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Model Soccer Shot Conversion

GoogleData Scientist · Technical Screen
HardData ScientistTechnical ScreenMachine Learning

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This problem tests the ability to design an end-to-end predictive model for sports events, focusing on feature engineering, handling spatial data sparsity, and evaluating probabilistic outputs.

Scenario

You are a Data Scientist at a sports analytics firm. You have been tasked with building an 'Expected Goals' (xG) model for soccer. An xG model calculates the probability that a specific shot will result in a goal based on the circumstances under which the shot was taken.

The Dataset

You are provided with a dataset of 500,000 recorded shots from professional leagues. Each record includes:

  • shot_coordinates: (x, y) coordinates on a 105x68 meter field.
  • angle_to_goal: The shooting angle relative to the center of the goal.
  • distance_to_goal: Euclidean distance from the center of the goal.
  • defender_proximity: Distance to the nearest defender.
  • is_header: Boolean flag.
  • goal_scored: Binary outcome (Target).
  • game_minute: Time in the game.

Your Task

  1. Propose a modeling strategy to estimate the probability P(goal=1 | features). Explain how you would transform the raw shot_coordinates into meaningful features that account for the non-linear relationship between location and scoring probability.
  2. How would you address the 'sparsity' problem, where shots taken from extreme angles or very far distances have very few historical examples?
  3. Define a proper loss function for this model. Why is Accuracy or Mean Squared Error (MSE) potentially insufficient for this specific use case?
  4. How would you calibrate the model to ensure that if the model predicts a 0.20 probability of a goal across 1,000 shots, approximately 200 goals are actually scored?

Hints

Hint 1

Consider creating features like the log-distance or interaction terms between angle and distance to better capture the 'danger' zones on the pitch.

Hint 2

For calibration, look into isotonic regression or Platt scaling to map raw model scores to true probabilities.

Hint 3

Brier Score or Log-Loss are preferred here as they reward confidence and penalize divergence from the actual probability distribution of outcomes.

Follow-up questions

  • How would you handle 'data leakage' if you accidentally included the 'goalkeeper_save' variable in your training set?
  • If the team wants to use this model to evaluate player performance, how do you distinguish between 'luck' (a player scoring a low-xG shot) and 'skill'?
  • How would you adjust the model if the team wants to account for the 'game state' (e.g., if a team is losing, they might take more low-probability shots out of desperation)?