Although champions that stack certain stats infinitely are obviously going to be powerful late game, they are not the strongest of all characters. Some champions have much higher effectiveness in the later stages of the game, since the infinite stackers have been built with glaring weaknesses that many champions can take advantage of. For example, ranged champions such as Veigar and Kindred have very low health and resistances, letting assassins kill them very easily. On the other hand, Nasus, Sion, Bard, and Thresh are kited and kept from being allowed to cause too much trouble from the enemy backline.
This leads to the question: Who is stronger than that? The immediate thought will be towards Vayne, the ultimate late-game hyper carry, with percent max health true damage (gosh, that feels dirty to even type). However, almost all of her damage is to be dealt one target at a time, leaving her vulnerable to be focused upon in teamfights. She has little survivability, compared to what damage she can be free to deal in a fight. This is why AD carries such as Jinx and Twitch are so strong; they can dish out damage to the entire enemy team at once, from a very long range away, Jinx's Lvl. 5 Q on Fishbones (cannon form) will have 700 range (750 with Rapidfire Cannon, 785 with Stormrazor and Rapidfire Cannon). Twitch's ultimate, Spray and Pray, gives him bonus attack damage and 300 bonus range, totalling him at 850 range (900 with Rapidfire Cannon, 915 with Stormrazor and Rapidfire Cannon). With Runaan's Hurricane, this damage can be dealt to the whole team from several light-years away, allowing them to have an enormous impact on fights.
For junglers, Master Yi and, surprisingly, Tryndamere being the only standouts, with Jax, Shyvana, Graves, Kayn doing quite well, but not of that nearly completely set-in-stone DUB that the two give. Master Yi can just obliterate the enemy team after he presses the R key on his keyboard. With the majority of crowd control in League of Legends being movement speed debuffs, Yi has the ability to negate all of that, and just run at the enemy. The only two ways to stop him are to have instant point-and-click crowd control, since he can outrun or dodge it otherwise, or to focus all damage on him. However, he can still dodge things such as Twisted Fate's gold card with his Q, Alpha-Strike, and continue to wreak havoc on the virginities of your 1900 HP Heimerdinger. For Tryndamere, the sample size is significantly smaller, but still reliable. His in-game play is very hard to stop, even with any crowd-control. He has a lot of survivability with his R, Undying Rage, which lets him be unable to die for the next 5 seconds, and can be cast under silences, polymorphs, stuns and suppressions. When securing objectives, this is crucial, since the enemy will try to kill or stop you from taking it, but the R means under no circumstances can you be bursted down.
For top laners, there is only Fiora. Although certain champions will beat her, and are not listed, that is because it is matchup-specific. Jax, Nasus, Yasuo and Kayle in the top lane pose considerable threats to her, but she is overall stronger, against more champions. Jax has one single leap on a relatively long cooldown, and if he gets punished by being knocked away or kited, there is no way he can deal any damage. Yasuo does flat damage with his critical strikes, which can be blocked by armour and health, and almost all of his playmaking comes from landing a crucial ultimate on high-priority targets. Kayle will shred a team, but her range is very short, and her ultimate, while providing survivability, lasts only 2 seconds. Fiora, like Vayne, deals percent max health true damage (2.5% of enemy max health + 4.5% per 100 bonusAD), but she is better for 2 reasons: First, it scales with attack damage, which means with runes like Gathering Storm, she can attain at least 18% per vital. Secondly, her build path, which can include items such as Sterak's Gage, Death's Dance, and Spear of Shojin, allow her survivability to surpass that of Vayne, since ADCs cannot buy Sterak's. Sterak's Gage gives a shield for up to 3.75 seconds equal to 75% bonus health, which start decaying after 0.75 seconds, and increased size and 30% bonus Tenacity for 8 seconds when triggered. She can survive almost any fight with the combination of these items, since Death's Dance will heal for incredible amounts for each Vital, Sterak's Gage will grant a shield and extra Tenacity, allowing her to negate the effects of most crowd control, and Spear of Shojin lowers all of her cooldowns (DESCRIPTION: After casting your ultimate, your next basic attack on-attack within 10 seconds grants AWAKENED DRAGON for 6 seconds (30 second cooldown). AWAKENED DRAGON: Gain 50% bonus attack speed, and basic attacks refund 20% of your remaining basic abilities cooldowns on-attack.). With this ability, she is able to use her W, Riposte, at least twice in a fight, and use her Q 20-40% quicker than already (At rank 5, with 40% cooldown reduction, her Q will have a cooldown of 1.92 seconds if it strikes a target. With the active Awakened Dragon, she can reduce this to between 1.5 and 1.15 seconds.) In a 1 vs 1 or 1 vs 2, maybe even a 1 vs 3 if lucky or if you have insane mechanics, you will almost certainly win.
