This paper investigates what students understand about algorithm efficiency before receiving any formal instruction on the topic. We gave students a challenging search problem and two solutions, then asked them to identify the more efficient solution and to justify their choice. Many students did not use the standard worst-case analysis of algorithms; rather they chose other metrics, including average-case, better for more cases, better in all cases, one algorithm being more correct, and better for real-world scenarios. Students were much more likely to choose the correct algorithm when they were asked to trace the algorithms on specific examples; this was true even if they traced the algorithms incorrectly.