Paul Johnson
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paulrjohnson.net
Paul Johnson
@paulrjohnson.net
1.6K followers 790 following 800 posts
Data Scientist interested in causal inference, machine learning, and statistics | He/Him

Website: https://paulrjohnson.net
Github: https://github.com/paulj1989
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paulrjohnson.net
Because I know no one really cares about the Bundesliga (and because I wanted to test how well the model generalises), I have tested it out on the Premier League too!

The results look pretty solid to me, though I have a little less faith in how the model does with the Premier League than the BuLi.
A table showing the Premier League 2025/26 season projections generated from 10,000 Monte Carlo simulations. The model projects Arsenal are the most likely to win the Premier League, with a 63.5% probability, with Manchester City, Liverpool, and Chelsea rounding out the rest of the top four. At the other end of the table, Wolves (72.6%), Burnley (52.3%), and Leeds (35.8%) are the most likely to be relegated. A table showing the predictions for the next round of Premier League fixtures, showing the predicted expected goals and the match outcome probabilities for each game. Arsenal have a 70.6% probability of beating Tottenham, while Liverpool are given a 68.2% probability of beating Nottingham Forest.
November 17, 2025 at 6:36 PM
paulrjohnson.net
The model uses Monte Carlo simulation to project outcomes in the Bundesliga for the 2025/26 season, but it also models team ratings across the league and predicts upcoming fixtures.
A screenshot of the Predicting Ball app showing the Team Strengths tab, displaying Borussia Dortmund's Team Metrics. The tab shows cards that display the overall rating (0.4), attack rating (0.39), defense rating (0.41), and project points (64), and below this are two plots showing how BVB compare to the rest of the league (overall they are the third highest rated team behind Bayern Munich and Bayer Leverkusen). A screenshot of the Predicting Ball app showing the Fixture Predictions tab, displaying the outcome probabilities for Bayern Munich's upcoming game against Freiburg (Bayern have a 86.2% probability of winning) and Borussia Dortmund's game against Stuttgart (BVB have a 54.7% probability of winning).
November 16, 2025 at 3:31 PM
paulrjohnson.net
Up the fucking scum
The outside of a British pub called the Southampton Arms
August 23, 2025 at 7:27 PM
paulrjohnson.net
Proper football
The table for Group A in the Club World Cup after one game. All four teams (Al Ahly, Porto, Palmeiras, and Inter Miami) are on one point, with a draw each, and no goals scored (or conceded).
June 17, 2025 at 8:52 PM
paulrjohnson.net
I may be a sourpuss but I still found this pretty endearing.
A plate with a pork banh mi and a smiley face drawn in sriracha.
March 30, 2025 at 3:50 PM
paulrjohnson.net
Always Reppin' The 713
A close-up of a pink bag with flowers and the words "Houston" and "The City of Houston" all over it
March 30, 2025 at 12:20 PM
paulrjohnson.net
No.
The header of an article written by Patrick Galbraith, "Stop scapegoating Britain's landed classes".
March 30, 2025 at 8:43 AM
paulrjohnson.net
A little boy enjoying his silly beers
March 28, 2025 at 9:23 PM
paulrjohnson.net
I made my own radler earlier today, with a can of Lightbulb and some homemade raspberry lemonade. Because I'm a fancy boy that deserves fancy little drinks.
A teku glass stands on a wooden chopping board, filled with a homemade radler made from a mix of Verdant's Lightbulb XPA and homemade raspberry lemonade. The XPA can and a jug filled with raspberry lemonade sit on either side of the glass.
March 22, 2025 at 6:39 PM
paulrjohnson.net
Sike it was delicious!
A bowl of sesame-fried spam with broccoli and garlic fried rice, with sriracha drizzled on top.
March 20, 2025 at 7:50 PM
paulrjohnson.net
Only the finest for my refined palette. You probably wouldn't appreciate it. You don't know the finer things like I do.
A tin of spam held to camera by the person (me) taking the picture. The person's hand and tattooed arm is in shot, with a bin, fridge, and the kitchen floor in the background.
March 20, 2025 at 6:42 PM
paulrjohnson.net
Fresh box of treats from Brewser. This month from Pomona Island. Decent mix of beers.
Eight cans of Pomona Island beer, stacked in two rows of four. The top row of beers are JACK BE NIMBLE, JACK BE QUICK (West Coast Pale), SQUIRREL-SQUASHING, DEER-SMACKING (West Coast IPA), ISÉ-MAIRI (Orange Small Pale), and CHECK OUT THE PARTY (Blackcurrant, Blackberry, Apple and Cinnamon Sour). The bottom row of beers are I WISH I COULD SHIMMY LIKE MY SISTER KATE (IPA), O'HANRAHA-HANRAHAN (Blackcurrant Gose), MY NAN'S GONNA LOVE HER CIRCULAR SAW (Salted Chocolate & Rosemary Stout), and ВІВBIТY-ВОВВІТY HAT (Pale).
March 19, 2025 at 7:54 PM
paulrjohnson.net
Getting nice little treats delivered to start the week right. I deserve my treats.
The packaging that the Borussia Dortmund 24/25 special edition neon kit comes in. A neon yellow box with splashes of black, with the BVB logo in the middle. The neon yellow 2024/25 special edition BVB kit, inspired by the 1994/95 kit.
