LoL Worlds 2021 - Knockout Stage Simulation

LoL Worlds 2021 - Knockout Stage Simulation

At long last, the League of Legends World Championship Knockout Stage. Eight teams are left, and I simulated the bracket to predict where each team is most likely to end up. Everyone's got their eyes on DWG KIA, but are they truly that dominant?

The bracket

First things first, we need to know what the bracket setup is:

source: lolesports twitter (

Single elimination, best-of-five matches. One loss and you're out, so there's no room for error. Both Chinese teams play each other in round one; they had looked like strong contenders but one of them is going home earlier than they should have. With all four of their teams having made it to the Knockout stage, Korea is looking well positioned for some deep runs. The last two teams represent Europe and North America, who have their work cut out for them.

Simulating the bracket

First place

If you've followed along, you know the drill by now. My model generated probabilities for each matchup, which I then ran through 50000 simulations to see how often each team won Worlds:

Team Name % 1st Place Median Place
Royal Never Give Up 28.64% 3rd-4th
DWG KIA 17.29% 3rd-4th
EDward Gaming 16.54% 5th-8th
Gen.G 11.25% 3rd-4th
T1 9.95% 3rd-4th
Hanwha Life Esports 5.96% 5th-8th
Cloud9 5.72% 5th-8th
MAD Lions 4.65% 5th-8th

In line with my power ranking before Worlds had started, Royal Never Give Up are the most likely team to win in my simulations. Data from the group stage was incorporated into the new predictions, but with only six games played for most of these teams, things weren't likely to shift too much.

Next up are DWG KIA, the incumbent World Champion, followed closely by EDward Gaming.

These probabilities are not just the same matchup power ranking in different form - they reflect how difficult of a run each team would have through the bracket as it stands. Gen.G have a relatively easy (one of the more lopsided) first round match against Cloud9, but then face one of the two Chinese teams, either of which would be a scary opponent. Of course, any team would have a tough matchup at least in the final, but three of them in a row makes a first place finish that much harder.

I've always shown median finishes here, but I wouldn't read into them too much in this instance. With only three rounds, there are only four possible placements: 5th-8th, 3rd-4th, 2nd, and 1st. Any team that is unfavored in the first round by definition has a 5th-8th place median finish, as that's where the 50th percentile will fall, and no teams are so dominant (or conversely, so weak) that any team has more than a 50% chance to make it to the final.


Speaking of... here's the probability of each team making it to the final (i.e. finishing in the top two):

Team Name % Top 2
Royal Never Give Up 41.85%
DWG KIA 39.17%
T1 28.20%
EDward Gaming 25.59%
Gen.G 20.99%
Hanwha Life Esports 18.53%
MAD Lions 14.10%
Cloud9 11.57%

RNG and DK are almost equally likely to get there, and that matchup is the overall most likely final scenario. Since a weaker team only needs two upsets in a row to get there, even C9 have an 11.5% chance - this is the equivalent of winning two 34% matchups in a row, which is their average probability against GEN and their potential semifinal opponent.

T1 were lower on my list of teams to win, but higher than both EDG and GEN in this list. This has to do with their position in the bracket. T1 are favored against HLE, and have a reasonable chance against DK, plus some probability of getting to face MAD instead in the semis. EDG immediately go up against RNG, my favorite, and almost certainly against GEN, who I believe are the second strongest Korean team. Likewise, GEN has to face one of the Chinese powerhouses in the semis.


If the favorite (according to my model) wins each matchup, here are the final placements:

Team Name Place
Royal Never Give Up 1st
Gen.G 3rd-4th
T1 3rd-4th
EDward Gaming 5th-8th
Cloud9 5th-8th
Hanwha Life Esports 5th-8th
MAD Lions 5th-8th

RNG and DK meet in the final, where RNG are favored. GEN and T1 win their respective first round matches, before losing to the two finalists. Nothing too exciting or controversial here, to be honest... there's just not a whole lot of variation that can happen when there are only seven matches to be played. I'm a strong proponent of double elimination tournaments, can you tell?

Still, seven is enough matches that any one exact outcome is still pretty unlikely. All seven matches are won by the favorite only 3.3% of the time in my simulations, so there's a very high chance of at least one upset.

Placement distribution

Across my simulations, here is the distribution of each team's placement finishes:

Alacrity's Worlds 2021 Knockout Stage Placement Distributions

Some of those path-dependent nuances can be more visible here. RNG are pretty unlikely to get second, as the only two teams that would give them a lot of trouble are EDG, who they face in the first round, and DK, who only make it to the final 39% of the time.

Each team is more likely to lose in the first round than they are to get any other specific place, which sounds weird but actually makes sense. Each other place requires a specific sequence of wins and losses - to get second, you need to win, then win, then lose, so that exact sequence is going to be less likely to occur than simply losing once. If each matchup was a perfect 50/50 coin flip, getting a tails on your first flip (50%) is much more likely than getting exactly heads and then tails (25%) on your first two flips.

"Final" thoughts

Mostly, this bracket comes down to Royal Never Give Up and DWG KIA. My model is a bit more favoring of the Chinese team, while general perception is on the side of the Korean prior World Champions. Their 6-0 group stage run certainly plays into that, and there's no doubt that they're an incredibly strong team. RNG's 4-2 group stage looks mediocre in comparison, especially since one of those two losses was Fnatic's only win after losing a key player.

In the grand scheme of things, six games hardly define a team, especially with all of these teams' long histories of professional play. If they can get back to their regular season form, RNG should be able to give DK a run for their money.

And hey, just because those are the most likely two finalists doesn't mean that they necessarily will be. EDG are one of the most likely teams to beat RNG, and might just knock them out right off the bat. Meanwhile, while MAD should be outmatched by DK, they've shown that with their backs against the wall they can fight tooth and nail.

The knockout stage plays out over the next two weeks, so you should have plenty of time to get any potential bets in on matches. You can also bet on various outrights, such as the overall winner, the region of the winner, and so on, but I'd generally advise against it as the vig on those types of bets is significantly higher. Keep an eye on my suggested bets to get match-by-match predictions of outcome probabilities, and where I'd suggest staking your money.

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