The real ranking factor is traits, not the band. A well-traited A-tier unit beats a poorly-traited S-tier one — reroll traits at the lobby's Upgrades facility before judging a unit.
SEndgame anchors — build around these
Sans (Mythical) Mettaton NEO (Secret) Asriel Undyne (Legendary Rare) Papyrus (Legendary Rare)
ALegendary Rare band — carries mid-game teams
Legendary Rare units generally F2P-reachable backbone of most accounts
BUltra Rare specialists worth keeping
Coverage / support Ultra Rares Economy units
CCommons & Rares — stepping stones
Starter units until first Rare+ pull

Why these five sit on top

UnitWhy
Sans (variants)Occupies the entire Mythical band — the highest summonable tier. Any pull here is an anchor.
Mettaton NEOSecret band — among the rarest obtainable units in the game.
AsrielNamed top-tier by community guides; absent from the wiki's older roster — newer addition.
Undyne / PapyrusLegendary Rare — the strongest band a free account can realistically reach.

Trait rolls — the actual endgame

12 traits, rolled at the lobby's Upgrades facility. These decide whether a unit performs.

TraitChanceEffect
Determination0.1% (1/1000)+50% damage, -25% attack cooldown
Kindness0.5% (1/200)-25% attack cooldown, +15% range
Perseverance0.7% (1/143)+20% range, +20% damage
Integrity1% (1/100)-25% deploy cost, -15% upgrade cost
Bravery1.5% (1/66)-30% attack cooldown, -5% range
Justice2% (1/50)+27.5% range, -2.5% damage
Patience3% (1/33)+25% damage, +10% cooldown
Boss Soul5% (1/20)+10% damage, -10% deploy cost — solid mid target
Royal Guard Soul15% (1/6)-5% attack cooldown
Monster / Ghost / Dog Soul30/25/20%Cost or range minor — early-game rolls

Roll priority: damage dealers first (they decide whether waves die), then economy units, then coverage. Don't burn rerolls on commons — save for a unit you're keeping.