Tournaments are widely used in the economy to organize production and innovation. We study individual data on 2775 contestants in 755 software algorithm development contests with random assignment. The performance response to added contestants varies nonmonotonically across contestants of different abilities, precisely conforming to theoretical predictions. Most participants respond negatively, whereas the highest-skilled contestants respond positively. In counterfactual simulations, we interpret a number of tournament design policies (number of competitors, prize allocation and structure, number of divisions, open entry) and assess their effectiveness in shaping optimal tournament outcomes for a designer.