There is a prevailing view in both the academic literature and the popular press that firms need to behave more entrepreneurially. This view is reinforced by a stylized fact in the innovation literature that R&D productivity decreases with size. However, there is a second stylized fact in the innovation literature that R&D investment increases with size. Taken together, these stylized facts create a puzzle of seemingly irrational behavior by large firms--they are increasing spending despite decreasing returns. This paper is an effort to resolve that puzzle. We propose and test two alternative resolutions: 1) that it arises from mismeasurement of R&D productivity, and 2) that firm size endogenously drives R&D strategy, and that the returns to R&D strategies depend on scale. We are able to resolve the puzzle under the first tack--using a recent measure of R&D productivity, RQ, we find that both R&D spending and R&D productivity increase with scale. We had less success with the second tack--while firm size affects R&D strategy in the manners expected by theory, there is no strategy whose returns decrease in scale. Taken together, our results are consistent with the Schumpeter view that large firms are the major engine of growth, they both spend more in aggregate than small firms, and are more productive with that spending. Moreover the prescription that firms should behave more entrepreneurially, should be treated with caution--one small firm strategy has lower returns to scale than its large firm counterpart.