Are Tennis Players Loss Averse? Field Evidence of Loss
Aversion in a High Stakes Environment
N0307949
This research project is submitted in part fulfillment of the degree of Bachelor of Arts
(Honours) Business Economics
Nottingham Trent University
Nottingham Business School
Summer 2014
Chosen Target Peer-Refereed Academic Journal:
American Economic Review
Declaration
I declare that I have personally prepared this paper and that it has not, in whole or in part,
been submitted as an assessment for any other module, degree or qualification. The work
here is my own, carried out personally unless otherwise stated. All sources of information,
including quotations, are acknowledged by means of appropriate referencing.
I declare that this project has been conducted in accordance with Nottingham Trent
University’s Regulations on Academic Irregularities, including those pertaining to research
ethics and Data Protection legislation.
Although experimental studies have documented systematic decision errors, many leading
scholars believe that experience, competition and large stakes will reliably extinguish
biases. We test for the presence of a fundamental bias, loss aversion, in a high-stakes
context: Professional tennis players performance in the 2013 Majors. Tennis provides a
natural setting for loss aversion because tennis players have the expectation the player to
hold their own service game. We find that in a competitive environment, even the best male
tennis players show evidence of loss aversion but salient reference point’s may change in
women’s tennis.
JEL Classifications: D03, D81, L83
Key words: Behavioral Economics; Prospect theory; Loss Aversion; Statistics
Loss aversion is a well-observed psychological decision displaying people’s preferences
when choosing between losses rather than acquiring gains. “The central assumption of the
theory is that losses and disadvantages have a greater impact on preferences than gains
and advantages” (Tversky, Kahneman, 1991. P. 1039). The same objective is the trigger for
risk aversion, where people evaluate the outcome in context of similar gains and losses; we
see a tendency to avoid losses to making gains.
Loss aversion is a psychological bias, which contradicts rational behavior. It is part of many
behavioral anomalies described throughout behavioral economics. Traditional economic
theory assumes rational individuals make objective decisions to maximize utility. It is
acknowledged that people cannot perfectly maximize their utility, but the deviations from
rational behavior are argued to be random. There are no further discussions of consistent
biases in this context. Behavioral economists take into account these deviations and have
developed models to test these consistent biases, allowing for natural human behavior that
is not considered in traditional economic theory. Factors such as inefficiency, impatience,
making decisions under pressure, and overconfidence are deviations from traditional theory
and an individual’s rational behavior. Key variables such as loss aversion need to be
considered if economists are to fully understand the economic decision making of
individuals.
Research by Israeli psychologist Daniel Kahneman and Amos Tversky marks the beginning
of behavioral economics as a significant field. Their publication of the paper “Prospect
Theory: An Analysis of Decision under Risk” (Tversky, Kahneman, 1979) is well recognized
and considered a seminal paper in this field. The paper constructs a framework modeling
how people frame economic outcomes as gains and losses and the effect this will have on
future economic decisions. Prospect theory therefore is a key topic within behavioral
economics, showing consistency with a number of observed biases that traditional model’s
of utility cannot explain.
We can regard the prospect model as descriptive, as it models real life choices rather than
optimal decisions. The theory can be seen as a psychologically more accurate description of
decision-making. Where expected utility theory shows a rational individual is indifferent to
the reference point, loss aversion takes this into account. Numerous studies have shown
that people feel losses more deeply than gains of the same value (Kahneman and Tversky
1979, 1991).
There is a significant amount of literature suggesting individuals violate standard economic
assumptions. Despite this, scholars including: List (2000), Levitt and List (2008) remain
skeptical to the idea. Critics of behavioral economic literature disregard the notion that
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biases persist in markets, and believe they are likely to be eliminated through competition,
large stakes and experience. Levitt and List (2008. P. 909) describe the challenges
associated with the bias literature; “Perhaps the greatest challenge facing behavioral
economics is demonstrating its applicability in the real world. In nearly every instance, the
strongest empirical evidence in favor of behavioral anomalies emerges from the lab. Yet,
there are many reasons to suspect that these laboratory findings might fail to generalize to
real markets”.
