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Tuesday, September 29, 2026

MLB Playoffs 2026 Bracket Math

Baseball continues to confound us, especially in the expanded postseason era with 12 teams - with a 162-game regular season, your fate comes down to a best of 3, and if you're a lower seed even with a better record, you have to take those games on the road of an inferior team (looking at you, Chicago White Sox).

As seems to be the case every year, the Dodgers are heavy favorites. Last time I ran these simulations in 2020 this was the case, and the Dodgers did a win the (very weird) title.

SeedTeamDivision SeriesChampionship SeriesWorld SeriesChampion
American League
1Tampa Bay Rays100.0%47.9%28.3%11.0%
4New York Yankees57.2%31.0%19.8%8.7%
5Boston Red Sox42.8%21.1%12.3%4.8%
2Cleveland Guardians100.0%56.7%24.0%8.0%
3Houston Astros57.0%25.8%9.8%2.9%
6Chicago White Sox43.0%17.5%5.7%1.4%
National League
1Milwaukee Brewers100.0%59.1%25.2%14.9%
4San Diego Padres47.8%17.8%5.1%2.3%
5Chicago Cubs52.2%23.0%8.3%4.4%
2Los Angeles Dodgers100.0%65.6%44.2%32.0%
3Atlanta Braves50.2%16.3%7.8%4.2%
6Philadelphia Phillies49.8%18.0%9.4%5.4%

The AL, on the other hand, is way more wide open. Only one team, the top-seeded Tampa Bay Rays, have a better than 10% chance to win it all, with the Yankees (9%) and Guardians (8%) right behind. 

I will admit, with a way worse record, it feels deeply unfair that Cleveland has a better chance of making the ALCS, given they won 13 less games than Tampa Bay. But due to the way the seeding breaks, a team with 85 wins or less is guaranteed to make it out of the 2/3/6 side, and worst case for 1/4/5 is the Red Sox at 87 wins.

Saturday, July 11, 2026

Simulating the 2026 World Cup: Semifinals

All four favorites advanced, leading to a heavyweight semifinals, and extremely, extremely level odds. The champion is once again guaranteed to be from Europe or South America.

GroupCountryMDS RatingFinalChampion
IFrance2.0945.09%22.09%
HSpain2.2954.91%29.61%
LEngland2.0044.36%20.02%
JArgentina2.2355.64%28.28%

All four potential Final matchups are pretty equally likely as well, with each outcome a heavyweight matchup. Every matchup is close to 50/50:

FinalMatchup %Champion OddsRunnerup Odds
Spain vs Argentina30.50%Spain 51.5%Argentina 48.5%
France vs Argentina25.10%Argentina 53.4%France 46.6%
Spain vs England24.30%Spain 57.1%England 42.9%
France vs England20.10%France 52.2%England 47.8%

Tuesday, July 7, 2026

Simulating the 2026 World Cup: Quarterfinals

We are on to the quarterfinals, and the odds continue to coalesce around the favorites.

Argentina continues to cheat death, Spain got past Portugal to now emerge as the favorite, England gets a huge boost by surviving the Azteca, and then France continues to look like the best team in the tournament. This leaves us with these four countries with 15%+ to win, with the following increases relative to the start of the tournament:

  • Argentina: +12%
  • Spain: +11%
  • France: +9%
  • England: +9%
We are also up to a 94% chance the champion once again is from South America or Europe - only Morocco stands in the way now that all three hosts flamed out.

GroupCountryMDS RatingSemisFinalChampionDelta
IFrance2.0962.81%32.00%17.07%9.38%
CMorocco1.5737.19%14.21%5.76%3.69%
HSpain2.2967.24%39.99%23.06%11.20%
GBelgium1.5632.76%13.79%5.66%3.42%
INorway1.5839.76%15.81%6.21%4.22%
LEngland2.0060.24%30.14%15.00%8.64%
JArgentina2.2366.58%39.64%21.67%11.60%
BSwitzerland1.5333.42%14.41%5.58%3.50%

Friday, July 3, 2026

Simulating the 2026 World Cup: Round of 16

We are on to the Round of 16, and the favorites have continued to win (for the most part) so there are no large changes in the overall odds.

Argentina's path to the final remains clear, but France's has also cleared considerably, up until Spain in the semifinal.

Biggest increases relative to the start of the tournament:

  • Argentina: +6%
  • France: +4%
It's still a wide open tournament, with no one better than ~16% odds to win it all. Argentina (16%), Spain (14%), and France (12%) remain the only teams above 10%. Egypt is the longest remaining longshot, with a 1% chance. 

