A recent paper by Jeffrey Ely (Northwestern University), Romain Gauriot (University of Sydney), and Lionel Page (Queensland University of Technology), published in the Journal of Economic Psychology (sorry I don't see an ungated version) provides us with some answer. The authors look specifically at the risk behaviour of servers on first and second serve:
When serving, players can opt for risky serves which are more likely to fail but are harder to return if successful or more conservative serves which are less likely to fail but are also easier to return.The key is whether players behave differently on first and second serves (more on that in a moment). However, simply comparing first and second serves is not so straightforward. The authors correctly note that there is:
...a potential caveat with raw data on tennis serve: it can be characterised by a selection problem. First serves are always observed while second serves are only observed when the first serve failed. This means that second serves may be more likely to be observed when serving is harder than usual either for natural reasons (e.g wind conditions), fitness (e.g. tiredness late in the match) or strategic reasons (e.g. opponent having learned how to return the player’s serve).Their solution is quite ingenious:
To cleanly compare first and second serves one ideally wants to observe some random events which determines in a given situation whether a serve is going to be a first or a second serve. We argue that such a situation occurs when the ball hits the tape (top of the net) on the first serve. The impact with the net gives the ball an unpredictable trajectory leading the ball to be either in or out. It introduces the required randomness as a first serve follows a ball let which lands in the court and a second serve follows a ball which lands outside the court.The serve immediately following a 'let serve' is randomly either a first serve (if the 'let serve' landed in) or a second serve (if the 'let serve' landed out). Ely et al. use a dataset from 3,188 matches, involving over 690,000 serves, of which 7,605 follow a 'let serve' and are the core sample of interest. They test four conditions which would imply that players are correctly maximising their chance of winning:
- That first serves are more risky than second serves (the probability that a serve lands in is lower for first serves);
- That first serves are harder to return than second serves (players are more likely to win the point on their first serve);
- Using two first serves is a suboptimal strategy (it leads to a lower probability of winning the point); and
- Using two second serves is also a suboptimal strategy.
They find that:
...the serves from professional tennis players meet four conditions which make them consistent with the optimal strategy of risk taking between first and second serves. This result is observed both overall and when splitting the sample by gender and ranking.So, it appears that professional tennis players are optimisers. Which we should expect - they are trained professionals who have developed skills in strategic play over many years.