This research paper examines field evidence of loss aversion, a fundamental bias and key
component of Prospect Theory (Kahneman, Tversky, 1979). By considering a market with
high stakes and experienced agents, the four Grand Slam Tournaments (also known as the
Majors) we set out to find that a degree of loss aversion persists for professional tennis
players. The Majors are the most important annual tennis events and offer the most ranking
points, prize money, and also attract the most public and media attention. In each
tournament, players are rewarded for the number of matches they win, with each match
seeing them progress further through the tournament with the ultimate goal of reaching,
and winning the final. To achieve this, the player must win the minimum number of points,
games and sets respectively before the opponent to win the match and progress forward in
the tournament, seeing their winnings roughly doubling on average with each new round
(Wimbledon, 2013).
Botond Ko, Szegi and Rabin (2006) have recently completed theoretical work that has
conceptualized the expectations as reference points. There is little work that has directly
tested this theory in field settings. With consideration on how to measure loss aversion
within the sport of tennis, we discuss rational and irrational behavior and collect data
samples for both men and women from the four Grand Slam tournaments in 2013.
We aim to find and examine any degree of loss aversion within the sport of tennis by
addressing the following research questions: A. Is there field evidence of loss aversion
within the sport of tennis? B. Are there differences in the degree of loss aversion between
male and female players?
Prospect theory will be a foundation pillar of this research paper, contributing towards the
research completed by Daniel Kahneman and Amos Tversky (1979). Furthermore, this
paper will be supporting the research completed by Pope and Schweitzer (2011). Their
paper “Is Tiger Woods Loss Averse? Persistent Bias in the Face of Experience, Competition,
and High Stakes” finds field evidence showing that even professional golf players experience
loss aversion.
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The rest of this paper is structured as follows; Section I. outlines existing literature on
Prospect theory and Loss Aversion, and also explains the field setting of tennis and the
sport that is played. Within section II. we provide a methodological approach and
hypotheses. In section III. we complete analysis on our dataset with section IV. Evaluation
and discussion. Section V. concludes.
I. Background on Loss Aversion and Tennis
A. Prospect Theory and Loss Aversion
The earliest literature that draws on the idea of behavioral decision-making was highlighted
by Adam Smith’s (1759) publication of The Theory of Moral Sentiments. Smith argued that
behavior was influenced by a combination of what he referred to as “Passion” and “Impartial
spectator”. Smith believed that behavior was under the influence of passions, but that
people could override passion-driven behavior by viewing their own behavior from the
perspective of an outsider; the impartial spectator, a “moral hector who, looking over the
shoulder of the economic man, scrutinizes every move he makes” (Grampp, 1948, p. 317).
Behavioral economics was taken further in Herbert Simon (1955) completed research on
what he called “bounded rationality” selling it as a solution to describe how humans do not
possess infinite decision making capabilities.
In this research project, we will examine field evidence of loss aversion, which is a key
component of Prospect Theory. Kahneman and Tversky (1979) propose that instead of
making consistent decisions over final wealth states, economic agents evaluate decisions in
isolation in relation to a crucial reference point. The paper “Choices, Values and frames”
(Kahneman and Tversky, 1983) considers the relation between decision values and
experience values. It concludes that although the hedonic reference point is largely
determined by the objective status quo, it is also affected by expectations and social
comparisons.
When considering Prospect Theory, Kahneman and Tversky (1979) suggest a theory of
choice that is reference-dependent, meaning economic agents value gains differently than
they value losses, in two key ways. The first is loss aversion, where an economic agent
value losses higher than they would value gains; with the “value function” kinked at the
reference point with a steeper gradient for losses than gains. The second explanation is that
economic agents are risk seeking in losses and risk averse in gains – we can refer to this as
a risk shift. This can be demonstrated with a convex utility function in the loss domain and
concave in the gain domain.
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The model described above has various implications associated with reference dependent
preferences. If economic agents were to separate two related decisions, the outcomes
chosen may differ. For example, loss aversion and the risk shift may cause an individual to
reject a series of small gambles with positive expected return but accept the aggregated
gamble. Shlomo Benartzi and Richard H. Thaler (1995) studied this obstacle with regards to
pension funds. Benartzi and Thaler (1995) found that people who evaluated their portfolios
frequently (and therefore made a series of related decisions) made different hypothetical
choices than did people who evaluated their portfolios infrequently.
In the simplest study showing reference-dependence, Knetsch (1992) endowed some
subjects randomly with a mug, while others received a pen. Both groups were allowed to
switch their good for the other at a minimal transaction cost, by merely handing it to the
experimenter. If preferences are independent of random endowments, the fractions of
subjects swapping their mug for a pen and the fraction swapping their pen for a mug should
add to roughly one. In fact, 22 percent of subjects traded. The fact that so few chose to
trade implies an exaggerated preference for the good in their endowment, or distaste for
losing what they have.