For mid laners, there is also only 1 champ that separates themselves from the others. That champ is Kassadin. He is near unstoppable with pure items and time. Without any cooldown reduction, at level 16, Kassadin can use his ultimate, Riftwalk, every 2 seconds. However, his build usually gives him between 30 and 45% cooldown reduction, so it goes down to 1.6 – 1.1 seconds. For those unfamiliar with Riftwalk, it is basically a flash summoner spell with a slower cast time that deals damage. Here are the stats: (After a small delay, Kassadin blinks to the target location, dealing magic damage to all nearby enemies on arrival. Each subsequent Riftwalk within 15 seconds doubles its mana cost and increases its damage, stacking up to 4 times. COST: 50 / 100 / 200 / 400 / 800 MANA; 80 / 100 / 120 (+ 40% AP)(+ 2% maximum mana); BONUS DAMAGE PER STACK: 40 / 50 / 60 (+ 10% AP) (+ 1% maximum mana); MAXIMUM MAGIC DAMAGE: 240 / 300 / 360 (+ 80% AP)(+ 6% maximum mana)). Since Kassadin has around 3000 to 4000 mana at the last stages of the game, his fully stacked ultimate will be doing 720 damage at 3000 mana with 0 AP. His full build will have around 650 AP, and with 3500 mana, a single uncharged ultimate will be dealing 450 damage every 1.2 seconds. However, this stacks. Therefore, he will deal (120+650*0.4)+(3500*0.02)+(360+650*0.8)+(3500*0.06) damage at full stacks. Since his build will always include Seraph's Embrace, which refunds 25% of his mana spent, he will only use 600 mana per R at full stacks, and his W refunds 8% of his mana, he can use his full charged ultimate at least 6 times in a fight. This is without the consideration of the passive of his other core item, Rod of Ages, which refunds 15% of the damage taken as mana. Long story short, he can deal over a thousand damage nearly every second in an area of effect, with a long cast flash in the same ability. Vladimir has very good teamfighting potential as well, as he is able to one-shot an entire team with a full combo. However, he lacks mobility and utility, so is just slightly below the level of Kassadin. He is, aside from Lissandra, probably the best teamfighting mage in the game considering all stages of time.
Lastly, for supports. Taric, and Sona are probably the best late game champions in any of the roles, with the exception of Kassadin. The end of the game is almost exclusively decided by teamfights, which these two champions excel at. They provide massive teamwide utility that has next to no chance of going wrong. Unlike Janna, Lulu, or Alistar, who can disrupt the carries' fighting, these two are completely devoted to helping their team. With huge ultimates, the two can provide eternities of protection for no cost in fights. Although, almost all supports are crucial in the last minutes of the game (no support champion has less than 53% winrate at 6 items). There are two ways to teamfight against these two. 1: Don't fight. 2. Lose the fight.
TL;DR: Infinite stacking champions have large weaknesses that prevent them from taking over games. Vayne does huge damage, but not efficiently, and can be bursted for it. Jinx and Twitch can deal slightly less single target damage, but make up for it by their range and AoE damage. Late-game junglers are strong because they cannot be stopped for objectives and fights; Master Yi and Tryndamere are the best. Fiora's scaling means she can outduel almost everyone in the game, and win 1 vs 2 on a basis that is more on her favour, Her build also gives her great survivability and synergy, so even though other champions can utilize this, Fiora just does more damage, and has more mobility. The few top lane champions that beat her are still relatively worse, with larger overall weaknesses. Kassadin has a 1 second flash that does 1000 damage. Vladimir is good too. Taric and Sona provide the best teamfighting in the game, and do not disrupt the damage of the carries, unlike other supports like Alistar, Lulu, or Janna.
Still TL;DR: Stacking champs have weaknesses. Vayne does not do AoE damage and has no range. Jinx and Twitch have range and AoE. Yi is Yi and Tryndamere has great fighting and objective control. Fiora scales with true damage and can survive well. Kassadin exists. Taric and Sona are good at teamfights.
All of this information is backed up by multiple stats pages. If there are blaring holes in this that I missed, please let me know, I will fix it as soon as possible. (I spent 5 hours on this xD) ALL OF THIS IS ASSUMING THAT THE GAME HAS ALREADY REACHED 40+ MINUTES.
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