Does nasus outscale jax and poppy?

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Sion gains free tankiness and thus can build full damage. Crit outscales Nasus's Q until something crazy like 1500 stacks or so. Also, thanks to his ult and Q, Sion can get free hits on Nasus while Nasus can do nothing to get free hits on Sion.

A 1000 stack Nasus loses to a 500 CS Sion with as items.

Assuming every 2 waves has a cannon minion (because canons spawn more frequently as a game goes on, capping at every wave). That means every 12 CS we add 1 CS and a big minion. This comes out to 38 double waves and 5 extra CS (around). So 461 small minions, 39 large. This gives Sion 1312 bonus health and Nasus 1617 stacks.

Assuming Nasus builds tanky he will have 303 armor, 135 magic resistance, and 3781 health (increased to 4381 during ult). Because of Last Whisper, his armor is an effective 197; if hit directly by E, his armor is effectively 158 for 2.5 seconds. To go with this, Nasus's AD is 152 (base 122) and Trinity will add 244 damage. A Nasus Q then will do 2123 damage (1617 base, 152 his AD, 244 Trinity, 110 base damage on Q) base, his E will do 233 damage summon (and then 46.6 damage a second while inside; reduces armor by 40 additionally), and his R will do 5.3% enemy max hp a second (max 240). Additionally, 6.25% of all damage his ult does is converted into bonus AD for the duration (shitty tooltips ho!).

Now for Sion. Defence first; 147 armor, 89.5 magic resistance, and 3669 health. 132 base AD, 225 bonus, 357 total. 55% critical strike chance, 90% bonus AS for a total AS of 1.449 AS. After Frozen Heart this is 1.232 AS. After Randuin's (so one attack) this is 1.047 AS. Also, Sion has 8% current health on hit, 10% max health damage (physical; once) and 10% lifesteal. For damage, his Q does 314.2-942.6 damage, W does 140 (+14% max hp; either 529.34 or 613.34 damage depending on Nasus ult), E does 210, and R does 540-1080 damage.

So, let's begin. Starting with a max distance Sion R for 1080 damage, 1.138 seconds stun. Assuming he activated W early, he can bomb it now for 669 damage. Let's also assume he E'd right after landing and then started charging Q; he has .862 seconds while charging Q in which Nasus can retaliate. During this time Nasus will EWRQ, for 233 damage, 5.3% max hp a second, and a 2123 damage Q. After this quick exchange, Sion finishes Q (942.6 damage) and stuns Nasus for 1.463 seconds.

Damage wise, Sion ult does 364 damage, W does 285 damage, E does 89, and Q does 365 damage. Nasus (after ulting) has 3278/4381 health left. Damage wise, Nasus E does 147 damage (one tick second damage), R does 102 damage (and provides Nasus 6 bonus AD), and Q does 1029 damage. Sion has 2391/3669 health remaining, and Nasus lifesteals for 20% of Q's damage, moving him to 3525/4381 health.

Second part. Sion uses his QSS cleanse for Wither. He has effectively one attack a second right now, with each attack doing an average (yes I know it's technically spikes, but I can use crit as an average you do x% more damage so I am) 182.5% damage, or 652 damage. BotRK will add 279 damage at Nasus's current health. Let's assume 5 autoattacks from Sion during this time. For Nasus, he still has his ER up, but let's go ahead and say after one more tick Sion leaves the E. During this time he gets one more tick of ER, 4 more ticks of R, and an autoattack, Q, autoattack autoattack Q (so a normal Nasus damage amount). Additionally, Sion's E wears off after one autoattack.

Damage wise, Sion does 361 (heals 36 health), is autoattack by Nasus for 62 (heals 12); Nasus's E+R deals 25 + 102 damage (+12 bonus AD on Nasus now). Sion 2238/3669, Nasus 3176/4381. Next, Sion does 304 (heals 30), Nasus does 864 (heals 207), R does 102 (+18 bonus AD on Nasus now). Sion 1302/3669, Nasus 3038/4381.

Need I go on? Yes, I know this isn't "1000 stack Nasus". I also know you aren't getting 500 CS in a game as Sion and cheating literally over 500 stacks from Nasus for this. Even at 1000 stacks (cutting Q after armor to 610 damage) Nasus would win easily. Nasus can afford to build tanky and do massive damage; his damage is not capped while Sion's is. Sure, Sion can build damage; but he's limited to a set DPS he cannot surpass, and if he goes for that DPS he stays as a massive health but still squishy champion, which is the best for Nasus thanks to Q and lifesteal. You cannot outdamage Nasus as Sion. You could attempt to out tank him, but Nasus, again, has infinite scaling damage and sustain. You'd prolong the fight but not change the outcome.