Lets compare how much damage Master Yi and Tryndamere with their highest possible damage builds.

The builds I'm using I've specifically chosen to maximize the damage these champions can do. Yes I've calculated it. Yes Master Yi technically does more damage with the provided build below than he does with devourer, according to the mathematics of it. No I don't think this build for Yi is practical, he needs devourer in the jungle and on hit items give him a great power boost that allow him to build tankier. That isn't the point of this thread. The point of this thread is just to compare their absolute optimal damage builds to see what sort of damage difference they have.

Like with the devourer, according to the math with these champions a black cleaver at 6 items technically provides more damage than something like bloodthirster because the additional +25 attack damage is overshadowed by as little as +15% total armor pen even against a target who has no bonus armor, and black cleaver provides 35% at full stacks.

I'm also aware that some of this looks stupid. Like the fact that Tryndamere has both black cleaver and trinity force, despite the fact that the rage passives don't stack. Well it doesn't matter, I didn't make the numbers the way they are. These are their optimal damage builds regardless of how stupid they appear.

Statik shiv provides an atleast 59 damage per auto for yi as calculated: 120 damage on hit *2.95 damage on crit with crit damage runes 8 attacks to fully charge assuming standing still Yi makes a free attack every 3 attacks, so there is a multiplier of 4/3. 120 * 2.95 / 8 * 4/3 = 59

Shiv provides trynd an average of 44.25 damage with the build given below: 120 * 2.95 = 44.25

Both champions have 18 / 12 / 0 masteries, grabbing all the multipliers, fervor of battle and Dangerous game.

I am not figuring in merciless mastery on either champion, so it shouldn't skew the results in any case.

As for the +45 crit damage runes, it turns out that is the best multiplier with an optimal damage build.

I'm assuming that they both have 3rd dragon buff and the +25 attack damage elixer. I didn't do 5th dragon or baron because it seems too gated, like the merciless mastery-- but it would increase both champion's damage by roughly the same amount, and would be a marginal increase, so it shouldn't create a discrepancy in the comparison.

I'm assuming botrk is worth 105 on hit damage on average, which would require a target to have 3333 hp, which seems like a reasonable middle ground between tanky and soft targets. The botrk does 200 on hit damage vs a target with that much health if they have full hp, and a minimum of 10 if they are basically dead, averaging that together makes 105.

Master Yi is in highlander with Wuju Style activated, and Tryndamere is at full fury with 1 health.

Tryndamere build: infinity, shiv, trinity, black, botrk, rage 36% crit damage runes and +9% attack speed runes AD 116 + 65 + 25 + 55 + 25 + 54 + 25 AS 49.3 + 60 + 9 + 4 + 35 + 15 + 40 + 64 CC 100 HIT 100 + 20 + 37.5 + 5.4 + 42.9

TOTAL DPS: (0.67 * (1 + .493 + 0.04 + 0.35 + 0.15 + 0.40 + 0.64)) * ((116 + 65 + 25 + 55 + 25 + 54 + 25) * (2.95) * 1.06 ) + 112 + 105+ 20 + 37.5 + 5.4 + 44.25) * 1.05 * 1.03 * 1.02

2950

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Master Yi build: infinity, deaths, essence, phantom, shiv, black 30% attack speed runes AD 111 + 65 + 80 + 80 + 55 + 25 + 41.6 AS 34 + 80 + 30 + 4 + 45 + 35 CC 100 HIT 42.9 + 122 * 4 / 3 = 158.6 because of a free on hit every 3 attacks double strike is basically a damage multiplier = (4 / 3) / 2 = 1.165

TOTAL DPS: 0.679 * (1 + 0.34 + 0.8 + 0.4 + 0.45 + 0.35) * (((111 + 65 + 80 + 80 + 55 + 25 + 41.6) * (1.165) * (2.95) * 1.06 + 112 + 59) * 1.05 * 1.03 * 1.02 + 158.6)

4957

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So master yi does 68% more damage than Tryndamere at peak power.

If we take into account counterbuilding merely via the attack speed slowing passives on frozen heart and randuins omen: Tryndamere DPS: 2950* 0.85 * 0.85 = 2131 Master Yi DPS: unchanged

And in that case, Master yi does atleast 2.3 times the damage of Tryndamere at optimal build under that scenario. I say atleast, because Tryndamere's damage is fully mitigated by resists but Master Yi also has an on hit true damage effect, so taking into account armor and magic resist would push that figure closer to 3 against the average target. How close it comes to 3 depends on the specific resistances of the target.

TLDR: Master Yi does around 3 times the damage that Tryndamere does with a glass cannon build.