Read, Loewenstein, and Rabin (1999) studied the issue of separating decisions extensively
and applied the term “narrow bracketing” to describe how individuals segregate related
decisions. Loss aversion has been documented in many laboratory settings (Thaler et al.
1997, Gneezy and Potters, 1997) and in several field settings (David Genesove and
Christopher Mayer 2001; Camerer et al. 1997; Fehr and Goette 2007; Odean 1998, and
Mas 2006). Scholars such as List (2003, 2004) however, have found evidence to suggest
that experience and large stakes may eliminate decision errors.
Kahneman, Knetsch and Thaler (1991) summarize that after more than a decade of
research, the endowment effect, status quo bias and loss aversion are both robust and
important to this field of study. To summarize, current research of choice under uncertainty
(Kahneman and Tversky, 1979, 1984) finds that the outcomes of risky prospects are
evaluated by a value function which has three important characteristics – Reference
dependence (The carriers of value are gains and losses defined relative to a reference
point), Loss Aversion (the function is steeper in the negative that the positive domain,
losses loom larger than corresponding gains) and diminishing sensitivity (the marginal value
of both gains and losses decrease with their size – these properties give rise to the
asymmetric S-shaped value function, concave above the reference point and convex below
it.
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More recently, Barberis (2013) has reflected on the application of prospect theory in his
paper “Thirty Years of Prospect Theory in Economics: A Review and Assessment”. Barberis
describes how prospect theory is still widely viewed as the best available description of how
people evaluate risk in experimental settings. However there are few broadly accepted
applications of prospect theory in economics. Some argue it has relevance in laboratory
settings only, however it difficult of to apply this theory to field settings. Barberis concludes
that more recently prospect theory has been incorporated into more traditional models of
economic behavior and empirical evidence is seeing progress (Barberis, 2013).
Research completed by Pope and Schweitzer (2011) finds field evidence of loss aversion in a
competitive setting, the PGA Tour. Their paper looks into whether golf players are loss
averse and finds that even the best golfers, including tiger woods, show evidence of loss
aversion. Their research on putts from the PGA Tour between 2004 and 2009 found that a
disproportionate number of putts for par were completed successfully compared with
attempts for a birdie. After analyzing 2,525,161 putts 82.9 percent of putts for par were
successfully completed compared against 28.3 percent putts for birdie completed. Allowing
for deviations in the putt difficulty and other variables, golfers still putted 3.7 percent more
shots for par compared to birdies. Therefore we see loss aversion remains a constant bias
and influential factor in a high stakes market.
There is also relevant literature that considers an economics approach with emphasis on
statistical probability and behavior useful to this research paper. O’Malley, (2008)
constructs probability formulas for winning a game in a tennis match, at different milestone
stages including winning a tiebreaker, winning a set, winning a match and recovering from a
break of serve. He also explores his assumption in constructing these tennis probability
formulas that the outcome of each point is identically and independently distributed, and
when during a tennis match this assumption could be violated.
Paserman (2007) uses data from Grand Slam tournaments to assess whether men and
women respond differently to competitive pressure in a real-world setting with large
monetary rewards. Paserman finds that the performance of both men and women
deteriorates in the final and decisive set, with women’s performance more pronounced than
that of men. He also discovers that as the importance of the point increases, the propensity
of women to commit unforced errors increases significantly, whereas men remain
unaffected by point importance.
This research paper aims to contribute to the literature of prospect theory and loss aversion
by testing our hypotheses using secondary data from a competitive field setting with large
stakes and very experienced agents. We hope to provide field evidence to add to the
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literature surrounding prospect theory (Kahneman, Tversky 1979) and support the findings
of Pope and Schweitzer. (2011). In addition, we will explore whether or not reference
point’s change based upon expectations (Koszegi and Rabin 2006).
B. Professional Tennis
The Grand Slam Tournaments, also known as the Majors, consists of the Australian Open,
French Open, Wimbledon and US Open. The Australian and US tournaments are played on
hard courts, the French on clay, and Wimbledon on grass. Wimbledon is the oldest, founded
in 1877, followed by the US in 1881, the French in 1891, and the Australian in 1905.
