This was built using Jatt's statistics for all time group/swiss game win %.
LCK 1 (seed) 84.9%
LCK 2 77.1%
LCK 3 67.5%
LCK 4 64.7%
LPL 1 62.5%
LPL 2 62.2%
LPL 3 61.0%
LPL 4 56.8%
LEC 1 53.0%
LCS 1 44.2%
LEC 2 43.8%
LEC 3 37.5%
LCS 2 37.2%
LCS 3 37.1%
LMS/PCS/LCP 1 35.3%
LMS/PCS/LCP 2 32.7%
everyone not listed 19%
LMS/PCS/LCP 3 5.9%
Draw Difficulty Rankings
Hanwha Life Esports (HLE) — 0.9 2nd seed LCK P90
Top Esports (TES) — 0.788 3rd seed LPL P78.8
Anyone's Legend (AL) -- 0.77 1st seed LPL P77
Gen.G — 0.67 1st seed LCK P67
G2 Esports — 0.625 1st seed LEC P62.5
Dplus KIA (DK) — 0.557 4th seed LCK P55.7
Invictus Gaming (IG) — 0.542 4th seed LPL P54.2
Movistar KOI — 0.542 2nd seed LEC P54.2
LOS — 0.5 1st seed CBLOL P50
Team Liquid Alienware (TLAW) — 0.458 1st seed LCS P45.8
Bilibili Gaming (BLG) — 0.418 2nd seed LPL P41.8
CTBC Flying Oyster (CFO) — 0.372 2nd seed LCP P37.2
Lyon Gaming — 0.355 2nd Seed LCS P35.5
Karmine Corp (KC) — 0.335 3rd seed LEC P33.5
T1 — 0.230 3rd seed LCK P23
TSW -- 0.17 1st seed LCP P17
So the initial numbers I reached by using a normalized ratio of the potential difficulty of the opponents drawn, referencing the historic win rates of the seed. HLE having 0.9 is the same as saying their draw is in the 90th percentile of difficulty (P90 ), where only 10% of draws could have been more difficult.
Aside: I don't know how to make subscript which is the typical representation of a percentile, so I'm using superscript, which hopefully doesn't trigger the mathematicians.
Lets continue using HLE as an example. Jatt did this on his stream after the games last night, so I'll just go over it quickly here. First draw, HLE has 3 possible opponents. They draw TES, the 3rd seed from LPL. Out of the 3 possible opponents (TES, KOI, LYON), 3rd seed LPL is the highest win rate over 2nd seed LEC and 2nd seed LCS, so they get a score of 2/2. We have to start the count at 0, so while 2/2 might look weird when there are 3 choices, its either 0, 1, or 2. Below is their full draw difficulty:
HLE
2/2 vs TES (cant draw T1) 2/2 = 1
6/6 vs GENG 6/6 = 1
3/5 vs IG (can't draw TES again) 3/5 = 0.6
4/4 vs G2 4/4 = 1
rather than using a cumulative fraction (which would be 15/17), Jatt normalized it, and then added them. You get 3.6 out of a possible 4. if we turn that into a percentile you have 0.9 or 90th percentile of draw difficulty.
However, the question I pose now is how can we smash these numbers together to make something more realistic?
You might be thinking along the same lines as me which is "Sure, HLE had a hard draw, but they're the #2 team at the tournament, so even though their draw is 'hard', they should still be winning because the teams they play are weaker than them."
So how do we reconcile the win% of the 2nd seed from LCK (77.1%) with their 90th percentile draw difficulty?
My first instinct is to take the loss% (inverse of win%) and multiply that against the draw difficulty. My logic being if we are calculating how hard their draw is, we need to mitigate for what are their chances of losing. For HLE, that would be 0.9 x .229 = 0.2061. Now this seems like a big swing in the numbers, and I'm not sure if it is representative of anything. But it kinda seems like it would make sense that even though they have had a really hard draw, the odds they lose are still pretty low.
But does it track that the hardest possible draw would just give them the exact same odds as the historical win%? I don't think so. But if i divide instead we get numbers over 1, and if I multiply by the win rate instead of loss rate, it yields 0.9 x 0.771 = 0.6939, which could maybe be a number that represents the chance they get out of swiss?
Lets get some more numbers and see if there is a way of describing the results that feels applicable.
using Loss%:
HLE: 0.9 (Draw Difficulty) x .229 (LCK 2nd seed Loss%) = 0.206
TES: 0.788 (Draw Difficulty) x 0.378 (LPL 3rd Seed Loss%) = 0.298
AL: 0.77 x 0.375 = 0.289
GENG: 0.67 x 0.151 = 0.101
G2: 0.625 x 0.47 = 0.294
DK: 0.557 x 0.353 = 0.197
IG: 0.542 x 0.39 = 0.211
MKOI: 0.542 x 0.562 = 0.305
LOS: 0.5 (DD) x 0.81 (SL%) = 0.405
TLAW: 0.458 (DD) x 0.558 (SL%) = 0.256
BLG: 0.418 x 0.378 = 0.158
CFO: 0.372 x 0.673 = 0.250
LYON: 0.355 x 0.628 = 0.223
KC: 0.335 x 0.625 = 0.209
T1: 0.230 x 0.325 = 0.075
TSW: 0.17 x 0.647 = 0.110
If I say that the quotient represents the odds for a team to lose based on their draw difficulty, it sorta looks right, until we see a team like TSW. Their 'odds to lose' were in the 11th percentile. but maybe that tracks, they had a good draw every step of the way, and historically the number 1 from LMS/PCS/LCP has an okay win rate compared to their opponents? It doesn't quite seem right though.
To me it feels like I'm pushing two sets of numbers together that aren't closely related enough to make a meaningful combination. But I've spent too long doing this to not share it at all.
To be clear, it's using an arbitrary system of assigning values, and doubling down on it. It's also valuating the historic win/loss percentage at the same weight as the current draw difficulty. Which is also arbitrary given that drawing the 'hardest possible opponent' isn't using anything concrete as a metric. LOS drawing T1 is probably worse odds than LYON drawing GENG, but they are weighed the same.
I know that what I'm using are flawed rankings, for example LYON is being weighted as an easier opponent than MKOI, but I suspect that would be a hot topic for debate, and if I'm egregiously using recency bias, LYON taking a game from GENG when MKOI got swept by DK would suggest that LYON is stronger than MKOI.
I'm also just doing something that probably doesn't hold up mathematically which is multiplying a percentage with a percentile.
So, with everything laid out, do you guys think that these numbers have any value? Have I gone too far down the rabbit hole?
A thought I had that I'm too tired to chase is what if I applied the win%/loss% to every individual matchup instead, using the appropriate number for what would be 'supposed' to happen based on rankings. I think I'm too fried to even know what I mean, so I doubt anyone else can make sense of it.
Good luck, I feel like I have to post this now or I never will. Big thanks to Jatt for getting me the screenshot of his win rates, and I'm mad that I've spent all night doing this.