A statistical look at the world.
Expected Goals: a Popular Football Statistic from an Econometric Perspective
A striker runs toward goal, receives a cross from his winger, takes a great first touch, and dribbles past the goalkeeper. Just before shooting, however, he missteps and the ball goes wide: no goal. Later in the match, a midfielder takes a gamble and shoots from 30 meters out, and the ball goes in. Which chance was “better”? In modern football analytics, this question is answered with a single number: expected goals, or xG. Behind this widely used but seemingly simple metric lies a classic econometric model. But how is this probability actually estimated?
Why Tough Courses are a High Variance Gamble
Most students would argue that they prefer an easy course over a challenging one. But does the data actually support this intuition? This article analyzes around one thousand course evaluations from the UMCG/FEB to investigate the relationship between course enjoyment and workload. The data is sourced from De Zwoegfactor, a growing platform and essential study tool that provides personalized academic advice based on student experiences.
Can success be explained by randomness?
Why do some people seem to succeed so effortlessly, while others, equally as skilled, fall short? A start up with a carefully strategic approach fails, while a similar one becomes a highly successful company. A student studying for hours and getting a passing grade, while another barely prepares and excels. We tend to explain these outcomes through skill, talent and hard work, but what part of this unexpected success actually comes down to luck?
The portrayal of mathematical genius in cinema
Studying mathematics is an arduous undertaking, testing one's patience while learning new, complex concepts and one’s tolerance for frustration. This is common to all of us, and fortunately so, as it reminds us that we are not alone in this journey. We are however led to believe that there exist some exceptions in our world, some people who possess a certain knack for mathematics. For them, mathematical expressions come as naturally as brushstrokes to an artist. When we talk about these numerical artists, we think of Euler, Gauss, Newton, to name a few giants. While we humble mortals are quite certain of never attaining such intellectual heights as they did, we are capable of appreciating their talents from a content-based perspective thanks to our quantitative background. For the layperson, however, their encounter with the notion of the “mathematical genius” is often shaped by popular culture. But does this mathematician on the big screen correspond to the mathematician in the real world?
The Improbability of a Nine-darter
The leg starts. A player approaches the dartboard, cool as ice. With a fluid motion, he bends his elbow, leans in, and releases a dart that finds its mark in the triple 20 as if it were the most natural feat in the world. Within a second, he follows with another throw, and another. Again, a perfect throw. Then another, and another, and another. By the time he reaches his seventh dart, the arena has fallen into silence. Everyone holds their breath and waits in anticipation. Two darts are left and 81 remains to be thrown. Triple 19. Just one dart left. Double 12. The place explodes. Nine darts, zero mistakes, and most importantly, game over. Surely a player this good could be doing this all the time? That, however, is completely false.
Interview with Lorenzo Sierra Perez - Trader at Flow Traders
I found out quite quickly during my studies that continuing the natural path of becoming a PhD was not for me. I really liked the content, as both physics and mathematics basically presented complicated puzzles that I wanted to solve, but there were a couple of specific things about a PhD which really irked me. Spending four years -a long time!- on a single topic, mostly by yourself, with relatively little reward for doing great as opposed to scraping by; it had a lot of things that I really did not want in a job. Instead, I flipped them around: what jobs are out there that are fast-paced, very diverse, team-based, where there is a clear feedback loop and you can get a lot of responsibility fast if you do very well? With these job traits to look for, I landed on two possible career paths: strategy consulting, and trading. I sent out some messages to members of my study association who were working in those fields, and after a lot of chats with them I was convinced I should at least try my hand at getting into trading. Now I am coming up to four years as a trader at Flow Traders and I'm still very happy being here.
Is the F1 championship already decided after two races?
Formula 1 seasons last more than twenty races, but championship battles often are predictable surprisingly early. After only two races, fans already speculate about who will become world champion. But how much information do the first races actually contain?
The Red Flag of the First Digit: How Benford’s Law Catches Fraud
If I asked you to invent a list of 100 random expenses for a fake company, you would likely try to make the numbers look as "random" as possible. You would sprinkle in some numbers starting with a 4, some with a 7, and perhaps a few starting with a 9. In your mind, randomness implies equality. However, doing this would result in you being caught rather soon. This is because real accounting data follows a hidden, logarithmic rhythm known as Benford’s Law.
Intuition and Definition of a Martingale
The concept of a martingale originates in the world of gambling, but the idea extends far beyond the roulette or poker table. Imagine a simple game: you start with €0, and in each round you toss a fair coin. If you win, you gain €1; if you lose, you lose €1. Each round is completely independent of the previous one; what happened before does not influence the outcome of the next toss.
Why continuity assumptions matter more than you think
In econometrics, many of the most important results depend on conditions that rarely receive attention. Buried inside proofs, often labeled as “regularity conditions,” these assumptions can look technical and secondary. Continuity is one of them. Yet continuity is not just a background detail. It is one of the structural features that makes estimation possible, inference meaningful, and models stable.