However, of these four, only Wimbledon was a major before 1924/25, the time when all
four became designated Grand Slam tournaments.
The majors bring professional tennis players together to play in a series of matches each
year. In Grand Slam tournaments men’s professional tennis players play the best three out
of five sets and women’s professional tennis players play the best 2 out of 3 sets. To win a
set, a player must win six games. If the score becomes five-games-all, a player must be
two games ahead to win a set. However, until the 1970’s, this meant sets could potentially
last indefinitely. Therefore in 1971 the All England Club introduced the tiebreak rule where
at six-games-all a tiebreak is played to decide who wins a set.
A tiebreak is played in all but the last set in tennis, the third set for women and fifth set for
men respectively. The player whose serve it is in the set continues their serve, followed by
two points played on the opponents serve. Following on the serve rotates back to each
player after every two further point until the tiebreak is over. The first player to reach seven
points wins the tiebreak and the set. For the purposes of this paper we have excluded any
points won/lost in tie breaks because they serve no relevant purpose to our analysis
comparisons.
Lastly, to win a game, the first player to win four points wins a game. The exception is if
both players win three points, this is called deuce. The winner is the first player to then win
two points in a row. A player therefore who has won one, two and three points has score,
15,30, and 40 respectively. A player who has not won any points is at “love”; e.g. three
points to zero is read as “forty-love”. If both points the score is duce and from this point the
game continues until one player has a two-point lead; a player who is one point ahead in
the game after the game has reached deuce has the “advantage”. If the serving player is
one point away from winning a game, the point is referred to as a “game point”; if the nonserving player is one point away from winning a game, the point is referred to as a “breakpoint”.
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Each tournament is initiated with 128 players and each player is then matched to another
With each match come’s a winner and a loser, the loser is then knocked out of the
competition. The 32 most likely players to win are seeded and arranged in the draw to
ensure no seeds meet in matches until the third round. The winner therefore progresses
forward in the tournament similar to a knockout style until two players emerge to play the
final. Each player who is seeded into any Grand Slam Tournament shares the total purse for
the tournament. (In 2013 the total purse for Wimbledon was approx. £8.5M). The
distribution of payments is highly convex, for example the winner typically earns 18 percent
of the purse (Wimbledon, 2013).
Tennis players switch service after each game is played, despite whoever won the previous
game. In a regular game, one player serves for the entirety. Within our methodology
section we discuss how a slower second serve is rational play. We shall therefore consider a
different measurement of loss aversion in tennis, explained in below. To the best of our
knowledge, this is the first paper that aims to provide empirical evidence of loss aversion
within tennis.
II. Methodology
In context of prospect theory, the first prospect tennis players would face is a compound
prospect, the first serve. This would then have two outcomes; the player will win or lose the
point. If the serve was out, then the player will face another prospect associated with the
second serve again with two outcomes, win or lose the point. Therefore, the first prospect is
whether the serve is in or not. If it is in, this will lead to a second prospect relating to how
the ensuing point is played. If the first serve is out, the player will face a second prospect
that leads to two outcomes. The point will be lost if the serve double faults, or if it is in the
player will gain another prospect relating to how the point is played.
We explore the possibility of measuring loss aversion in a highly observational frame, the
first and second serve speed within a tennis match. A fast first serve is observed followed
by (if the serve is a fault) an almost always-slower second serve. If a compiled data set
showing the relationship between first and second serve provided evidence on our predicted
observations, this would prove tennis players are loss averse. This is because we would
assume a rational player would maximize their probability of winning his service game by
playing two ‘first serves’.
In reality, a player is faced with a wide variety of compound prospects, each representing
different combinations of first and second serve speeds, followed by how any points will be
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played if the serve is in. A perfectly rational player therefore will select the prospect with
the optimal combination of first and second serve speeds to maximize their probability of
winning a point. With a large amount of data showing most players do not hit two ‘first
serves’, we must consider whether this is rational behavior. A simple framework can be
constructed to describe the variety of serves a tennis player can utilize and actually show
that two first serves would actually be irrational behavior.
Let 𝑥 be the likelihood the serve goes in and the point is lost and 𝛾 the likelihood the serve
goes in and the point is won. The probability of a fault, the serve goes out is therefore
represented by 𝑥 + 𝑦 ≤ 1 and 1 − (𝑥 + 𝑦). The combination of (𝑥, 𝑦)therefore represents the
variety of serves that can be used by the player.
