The strategy that wins in every regime but loses overall

Question

A desk compares a New strategy (N) against the Old one (O), counting a day as a win if it ends profitable. They split days into calm and volatile markets.

Calm days: N wins 95 of 100 (95%); O wins 180 of 200 (90%).
Volatile days: N wins 130 of 200 (65%); O wins 55 of 100 (55%).

Pooling everything, N wins 225 of 300 (75%) while O wins 235 of 300 (about 78%), so O looks better overall.

Which strategy is actually better, and why does the pooled table point the other way?

Accepted Answer

Strategy N is better. It beats O on calm days (95% versus 90%) and on volatile days (65% versus 55%). It wins more often in every market condition. The pooled comparison reverses this, a pattern known as Simpson's paradox, and the reversal is caused by a confounder. The confounder is market regime. Volatile days are simply harder: everyone's win rate is lower there. Notice how the two strategies were tested on very different mixes of days. N was run mostly on the hard volatile days (200 of its 300 days), while O was run mostly on the easy calm days (200 of its 300 days). So O's pooled number …

The strategy that wins in every regime but loses overall

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