Is Roger Federer more loss averse than Serena Williams?

I've really enjoyed watching the French Open tennis the last couple of weeks, and congratulations to Jelena Ostapenko and Rafael Nadal for their excellent wins. I especially like watching tennis because I can read a book in between points (and watching Nadal helps with this too, since he takes so long between points I can read a lot more!), and the payoff is likely to be a couple of quick book reviews on my blog (in spite of also reading a Terry Pratchett novel as well).

Anyway, the point of this post is in the title, which is also the title of a new paper published in the journal Applied Economics (ungated earlier version here), authored by Nejat Anbarci (Deakin University), Peren Arin (Zayed University in Abu Dhabi), Cagla Okten (Bilkent University in Turkey), and Christina Zenker (Zayed University). In the paper, the authors use data on the service speeds from 32 matches (19 men's; 13 women's) from the 2013 Dubai Tennis Championships, to investigate whether player efforts obeys Prospect Theory.

Prospect Theory was introduced by Daniel Kahneman and Amos Tversky in this 1979 paper. The theory suggests that not only are people loss averse (they value losses as much worse than they value equivalent gains), people are risk averse when they are in the domain of gains (relative to their reference point), but risk seeking when they are in the domain of losses. What that all means is that:

1. People will exert more effort to avoid losses than they will to capture equivalent gains; and
2. People will engage in more risky behaviour if they are 'behind' than if they are 'ahead'.

Anbarci et al. test this with their data. They have a measure of whether players are ahead or behind (based on the score in the current game, the current set, and the match overall), and a measure of player effort (their service speed). They find that:

...(i) a server will put more effort into his/her serve speed when behind in score than when ahead in score, (ii) players’ effort levels and thus serve speeds get less sensitive to losses or gains when score difference gets too large and (iii) overall servers will be more risk averse in the domain of gains than in the domain of losses.

This seems to support Prospect Theory. And when they look at male and female players separately, they find that:

...male players are more risk seeking in the loss domain as they increase serve speed when behind in set score while female players are more risk averse in the gain domain since they decrease serve speed when ahead in set score. Hence, although we find evidence for behaviour consistent with loss aversion for both males and females, its manifestation differs significantly between the two sexes.

So the results are not unequivocally in favour of Prospect Theory, but at least they are consistent with it. The only issue I see with the paper is that the sample size is relatively small, based on data from a single tournament. This means that, when the authors try to exclude other explanations for their results, the statistical insignificance of those findings is not altogether convincing. They also don't answer the actual question that is the title of their paper (and this post), but with sufficient additional data it might be possible to assess the loss aversion of individual players. Hopefully, some intrepid souls are following up this work with some more in-depth analysis involving many tournaments.