is about what Boromir actually did, until he got ganked by archers. Against an equal number of Guards Boromr would have won easily.
In a standard dungeon corridor held to a column two wide the caracole breaks down further, no more than 12 could possibly attack in a round. Boromir probably still loses, but he'll take a lot more with him.
Now with feats? GWF and Heavy Armour mastery would help a lot. GWM would drop an orc with every hit and he still hits 3/4 of the time, it also give him a bonus attack, lifting him up to a possible 5 kills a round, not incuding action surge. If Boromir had a magic weapon he would almost certainly drop an orc with every swing even without GWM. I'm too tired to try to game it out.
From this I conclude that Champions are hamstrung without access to the feat system, and level appropriate gear helps. Also that Orc aggressive trait is really dangerous.