Using this framework, the second serve should have the highest value of 𝑦 of all possible
serves that can be made. Assuming professional tennis players remain competitive, we can
disregard any behavioral anomalies which would violate the assumptions made in this
framework making tennis players less competitive during their second serve. Such
anomalies would include behavior such as remaining in the point, avoiding giving away free
points and ‘playing it safe’ beyond the extent to which those factor into maximizing 𝑦 the
probability of the serve going in and winning.
However, we cannot conclude theorizing that the second serve should be as optimal as the
first serve because the first serve needs to be actually worse. Not just 𝑦 is important on the
first serve because a second serve is available to the player as a back-up. Players will
leverage their second serve because if a point is lost it might as well come from a faulted
first serve rather than a first serve that goes in but is lost in the second prospect, the
ensuing point that is played.
Therefore, if the second serve is maximizing 𝑦, the first serve has to have a lower 𝑦
resulting in a lower 𝑥. Players will therefore play an intentionally risky first serve, which is
often more decisive, (resulting in an ace) and be willing to fault more to achieve this. The
optimal first serve would theoretically reduce 𝑥 to zero with no reduction of 𝑦. Furthermore
a player would not want to reduce 𝑦 to zero either. A margin is established through a
calculated rate of substitution of 𝑥 and 𝑦, therefore resulting in a very fast first serves and
slower second serve.
As a result, we can conclude that by observing a faster first serve and slower second serve
by almost all tennis players, this behavior is rational through the prospects a tennis player
faces and substitution of 𝑥 and 𝑦 to maximize their chances of winning the ensuing point.
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We shall therefore focus our measurement of loss aversion in a similar fashion to the work
of Pope and Schweitzer (2011) who compare the accuracy of play, and therefore
concentration and effort between two scenarios, putting for par and putting for birdie. They
found evidence of loss aversion because golf players exert a higher level of concentration
and effort when putting for par, rather than for birdie. Both putts should be of equal value –
in context of loss aversion as a golf player is rewarded on how many shots above or below
par they complete the course. Therefore in terms of framing, the golf player values losing a
putt for par higher than losing a putt for a birdie.
If we apply this methodology to tennis, we can ideally construct a framework and research
hypotheses to test based on the appropriate data. A rational tennis player will utilize the
highest combination of first and second serve speeds to maximize their chances of winning
the ensuing point. The best golf and tennis players theoretically are able to play a point
completely independent of their performance on the previous point, eliminating any
psychological effects winning or losing three points in a row may have to ensure their play is
consistent.
As a result, we would expect to see a consistent level of play for a tennis player throughout
the whole match, including performance when the importance of the point is high, for
example break point. A rational player should not arbitrate between points played on serve
and return, and would frame a loss on either equally as important. The key assumption is
that tennis players are expected to hold their service game and to lose on the return
service. A tennis player will frame the expectation to hold their serve the same way a golf
player will frame keeping to par, thus acting as a reference point. Any point lost on service
or shot missed on par will be framed as a loss and any point won on return framed as a
gain.
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Diagram 1. Value function in context of Prospect Theory in Tennis.
Break Point
Win game on return
Break Point
Lose game on service
Win point on serve
Lose point on return
Source: Kahneman, Daniel, Knetsch, Jack L, Thaler, Richard H. 1991. “Anomalies: The
Endowment Effect, Loss Aversion and Status Quo Bias“ 5(1) 193-206
We will test for loss aversion by looking at the total amount of points won during a match
for serve and return separately to act as a baseline and compare this against the number of
points won whilst break point down (a point which carries a high importance during a
match) on serve and return. In absolute terms, obviously the player will win more points on
serve and return than on break point down. By looking at their relative performance on
break point down against all points on serve and return we should be able to measure any
degree of loss aversion.
In tennis, the definition of break point on service means that the receiving competitor has a
chance to win the game with the next point. At this point, the receiver is ahead by one or
three points and the receiving competitor only needs one point to win the game and break
the server's serve. A break point on return however, may be misinterpreted. For the
purposes of this research point when we refer to break point on return, this is simply
another way of expressing a ‘game point’ in favor of the server. This refers to the server
being one or three points ahead of the receiver, and only needs one more point to win his
service game. The purpose of this variable is to capture the point played when the player
faces an immediate loss on return. Please refer to the following examples of break points
below: The left hand example we show situations for Player 1, being the receiver, facing an
immediate loss if he loses the following point in favor of player 2, the server. The right hand
example shows the same situation when considering break point down points on return for
player 2.
