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Optiver·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Apr 2026

Summary

Quant Engineer round at Optiver with a pretty gnarly probability/statistics question dressed up as a sports analytics problem. No fluff, just math and reasoning under pressure.

Questions Asked (1)

Q1

You're given a full round-robin results table for five soccer teams. For an upcoming match between two of them, rank three events by probability: one team wins, the match draws, or total goals exceed 2.5. Justify your ordering using the empirical data from the table.

Product Analytics & MetricsTechnical Trade-offsAlgorithms & Data Structures
Author's notes

This one wrecked me a little.

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AI HintsAI Generated

Suggested Approach

First, extract relevant statistics from the round-robin table: for the two teams, compute their average goals scored and conceded, and the frequency of draws and high-scoring games in their matches. Then, use these empirical frequencies to estimate the probability of each event, and rank them accordingly. Clearly state any assumptions, such as treating historical frequencies as probabilities.

Pro tip: Emphasize that you're using empirical data, not assumptions, and that you'd validate with more data if available. This shows analytical rigor and awareness of limitations.

1. Extract relevant data

From the round-robin table, isolate all matches involving the two teams. For each, note the goals scored by each team and the match outcome (win, draw, loss).

2. Compute team statistics

Calculate each team's average goals scored and conceded, as well as their win/draw/loss rates. Also compute the overall frequency of draws and matches with total goals > 2.5 in the entire table or for these teams.

3. Estimate event probabilities

Use the statistics to estimate the probability of each event: P(Team A wins), P(draw), P(total goals > 2.5). For example, use the teams' scoring rates to estimate expected goals and then apply a Poisson model, or use historical frequencies directly.

4. Rank and justify

Compare the estimated probabilities and rank the three events from most to least likely. Justify your ranking by referencing the empirical data and any assumptions made.

Key Points to Mention

  • Use of empirical frequencies from the table as probability estimates
  • Calculation of average goals scored and conceded for each team
  • Consideration of draw frequency in the league or between the teams
  • Estimation of total goals > 2.5 using historical scoring rates
  • Assumption that past performance is indicative of future results
  • Acknowledgment of small sample size and potential need for more data

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.