The data suggest that players should serve big on the second serve as well as their first. And distinguished psychologist and Nobel Prize winner Daniel Kahnemann offers an explanation:

“People prefer losing late to losing early,” Daniel Kahneman, a Noble Prize-winning psychologist and professor emeritus at Princeton, wrote in an e-mail.

Some of Kahneman’s best-known research, with Amos Tversky, focused on decision-making and people’s aversion to risk, even when given identical potential outcomes.

“Imagine a game in which you have a 20 percent chance to get to the second stage and an 80 percent chance to win the prize at that stage,” Kahneman wrote. “This is less attractive than a game in which the percentages are reversed.”

But this is not an individual decision-making scenario, it is a game so we have to account for how the receiver will respond to the change in strategy by the server.   One model: the receiver has a budget of effort to expend on the two serves.  In the slow second serve and fast first serve scenario, he saves some effort for the second serve.  Hence, the first-serve win percentage for the server is large.  If the server serves hard on both serves, there is less incentive to save effort for the second serve as it is fast anyway.  So, transfer effort to the first.   For the server, the win percentage will go down on the first serve and up on the second.  I guess the server might be worse off as result.  No-one is imagining any of this is explicitly calculated by either player but perhaps learning by trial and error, a process that should work well in zero sum games, should find the optimum.

Who knows is this is realistic or formalizable.  But the qualitative point is the most important:  in a game when one player evaluates a change in strategy based on data, she should carefully think through the response of other players to her change.

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