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Diagram 2 – Examples of ‘break point’ for a receiver in context for the purposes of this
paper
Player 1
Player 2
Player 1
Player 2
(Receiver)
(Service)
(Service)
(Receiver)
15 - 40
40 - 15
30 - 40
40 - 30
40 - A
A - 40
This paper will use a statistical paired T-test to assess the significance of data found to
measure the degree of loss aversion within tennis matches. This test is relevant to our
analysis because a paired sample t-test is used to determine whether there is a significant
difference between the average values of the same measurement made under two different
conditions. Both measurements are made on each unit in a sample, and the test is based on
the paired differences between these two values. The null hypothesis is that the difference
in the average performance (mean) values is zero, i.e. there is no difference in performance
on aggregate compared to ‘break points’. The hypothesis we shall propose therefore is that
there is a difference in performance between the two variables described above, for each
test on serve and return for men and women respectively.
The scope of our data will be restricted to the final fifteen matches in each of the four Grand
Slam Tournaments for ATP and WTA singles in 2013. We shall collect data from the official
Wimbledon website which is backed by IBM Slam Trackers technology (Wimbledon, 2014)
and also from Flashscore (Flashscore, 2013) which is an accurate tennis scores website
which visualizes each match played on a point by point level – a unique feature which
allows us to specifically identify break points and whether they were won or lost respectively
for each players observation.
We shall collect data to represent the following variables we need to compare to test for
loss aversion: A. What percentage of points does the tennis player win on their service? B.
What percentage of points does the tennis player win on their return? C. What percentage
of points does the tennis player win on their serve when break point down? D. What
percentage of points does a tennis player win on their return when break point down?
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III. Data Sources and Results
We analyze over 240 observations between the ATP and WTA singles series by collecting
data from the final fifteen matches in each of the four Grand Slam tournaments for the ATP
and WTA singles. This included 8 fourth round (or last sixteen), 4 quarterfinals, 2
semifinals, and the final. In total, we have compiled a dataset of 120 matches consisting of
three different court types. Previously mentioned, Wimbledon being a grass court, and the
fastest surface. The French Open is a clay court and is known for being the slowest surface.
Both the US and Australian Open are hard courts and are in the middle in terms of surface
speed.
A. ATP Singles – Aggregate Performance
To obtain a baseline for a players performance over the duration of the entire match,
allowing for the number of sets that were played, we considered the total points played on
serve and return and how many of those points were won and lost. We will analyze first the
men’s data followed separately by the women. Predictably, we found that male’s players
win a very high proportion of their overall points on their serve.
Table 1 – Total points won on aggregate, ATP single’s tennis. - By tournament
Game Type
ATP Tournament
Points
Won
Serve
Total
Points
Win
Ratio
Points
Won
Return
Total
Points
Win
Ratio
Australian Open
2013
2223
3437
0.647
1214
3437
0.353
French Open 2013
1989
3222
0.617
1233
3222
0.383
Wimbledon 2013
2399
3639
0.659
1240
3639
0.341
US Open 2013
2234
3601
0.620
1367
3601
0.380
8845
13899
0.636
5054
13899
0.364
Total
We observe that overall men win an average of 63.6 percent of points played on their
service game. Furthermore, men win an average of 36.4 percent points played on their
return, therefore equalizing both points won and lost to summarize all points played
throughout the observations.
We also find that on the fastest court surface, Wimbledon, men on average win an even
higher percentage of match points on their service, 65.9 percent. On the slowest surface,
Clay, men on average win a lower percentage of points on their service, 61.7 percent.
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In professional games of tennis the server is usually able to hold the point from the very
beginning. Pro level tennis players when serving are therefore expected to hold their serve
and win the majority of their service games. This is because at this level, tennis players
possess a strong serve, therefore if the serve is not an immediate ace it will put the
returner at a disadvantage and on the defensive, allowing the server to stay in control of
the point to win the game. Our findings are consistent with this theory, with men’s service
winning on average over two thirds of the overall points played during a match this way.
Therefore, break points are an important stage at the pro level in men’s tennis, because if a
player loses a single service game it is often enough to lose the set.
