Simpson's paradox with two trading regimes
Asked at DE Shaw
Two execution strategies were evaluated over a year that contained calm and volatile days. Win rates:
| Calm days | Volatile days | Overall | |
|---|---|---|---|
| Strategy A | 80/100 (80%) | 200/1000 (20%) | 280/1100 (25.5%) |
| Strategy B | 780/1000 (78%) | 18/100 (18%) | 798/1100 (72.5%) |
Strategy A wins more often than B on calm days (80% vs 78%) and on volatile days (20% vs 18%), yet B's overall win rate crushes A's (72.5% vs 25.5%).
Explain the paradox. Which strategy is actually better, and what is the general lesson?
Show a hint
Look at which days each strategy was used on. The group sizes are wildly unbalanced, and in opposite directions.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.