Do agents maximise? Risk taking on first and second serves in tennis

•We investigate whether top agents are able to optimally make risk-return trade-offs.•We look at the tennis players’ ability to choose the degree of risk on their first and second serves.•We use a large data set on ball tracking in tennis matches.•We isolate “let” serves as creating the setting for a quasi-experiment.•We find that male and female players respect 4 conditions derived from a small model of risk return trade-off.