B. WTA Singles – Aggregate Performance
Table 2 - Total points won on aggregate, WTA single’s tennis. - By tournament
Game Type
WTA
Tournament
Serve
Points Won
Return
Total Points
Win
Ratio
Points Won
Total Points
Win
Ratio
Australian Open
2013
1156
2088
0.554
932
2088
0.446
French Open 2013
1156
2087
0.554
931
2087
0.446
Wimbledon 2013
1350
2354
0.573
1004
2354
0.427
US Open 2013
1125
2075
0.542
950
2075
0.458
4787
8604
0.556
3817
8604
0.444
Total
The data collected on the women’s WTA tournaments shows that the balance between
average points won on serve and return are more equal. We find that in women’s singles
matches, on average they win 55.6 percent of total points played on their service,
significantly less than men’s singles. Therefore, we observe women winning a higher
proportion of points played on return, 44.4 percent.
Furthermore, we find that on the fastest court surface, Wimbledon, women on average win
a higher proportion of points on their service, 57.3 percent. On the slowest surface, clay,
women on average win a lower percentage of points on their service, 55.4 percent. These
results are consistent with men’s performance on average on the different court types.
From our initial analysis and supported by existing literature, we can see that men and
women’s tennis matches differ significantly. Break points are of much higher significance in
men’s singles than women’s, due to their difficulty to convert. With more aggressive play, a
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pro level tennis player will be able to control their service point for longer following a
stronger, and faster serve. This gives the returner less opportunity to break the serve in
comparison to women’s singles tennis where winning points on return and less on serve is a
lot more common.
C. ATP Singles – Break Point Performance
To investigate whether players performance is influenced by the importance of the point
and whether loss aversion exists, we will now compare a players proportion of winning
points on break points only on serve and return, and compare against the initial analysis
which forms a baseline for their average performance.
Table 3 – Break points won on aggregate, ATP singles – By tournament
Game Type
ATP
Tournament
Serve
Break
Points Won
Return
Total Break
Points
Win
Ratio
Break Points
Won
Total Break
Points
Win
Ratio
Australian Open
2013
161
254
0.634
234
676
0.346
French Open
2013
186
308
0.604
193
580
0.333
Wimbledon 2013
193
277
0.697
237
724
0.327
US Open 2013
Total
200
734
328
1167
0.610
0.634
225
889
651
2631
0.346
0.338
In men’s singles, we observe that out of a total of 1167 break point occurrences on the
players service game, the player wins 734 of those points when break point down on serve.
The relative breakpoint performance of 63.4 percent compared to an average point win
proportion of 63.6% shows performance to be slightly lower while break point down on
serve. When break point down on a return game, we see a player win 889 points out of a
total of 2631 break point down occurrences on return. This performance of 33.8 percent is
actually lower than their average performance of 36.4 percent on return throughout a
match.
A paired T-test for total points won on service to points won break point down gives us a Tvalue of -0.28 and a P-value of 0.783 at a 95 percent confidence level. In statistical terms,
this result shows the relationship to be insignificant. Therefore, there does not appear to be
any significant difference between points won on aggregate and points won on break points
on the service game. When considering the relationship of total points won on return
against return ‘break points’, the T-test gives us a T-value of 3.93 and P-value 0.000 at a
14
95 percent confidence level. This tells us the difference is significant between return points
and break-point return points.
Although the initial T-test results for the difference between service points and break point
down points won appear to be statistically insignificant, this in the context of our analysis is
actually significant. The fact the difference is insignificant, tells us that male players clearly
show more emphasis on winning break points on their service in comparison to their return,
which is significantly lower than baseline performance on return.
The above data sample shows us men are very close to being as accurate when winning
points on break point down than any other type of point played on his serve. These initial
results therefore, displays an certain degree of loss aversion, with players focusing on
winning a significantly higher proportion of break down points on serve compared to
winning a lower proportion of break down points while on return. A rational player would
value both points of equal importance because to win a match, he must be the first to win
three sets out of five, with each set won by the player being the first to win six games. He
should therefore exert the same level of effort to win such break points regardless of
whether it is on his service or return.
In a professional tennis environment, break points are the crucial part of a match. By
viewing the loss as losing his service, rather than the return, he exerts effort to hold his
serve at a higher level than on return, we see evidence of loss aversion influencing his
decision making on an important break point in the game. A rational player should be
indifferent on losing a break point on serve or return, because, both are the loss of a point.
