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This is a easy difficulty Statistics & Math question, commonly asked during Onsite rounds at Waymo.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Waymo during technical interviews.

Model wins-until-failure and expected future wins

Quick Overview

This question evaluates probabilistic modeling and statistical inference skills for censored time-to-event performance data, focusing on estimating player-specific win probabilities and predicting expected future wins from observed "wins before first loss" records.

You are given a DataFrame df where each row summarizes a player’s performance until their first loss.

Input

df columns:

player_id (string/int)
wins_before_first_loss (int, $k\ge 0$ ): number of consecutive wins observed before the first loss occurred

Interpretation: for each player, you observed a sequence of games that ended with a loss, e.g., WWW...WL, and wins_before_first_loss = k.

Questions

Compute the expected number of additional wins before the next loss for each player.
- You may assume each player has an underlying win probability $p_i$ that is constant across games.
- Show how you would compute this expectation from the observed data (code/pseudocode is fine).
Propose a probabilistic model for wins_before_first_loss and explain how you’d estimate parameters.
Given a plot of the computed expectations across players (distribution/shape), interpret what it suggests (heterogeneity, outliers, model misfit).
How would you evaluate the model and use it to make a decision (e.g., ranking players, allocating resources, setting thresholds)?

Quick Overview

You are given a DataFrame df where each row summarizes a player’s performance until their first loss.

Input

df columns:

player_id (string/int)
wins_before_first_loss (int, $k\ge 0$ ): number of consecutive wins observed before the first loss occurred

Interpretation: for each player, you observed a sequence of games that ended with a loss, e.g., WWW...WL, and wins_before_first_loss = k.

Questions

Compute the expected number of additional wins before the next loss for each player.
- You may assume each player has an underlying win probability $p_i$ that is constant across games.
- Show how you would compute this expectation from the observed data (code/pseudocode is fine).
Propose a probabilistic model for wins_before_first_loss and explain how you’d estimate parameters.
Given a plot of the computed expectations across players (distribution/shape), interpret what it suggests (heterogeneity, outliers, model misfit).
How would you evaluate the model and use it to make a decision (e.g., ranking players, allocating resources, setting thresholds)?

Model wins-until-failure and expected future wins

Quick Overview

Input

Questions

Solution

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Model wins-until-failure and expected future wins

Quick Overview

Input

Questions

Solution

Comments (0)