ノート
記事
確率研究、モデルのスナップショット、WC2026 に関する短いメモ。
11 Jun 2026
Five places the model disagrees with the consensus
Models don't know narratives. They read results, schedules, and xG rates. Here are five places ours diverges most from the consensus, from Ecuador over Germany to Raphinha as the #1 anytime scorer, Iran at 81%, Spain and Argentina pulling away, and the USA as the underdog in every group match at home.
#model-vs-consensus#world-cup-2026#methodology#group-stage
11 Jun 2026
Argentina and Spain: 0.6 points apart, nothing else in common
The model's two most likely World Cup winners sit at 17.5% and 16.9%, a gap well inside simulation noise. They get there via opposite paths. Argentina runs through the best defensive rating in the field and a penalty advantage worth 5 percentage points on its own; Spain runs through attacking volume and a Barcelona spine. Both teams' nearest historical analogues exited earlier than expected.
#spain#argentina#world-cup-2026#model
11 Jun 2026
Why prediction markets keep underrating World Cup draws
Prediction markets, including Polymarket, consistently compress draw probabilities in World Cup openers. The model disagrees. Here's why the structure of prediction markets makes draws hard to price correctly, and what the numbers say about today's two Group A matches.
#prediction-markets#draws#model-vs-consensus#world-cup-2026
10 Jun 2026
The model never stops predicting. Here's the number we grade ourselves on
The model retrains nightly and its published probabilities move by the hour. The rows it gets graded on do not. Every group-stage forecast froze this morning, at least 24 hours before kickoff; a second freeze pins the published number three hours before each match; both land in public JSON files; and the Internet Archive holds receipts that the numbers came first.
#world-cup-2026#methodology#calibration#accuracy
9 Jun 2026
Brazil vs Morocco is a coin-flip. The model has it 50–30–20.
Our model gives Brazil a 50.1% probability of winning their Group C opener against Morocco — essentially a coin-flip between Brazil winning and not-winning. Morocco, the first African nation to reach a World Cup semifinal, is rated far closer to Brazil than most people expect. The group picture tells the rest of the story.
#brazil#morocco#group-c#match-preview
8 Jun 2026
Luka Modrić was six years old when his grandfather was killed and his family fled. He's 40 now. This is his last World Cup.
In 1991, six-year-old Luka Modrić became a refugee. In 2018, he dragged a nation of four million to the World Cup final and won the Ballon d'Or. In 2026, at 40, he will captain Croatia one last time — opening against England, the team he beat in that 2018 semifinal. The arc of a career that started in a hotel parking lot in Zadar.
#croatia#modric#last-dance#veterans
7 Jun 2026
What it takes to beat an animal oracle
A psychic octopus called all eight of its 2010 World Cup matches correctly. That is a one-in-256 coin streak, and it is the wrong thing to envy. The thing a model can do that an animal oracle never could is tell you how sure it is — and then be held to it across hundreds of matches. Here is what "beating the oracle" actually means.
#calibration#methodology#forecasting#research
7 Jun 2026
What the 48-team format actually changes
The 2026 World Cup expands from 32 to 48 teams, adds a Round of 32, and lets eight third-place finishers advance. Our model shows what these structural changes do in practice — two-thirds of the field advances, four teams hold 53% of the championship probability, and the group stage becomes a near-formality for 13 nations. The format creates more football, more representation, and a sharper divide between the teams that are there to compete and the teams that are there to participate.
#world-cup-2026#format#expansion#analysis
6 Jun 2026
Germany ranks first of 48 at both ends of a shootout — and is still only the model's 7th-likeliest champion
The cliche that Germans never miss from the spot is, for once, literally true in the model. Of all 48 teams, Germany ranks first in penalty conversion and first in penalty save rate — the only side top of the field at both ends of a shootout. Yet the model still puts Germany seventh in champion probability, at about 5.2%. A scenario test that resets its spot-kick numbers to league average cuts that title probability by roughly a third — so the shootout advantage is real, already counted by the model, and still not enough.
#world-cup-2026#germany#penalties#shootouts
6 Jun 2026
The three hosts have a combined 1.2% chance of winning their own World Cup
The 2026 World Cup opens June 11 at the Estadio Azteca, where Mexico plays the first match of a tournament its country is co-hosting. The model gives Mexico, Canada and the United States, added together, about a 1.2% chance that one of them lifts the trophy — roughly 1 in 87. The host advantage is real but it lives in the group stage, not the final.
#world-cup-2026#hosts#mexico#usa
6 Jun 2026
Set-piece teams and open-play teams: where the contenders actually score
Not every team scores the same way. We took every shot from the last three major-tournament cycles (World Cups, Euros, Copa América, the Africa Cup of Nations) and sorted every goal by how the move began, into open play, set pieces, counters, and penalties. The split is wide. Uruguay scores 58% of its goals from set pieces, the most of any well-sampled qualifier; Spain and Germany take two of every three from open play. How a team defends set pieces is its own story. The Netherlands, Morocco, and Brazil each concede close to half their goals from dead-ball situations. A guide to how the World Cup's contenders actually put the ball in the net, and how they let it in.
