糖心TV

Larger samples yield more precise estimates by reducing variability around the true value. We examine whether sophisticated agents adhere to this foundational statistical principle when forming beliefs in a real-world, high-stakes setting. Specifically, we use tennis betting markets as a quasi-natural laboratory that offers three key advantages: bookmakers are highly incentivized professionals; their beliefs can be directly inferred from their quoted odds; and match length varies exogenously across tournaments, playing a role analogous to sample size, as longer matches reduce randomness, making outcomes more reliably reflective of underlying skill. We find that professional bookmakers exhibit sample size neglect, leading to systematic biases in their beliefs and lower profits. A laboratory experiment shows that this bias is twice as large among students, who are less sophisticated with lower incentives than bookmakers. Moreover, we find that match length is incorporated in beliefs more strongly when it becomes more salient. Finally, extending to financial markets, we show that while the consensus analyst forecast is more predictive of earnings when based on more analysts, stock prices seem to underreact to the component of forecasts attributable to analyst coverage. Overall, our results suggest that sample size neglect leads to systematic biases in the beliefs of sophisticated agents even in relatively simple settings.