Additionally, still an 82% chance the winner comes from Europe or South America, as has happened every single World Cup ever played. Of that 18% where it's not, the vast majority (14%) comes from the three hosts with some home field advantage: Mexico, United States, and Canada.

GroupCountryMDS RatingQuartersSemisFinalChampion
DParaguay1.3331.78%13.78%4.83%1.70%
IFrance2.0968.22%42.28%22.57%12.16%
BCanada1.2251.29%22.95%9.18%3.72%
CMorocco1.5748.71%20.99%8.63%3.53%
KPortugal1.9341.22%23.78%12.83%6.38%
HSpain2.2958.78%38.70%24.14%14.19%
DUnited States1.2853.15%20.64%10.35%4.39%
GBelgium1.5646.85%16.87%7.49%3.09%
CBrazil1.9558.80%29.59%14.97%7.67%
INorway1.5841.20%17.15%7.35%3.12%
AMexico1.4445.89%23.49%11.26%5.65%
LEngland2.0054.11%29.77%15.41%8.09%
JArgentina2.2374.73%46.63%27.42%15.83%
GEgypt1.1525.27%9.19%3.02%1.00%
BSwitzerland1.5342.11%16.91%7.00%2.86%
KColombia1.8557.89%27.27%13.56%6.64%

Sunday, June 28, 2026

Simulating the 2026 World Cup: Knockout Edition

The knockout rounds are set, and because of the new extremely convoluted third place advancement rules (path 67 occurred, for those wondering), some teams have far easier paths than others.

Because of this, we have a new favorite - Argentina! Spain is still a contender like at the start, but two teams with 5%+ odds have jumped considerably (italicized below):

  1. Argentina: 15% (+5%)
  2. Spain: 11% (-1%)
  3. France: 8% (+1%)
  4. England: 7% (+1%)
  5. Colombia: 6% (+2%)
  6. Brazil: 5% (no change)
Argentina and Colombia got the soft half of the bracket:

GroupCountryMDS RatingRound of 16QuartersSemisFinalChampion
EGermany1.8663.18%32.19%18.12%9.22%4.75%
DParaguay1.3336.83%14.22%6.08%2.33%0.85%
IFrance2.0974.00%44.46%27.49%15.31%8.47%
FSweden1.0426.00%9.13%3.25%1.07%0.34%
ASouth Africa0.8030.52%8.84%2.37%0.61%0.16%
BCanada1.2269.48%33.21%15.11%6.58%2.83%
FNetherlands1.8255.98%33.88%16.99%8.41%4.10%
CMorocco1.5744.03%24.07%10.59%4.63%2.05%
KPortugal1.9356.93%27.20%16.14%8.60%4.44%
LCroatia1.6443.07%17.44%9.25%4.35%1.97%
HSpain2.2970.87%43.64%29.69%18.60%11.32%
JAustria1.4029.14%11.73%5.46%2.22%0.87%
DUnited States1.2872.29%38.60%16.52%8.11%3.63%
BBosnia and Herzegovina0.7127.71%8.33%1.79%0.46%0.11%
GBelgium1.5650.90%27.23%10.90%4.94%2.10%
ISenegal1.5349.10%25.85%10.24%4.57%1.92%
CBrazil1.9556.35%35.49%19.08%10.19%5.40%
FJapan1.6943.65%24.84%11.73%5.56%2.54%
EIvory Coast1.1238.74%12.69%4.31%1.54%0.50%
INorway1.5861.26%26.99%12.10%5.34%2.31%
AMexico1.4454.54%28.49%15.23%7.84%4.00%
EEcuador1.6645.46%21.86%10.78%5.09%2.31%
LEngland2.0077.42%43.40%24.97%13.62%7.24%
KCongo0.7922.58%6.25%1.79%0.51%0.12%
JArgentina2.2384.24%61.94%40.68%24.65%14.63%
HCape Verde0.6115.76%5.58%1.57%0.37%0.09%
DAustralia1.2652.76%17.79%7.55%2.78%0.99%
GEgypt1.1547.24%14.68%5.90%2.10%0.69%
BSwitzerland1.5358.48%28.44%12.25%5.36%2.28%
JAlgeria1.1841.52%16.92%6.04%2.17%0.73%
KColombia1.8577.26%47.32%24.15%12.44%6.15%
LGhana0.6422.74%7.33%1.85%0.45%0.11%

Odds a country outside of Europe/South America wins: 20%. This is double last knockout round in 2022, given we have double the teams at this stage (32).

Also recall that teams that achieve 9 points in the group stage rarely win the whole thing, and in 2022, no knockout teams did this! We have three candidates here this year, including two of the top contenders: France, Argentina, and Mexico.