The 2022 World Cup left a public dataset of shots on target with coordinates, body part, type of play and whether the keeper saved. I wanted to answer a question that sounds simple: given a shot, what is the probability the keeper stops it, and where should the keeper be waiting?
Why logistic regression
With 577 labelled shots, a complex model learns the noise. But the main reason was another: I wanted a model whose coefficients I could read. Logistic regression tells you, for each variable, how much it changes the log-odds of a save: distance, angle, foot or head, set piece. A coach can argue with that; with a neural network, they cannot.
That decision connects with what I was learning in Probability II: logistic regression is not a machine-learning recipe but a generalized linear model with a link function, and its coefficients are estimators with variance.
Honest uncertainty with Monte Carlo
A point probability misleads. With small samples, the difference between 62 % and 68 % may be noise. I used Monte Carlo over the model parameters to obtain, for each shot, not a number but a distribution of save probabilities, and reported bands instead of single values. Watching the bands widen in the areas of the pitch with few shots was the project’s best statistics lesson.
Entropy and the grid search
The second question was positioning. I defined a grid of possible keeper positions and, for each shot, evaluated the save probability depending on where the keeper stood. Then I used the entropy of the outcome distribution to identify the zones where the keeper’s decision changes the result most, that is, where positioning genuinely matters, versus zones where the shot is almost a goal or almost a save whatever the keeper does.
The result is a map: for each shooting zone, a recommended position and a confidence level. It is not a system for a professional league; it is a prototype that turns a model into an actionable recommendation, which was the goal.
What I take with me
That choosing the simplest model that answers the question is an engineering decision, not a lack of ambition. That reporting uncertainty is more honest and more useful than reporting a number. And that an analysis is finished when it produces a decision, not when it produces a metric.