I have been playing a Fighter with the Battle Master archetype (PHB, p. 73-74), and most of my companions in my party are new to the game. I was trying to play a supportive-type character, even if I'm playing a Fighter – I'm mostly shoving people so they can attack with advantage and playing with the Polearm Master feat (and the Sentinel feat in the future) so I can zone out monsters and protect our Sorcerer and Rogue that don't know how to position very well.
Our DM chose to not allow sources other than the PHB for characters.
With Battle Master, I intend to get the Trip Attack, Precision Attack, and possibly Commander's Strike maneuvers so I can keep being supportive and making them feel useful.
Commander's Strike says:
When you take the Attack action on your turn, you can forgo one of your attacks and use a bonus action to direct one of your companions to strike. When you do so, choose a friendly creature who can see or hear you and expend one superiority die. That creature can immediately use its reaction to make one weapon attack, adding the superiority die to the attack’s damage roll.
Action economy wise, Commander's Strike seems to suck. Mainly when I am the person hitting the hardest in the party. At 4th level with Great Weapon Fighting, a Glaive, and Polearm Master (even if I go for 18 STR instead of Great Weapon Master), I would be doing more damage with a Glaive Attack + Polearm Master + Trip Attack than if I used Commander's Strike and allowed our Ranger to attack with Hunter's Mark and Colossus Slayer or allowed our Rogue to attack with Sneak Attack. Besides, with Trip Attack I can actually choose to use the Superiority Dice only after I hit, and it doesn't spend my ally's reaction.
When is Commander's Strike worth it? Are there actual scenarios where a considerably optimized Fighter would choose to forego one of his attacks and a bonus action so an ally can attack? I will probably still be using it just to make them feel good about doing 3d8 + 1d6 + 3 damage at 3rd level, but I would like to use it knowing it's actually my best choice.
Our party is currently going to 3rd level, we are playing Princes of the Apocalypse. There are lots of people, the composition is: Tiefling Sorcerer, Human Dual-Wielder Ranger, (Some-kind-of) Elf Rogue, Dragonborn Paladin, Half-Elf Warlock, Dwarf Cleric, (No-Idea-What-Race) Monk and me, Human Fighter.
The Rogue has a +1 Longbow, which I forgot to include in my math, whoops. The Ranger is dual-wielding two Rapiers (and has the Dual Wielder feat).
When another's attack would do more damage/be more impactful than yours.
Not going to lie: I don't feel like going through your party and doing the math, but suffice it to say that there are times--even when playing a Great Weapon Master--that someone else's attack is expected to do more damage. Like when you can direct your Sharpshooting ranger to take a shot at the dragon overhead that you can't reach. Or when your L15 rogue is doing 8d6 or so on a hit.
I recently played a Battlemaster in a L18/19 party--being able to forego 1 of 3 attacks to give the rogue a sneak attack for 10d6 was pretty nice. (Especially when my first attack had been a Distracting one to ~double the rogue's chance of critting and doubling those dice!)
At low level, though, you're right: your attacks are generally going to have more "OOMPH" to them; delegating one to another party member is likely to be a strategic move: interrupt a caster's concentration when you can't reach them, an ally has a time-limited buff, you have disadvantage from being blinded, &c.
TL;DR: Commander's Strike gives you, as an option to replace any one of your attacks with any one of your allies' attacks. Options=power. The cost of that option is a bonus action and the opportunity cost of choosing Commander's Strike over another maneuver. I've generally found it worthwhile as a 4th or 5th maneuver pickup.