Simpson's paradox: the sharper agent with the lower resolution rate

Question

Two support agents are compared by first-contact resolution rate (resolved on first contact / tickets), split by ticket complexity:

	Simple tickets	Complex tickets	Overall
Nova	96/100 (96%)	450/900 (50%)	546/1000 (54.6%)
Orion	855/900 (95%)	45/100 (45%)	900/1000 (90%)

Nova resolves more simple tickets (96% vs 95%) and more complex tickets (50% vs 45%) on first contact, yet Orion's overall rate is far higher (90% vs 54.6%).

Which agent is more effective, and explain the paradox.

Accepted Answer

This is Simpson's paradox. The confounder is ticket complexity: first-contact resolution is easy on simple tickets (about 95 to 96 percent) and hard on complex ones (about 45 to 50 percent), and the two agents handle opposite mixes: - Nova is routed 900 of 1000 complex tickets, the hard queue. - Orion handles 900 of 1000 simple tickets, the easy queue. Orion's higher overall rate reflects what it is handed, not sharper support. The overall rates are complexity-weighted averages: 	ext{Nova: } 	frac{100}{1000}(0.96) + 	frac{900}{1000}(0.50) = 0.546, \qquad 	ext{Orion: } 	frac{900}{1000}(0.…

Simpson's paradox: the sharper agent with the lower resolution rate

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