#world-cup-2026#set-pieces#open-play#tactics
2 Jun 2026
The conditions draw: who got the altitude, who got the heat
The 2026 World Cup is the first to mix the thin air of Mexico City with the Gulf-coast heat of the American South in one tournament. But altitude and humidity don't punish everyone equally — they tax the teams whose players never train in them and barely touch the teams who do. Mexico, Colombia, and South Africa drew altitude they're built for; the Czech Republic, South Korea, and Uzbekistan are sea-level sides sent up high. In the heat group, the hottest draw — Japan — may be the best prepared for it, while cool-climate Sweden and the Netherlands feel it most. A venue-by-venue guide to who the conditions draw quietly helped, and who it taxed.
#world-cup-2026#conditions#altitude#weather
2 Jun 2026
Five projected starting captains at WC2026 are 35 or older
Cristiano Ronaldo, Luka Modrić, Edin Dzeko, Lionel Messi, and Riyad Mahrez are all projected to start as captains in their opening match. The youngest is 35. The oldest is 41. WC2030 starts in summer 2030, four years from now, when each of them is between 39 and 45. For most of them, this is the last World Cup.
#veterans#captains#last-dance#ronaldo
2 Jun 2026
The 2026 map punishes some teams more than others
The first 48-team World Cup is also the first spread across three countries and four time zones. That geography lands unevenly. We measured the in-tournament travel each team faces in the group stage — the distance between their three assigned venues. Bosnia and Herzegovina drew the longest internal itinerary at roughly 5,060 km, Toronto to Los Angeles to Seattle. Argentina, the model's favourite, drew one of the shortest at about 740 km. The flight maps behind the draw, and why the host nations are not all spared.
#world-cup-2026#travel#schedule#venues
30 May 2026
France will have six players in the final — on both benches
Six France internationals start tonight's Champions League final, five for PSG and one for Arsenal — Ousmane Dembélé against William Saliba, club rivals who become teammates in 12 days. The model has France 9.0% to win the World Cup, and rates Dembélé its #28 tournament scorer.
#france#world-cup#ucl#psg
30 May 2026
Portugal's World Cup spine plays the Champions League final tonight
Four of PSG's starters in tonight's Champions League final — Vitinha, João Neves, Nuno Mendes and Gonçalo Ramos — are bound for Portugal at the World Cup. The model gives Portugal a 7.5% chance to win the tournament, and rates Gonçalo Ramos its #21 tournament scorer.
#portugal#world-cup#ucl#psg
30 May 2026
PSG vs Arsenal: what the model sees in the Champions League final
Our club-football model makes Arsenal clear favourites in tonight's Champions League final — 54% to win, 25% draw, 21% PSG — on a ClubElo advantage of nearly 100 points and an expected-goals split of 1.73 to 0.98. The most likely scoreline is 1-1, but the distribution tilts firmly to Arsenal.
#ucl#champions-league#psg#arsenal
29 May 2026
Morgan Gibbs-White had the best season of his life. So why was he left behind?
Morgan Gibbs-White had the best season of his life — 15 goals, Forest's top scorer, a European semi-final — and England still left him behind. The outrage went to Palmer and Foden instead, both off down years. Our model rates Gibbs-White ninth among England-eligible players, and of everyone left out, his is the case that's hardest to argue with.
#england#squad#omissions#gibbs-white
28 May 2026
Model notes — how onthepitch predicts the 2026 World Cup
A complete reference for the prediction system behind onthepitch. Three component models (Elo, Dixon-Coles, Hierarchical Poisson), a calibrated ensemble, and a Monte Carlo bracket simulator. Every parameter, every design choice, every backtest number — in one place.
#methodology#model#ensemble#calibration
28 May 2026
Eight Barcelona players in Spain's squad — what club concentration means at a World Cup
Spain's 2026 World Cup squad has eight Barcelona players out of 26 — among the heaviest single-club blocs in the 48-team field, and the largest from a Champions League club. Players who share a club share passing patterns, spatial habits, and a tactical language that doesn't need to be rebuilt in a two-week camp. Our model rates Spain as the tournament's most likely winner at 16.7%.
#spain#world-cup-2026#squad#squad-cohesion
28 May 2026
The USA is the underdog in every group match at their own World Cup
Group D is the most competitive group at the 2026 World Cup by a massive margin. Our model gives the USA just a 73.0% chance of advancing — the lowest of any host nation — and rates them as the underdog in all three group matches. No other group in the 48-team field comes close to this level of uncertainty.
#usa#world-cup-2026#group-d#turkey
28 May 2026
Ten ideas the model tried and rejected
We tested 19 model variants before settling on the current ensemble. Ten of them failed the walk-forward Brier + ECE gate and were not shipped. Here's every hypothesis, every test result, and every reason for the no-ship — because the ideas you don't use say as much about a model as the ones you do.
#methodology#negative-results#model#calibration
25 May 2026
Three numbers for the same question: how accurate is the model on tournaments?
We answered one question — how well does the model predict tournament matches? — three times, and got a worse answer each time we made the test more honest. 0.510 on the headline backtest, 0.545 once we sliced to tournaments only, and 0.572 once we removed a subtle data leak and rebuilt every tournament from 2014 to 2024 as it stood the day before kickoff. 0.572 is the honest expectation for WC 2026.
#methodology#calibration#brier#backtest