Predicting a penalty

cold → hot 🥅 The heat map behind the keeper: where penalties really go

A penalty is over in half a second, too fast for a keeper to react to the ball. So keepers guess before it is struck, and the best guesses come from data. In this lesson you will predict where a kick goes using the real patterns, then take penalties yourself.

Why this is a prediction problem

Split the goal into nine zones, three across and three high. "Where will the ball go?" is now a question with nine possible answers. Picking one is called classification, the same family as Lessons 2 and 3, just with nine classes instead of two.

A keeper cannot wait to see the ball; there is not enough time. So they play the odds, leaning the way the data says a shot is most likely. A model trained on thousands of past penalties learns exactly those odds.

The real numbers

Across analyses of thousands of professional penalties, the placement is far from random. The bottom corners are the most popular targets, dead centre is used least (keepers rarely stay still, but they usually dive), and the top corners are the hardest to save yet also the easiest to drag wide.

Figures are rounded from public analyses of large penalty datasets and vary by study; use them as a guide, not gospel.

Take the penalty

The grid below is shaded by how often penalties land in each zone (darker means more common). Predict where the next kick will go by clicking a zone, then take the penalty and see where it actually flies. Play a few and watch your accuracy climb as you learn to trust the data.

How a real model does better

Guessing a bottom corner every time is a decent baseline, but a real model does more. It uses features about this exact kick to shift the nine probabilities: which foot the taker uses, their run-up angle, the score in the game, and above all where this player has put past penalties. Feed those in and the model might say "72% chance bottom-left for this left-footer under pressure," and the keeper dives early with confidence.

This is the same toolkit from the whole course, pointed at one tiny, high-stakes moment. And it is real: elite keepers study these probability sheets before every shoot-out.

How it is actually done

The grid you just played with only knows the crowd average. A real penalty model is a small data pipeline that tailors those nine numbers to the exact kicker, the keeper, and the moment. Here is the whole chain.

1. The data it learns from

Analysts feed the model event data: every professional penalty on record, each one tagged with who took it, which foot, the keeper, the score and the minute, the run-up, and the zone the ball ended up in. Top clubs add tracking and pose data pulled from video, the taker's body angle and the keeper's early lean, captured frame by frame.

2. The features that matter

From that raw log, a handful of features do most of the work:

• Which foot and the favoured side: right-footers tend to open up one way, left-footers the other.
• Run-up angle and speed: a wide, fast approach often hints at power aimed for a corner.
• The taker's own history: where has this exact player put past penalties, especially under pressure?
• Game state: the score, the minute, and whether it is a shoot-out all tug on nerves and choices.
• The keeper: some dive early, some wait, some quietly favour a side.

3. The models that turn features into odds

Predicting one of nine zones is multiclass classification. The gentlest model for it is the direct big sibling of Lesson 2's logistic regression, called softmax. Logistic regression squashes into one probability; softmax spreads scores across all nine zones so they add up to 100%:

Each zone $j$ gets a score $z_j$ from the features, and softmax turns the nine scores into nine probabilities. That is the core idea. In practice, teams reach for a few model families:

• Softmax (multinomial logistic regression): the nine-class version of Lesson 2. Quick to train and easy to explain to a coach.
• Tree ensembles (random forests, gradient boosting, XGBoost): Lesson 3's decision trees, hundreds of them voting together. On messy tabular data like "foot, angle, history, score," these are usually the strongest, and the analyst's default.
• Neural networks with computer vision: Lesson 5's networks reading video of the run-up and body shape, catching tells a table never records. Reading the body this way is called pose estimation.

Turn counts into odds yourself

Before any fancy model, the core move is simply turning past counts into probabilities. Press Run to watch the nine zone counts become a clean set of odds that add up to 100%.

import numpy as np

# how often past penalties landed in each of the 9 zones (a 3x3 grid)
counts = np.array([[ 9,  3, 11],
                   [13,  6, 13],
                   [19,  7, 19]])

# turn counts into probabilities: divide each by the total
probs = counts / counts.sum()

print("Chance the ball lands in each zone (%):")
print((probs * 100).round(1))
print("Best single guess: a bottom corner at 19%")

Chance the ball lands in each zone (%):
[[ 9.  3. 11.]
 [13.  6. 13.]
 [19.  7. 19.]]
Best single guess: a bottom corner at 19%

A real model does the same thing, then bends each number using the features above, which is how the flat heat map at the top of this lesson becomes a sharp read for one exact kick.