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r/StatisticsZone

100 Million World Cup Brackets
▲ 18 r/StatisticsZone+13 crossposts

100 Million World Cup Brackets

I've created a website that tracks 100 million FIFA World Cup 2026 knockout stage brackets live to see how they evolve throughout the tournament—and ultimately how many matches it takes before there isn't a single perfect bracket left.

Each of the 100 million brackets is generated using a Monte Carlo simulation. The model is driven primarily by my own team ratings, which are similar in concept to advanced metrics like KenPom for college basketball, while also incorporating factors such as betting markets, injuries, recent form, home-continent advantage, travel, and other matchup-specific adjustments. Every bracket is an independent simulation of the entire knockout stage.

I'll update the website match by match in chronological order, allowing everyone to experience exactly how the live tracker will work once the real World Cup starts.

You can follow along at brackit.us and watch the surviving perfect brackets disappear one match at a time.

u/dombaby18 — 5 days ago
▲ 72 r/StatisticsZone+12 crossposts

The sample mean as a projection onto the span of the ones vector

I’ve been thinking about the sample mean from a linear algebra perspective.

If y is a data vector and 1 is the vector of all ones, then the average can be seen as the scalar you get when projecting y onto span(1).

So the projection has the form:

y-hat = y-bar · 1

where y-bar is the usual sample average.

I like this because it makes the average feel like the simplest possible least-squares problem: find the constant vector closest to the data vector.

It also connects naturally to ordinary least squares regression, where y gets projected onto the column space of X instead of just the one-dimensional space spanned by 1.

Does this seem like a good way to introduce projections/least squares, or would you teach it differently?

youtu.be
u/CubionAcademy — 14 days ago