March 17, 2025 at 12:14 PM
paulrjohnson.net
The host of the TV show To Catch a Predator, Chris Hansen, looking at the camera.
March 15, 2025 at 12:26 AM
paulrjohnson.net
My pals and I have been coding your vibe from across the bar, and we were wondering if you'd like a sniff of my lizard.
RFK Jr, flanked by Russell Brand in a wide-open leopard skin shirt and a shirtless Dr Oz, presenting a lizard to the camera like a gift.
March 8, 2025 at 1:51 PM
paulrjohnson.net
Can I offer you a picture of a dog in this trying time?
A small dog (breed: ratcha) nestled into blanket looking very cozy, staring at camera as she falls asleep.
March 8, 2025 at 9:32 AM
paulrjohnson.net
Brewser sent me some delicious treats. Good way to start a week off.
Eight cans of Verdant beer, stacked in two rows of four. The top row of cans are De-Bleaker (IPA), Sundialer (Pale Ale), Light Bulb (XPA), PuTTTy (TIPA). The bottom row of cans are Sniffing the Wrong People (IPA), There is Only Now (Pale Ale), People Money Space Time (Session IPA), Remarks (IPA).
March 3, 2025 at 4:48 PM
paulrjohnson.net
To celebrate the release of Flashes, please enjoy a splendid dog.
A small dog laying on a sofa submerged by a fluffy blanket, with just her eyes, nose, and feet poking out.
February 27, 2025 at 12:21 AM
paulrjohnson.net
The "I just need to" meme but with "I just need to buy another train."
February 21, 2025 at 11:57 AM
paulrjohnson.net
Okay this haul feels a little excessive.
14 cans of beer stacked on top of each other, in two rows of seven, on a desk. Eight of the beers are Vault City sours (and one stout), and the others are the six beers produced by various brewery collaborations for Brewser's ProjectX 2024.
November 23, 2024 at 7:59 PM
paulrjohnson.net
Unfortunately, Southampton are just bad. I didn’t include the figure below in the blog post because I have been forced to accept that no one else cares about Saints, but I’m posting it here because I need the world to know how silly they are.
A time-series plot visualising Southampton's total and predicted points each season from 2012/13 to 2022/23, including a fitted line that visualises the trends in predicted and total points. Southampton overperformed expectations, on average, in the first half of the seasons being studied but started to decline after the 2016/17 season, both in terms of their predicted and total points, before a considerable dip in their total points (which is also a massive underperformance of their predicted points) which resulted in their relegation.
November 11, 2024 at 10:06 PM
paulrjohnson.net
The model performs pretty well but struggles a bit with the Premier League. It overestimates the worst teams, and the best consistently overperform because the rest of the leagues are dragging the predictions down a bit. Man United did break the model, though (discussed a little in the blog post).
A time-series plot visualising Arsenal, Chelsea, Liverpool, Man City, Man United, and Spurs's total and predicted points each season from 2012/13 to 2023/24, including a fitted line that visualises the trends in predicted and total points. Arsenal significantly underperformed expectations midway through the period but in recent seasons have experienced similarly significant overperformances, while Liverpool and Arsenal have consistently overperformed expectations recently. Manchester United and Tottenham have performed above expectations in earlier seasons but have otherwise met expectations. Finally, Chelsea have the largest swings, with massive overperformances in the early seasons and similarly significant underperformances in other seasons.
November 11, 2024 at 10:06 PM
paulrjohnson.net
The findings highlight that the Premier League is an outlier. The rest of the Big Five are relatively similar (when you account for the BuLi & Ligue 1 diverging due to fewer games), but the Premier League is just too rich to be normal.
A regression plot visualising the relationship between squad market values and the model's predicted points in the Big Five leagues from 2012/13 - 2023/24. The plot includes fitted regression lines for each league. The five regression lines are similar in shape. However, the Premier League slope is more gradual with a smaller intercept, suggesting that Premier League teams need more expensive squads to compete and increases in squad value are worth fewer points. The Premier League line also extends further on the x-axis because the most expensive squads in the Premier League are worth significantly more than the rest of the leagues. The intercepts for the other four leagues are very similar, but the Bundesliga and Ligue 1 tail off as squad value increases due to playing fewer games in a season and, therefore, having fewer available points that the increases in squad value could gain. Finally, La Liga and Serie A have similar slopes. The endpoint of the La Liga line is further along the x-axis due to the significantly larger Real Madrid and Barcelona squad values.
November 11, 2024 at 10:06 PM
paulrjohnson.net
I cannot move in case I disturb this perfect angel. My day is over. Potentially my whole week.
A beautiful black and white dog (a ratcha) asleep in the arms of their owner, under a fluffy blanket, with their tongue poking out.
November 11, 2024 at 12:22 PM
paulrjohnson.net
For reference, these three are on the bookshelf, and I've got The Effect and Causal Inference in R open in tabs in my browser right now too.
A closeup of multiple causal inference books on a shelf, among others about related topics. The three books are Cunningham's Causal Inference: The Mixtape, Pearl & Mackenzie's The Book of Why, and Rosenbaum's Causal Inference.
August 21, 2024 at 5:38 PM