D. WTA Singles – Break Point Performance
We also conduct the same analysis for women; to test for any degree of loss aversion, and
if so, whether there is a difference in the degree of loss aversion between male and female
tennis players.
15
Table 4 – Break points won on aggregate, WTA singles – By tournament
Game Type
ATP
Tournament
Serve
Break
Points Won
Return
Total Break
Points
Win
Ratio
Break Points
Won
Total Break
Points
Win
Ratio
Australian Open
2013
144
259
0.556
127
332
0.383
French Open
2013
133
252
0.528
155
350
0.443
Wimbledon 2013
130
238
0.546
199
431
0.462
US Open 2013
Total
121
528
257
1006
0.471
0.525
149
630
334
1447
0.446
0.435
We find women won 528 out of 1006 break point down occurrences on their service, giving
a lower relative performance of 52.5 percent compared against the average points won on
service of 55.6 percent. Whilst break point down on return we observed a higher relative
win percentage, 630 of 1447 points won. Therefore women win 43.5 percent of break point
down points on return, a lower relative performance compared to the average proportion of
points won during a match of 44.4 percent.
Our paired T-test of the relationship between total service points and service break points
won gives us a T-value of 2.70 and P-value 0.008, showing the relationship to be significant
at a 95 percent confidence level. Therefore, the difference between our sample of service
points won and service break points won is significant. The results for total return points
won and ‘break points’ on return won present a T-value of 1.45 and P-value of 0.148
showing the difference to be insignificant at a 95 percent confidence level.
Table 5 – Summary of aggregate win ratios and significance levels for ATP and WTA singles
Win Ratio
ATP Singles
Serve
WTA Singles
Return
Serve
Return
Baseline Performance
0.636
0.364
0.556
0.444
Break Point Down Points
Won
0.634
0.338
0.525
0.435
-0.002
-0.026
-0.031
-0.009
Insignificant
Significant
Significant
Insignificant
Deviation
Paired T-test Results
We observe that, for female break point down conditions, both performance on service and
return suffer. We should note however, that the suffered performance is a lot greater on
service than return. This suggests that women place more emphasis and effort on their
return game whilst break point down to get as close to their baseline (average performance
16
on return) as possible. This is supported by our paired t-test results, showing that the lower
performance on women’s service break points to be of significant value in comparison to the
lower performance on women’s return ‘break points’ which are insignificant.
We observe that men’s performance also suffers under break point down circumstances,
however men appear to place emphasis on their service performance whilst break point
down rather than return. Our test results show the difference in lower performance on
return ‘break points’ to be significant whereas men’s performance on service break points,
being close to the baseline, is insignificant.
These results are most interesting, as we see the opposite effects in women’s WTA singles
tennis to men’s ATP singles. To further understand the reasons behind these results, we
should consider further explanations for such behavior.
IV. Evaluation and Discussion
A. Main Effects
We have observed that as the importance of the point increases, on average both men and
women’s performance suffers as a result. Men show evidence of loss aversion by increasing
their exerted effort into their service game, which is irrational behavior. Women however
give a higher performance in their return game on break points in comparison to their
service.
We should note that, the exception to this behavior is on the fastest court surface,
Wimbledon, where for men performance on service exceeds the baseline and for women
performance on the return exceeds the baseline. It would appear that a faster court service
allows players to place faster and more strategic shots, thus for men allowing the server to
exert more effort effectively into break points on service, which would explain the higher
performance on service. In comparison, the faster surface allows women to place more
strategic and faster volleys to improve their return game.
Research by Paserman (2007) proves women make more unforced errors under pressure,
where men are able to handle the pressure more effectively making less unforced errors.
Moreover, his research shows that performance deteriorates in the decisive set for both
men and women. We can associate this behavior to nervousness, an alternative
psychological explanation. Previous research such as McCarthy and Goffin, (2004) Beilock,
(2008) and Dan Ariely et al. (2009) has found that people often feel anxious or nervous
17
when facing high stakes in a competitive environment, and the Majors hold large financial
consequences.
If we assume the expectation to hold serve is true for both men and women, we can predict
that on break points, the server will experience a higher level of pressure than the returner.
Knowing women are likely to make more unforced errors than men, under break point
pressure we would expect to see a higher level of unforced errors resulting in the loss of
break point for the server in favor of the returner in women’s tennis.
Paserman (2007) explores risk aversion within tennis and the differences between genders.
Croson and Gneezy (2004) highlights the literature providing a large amount of evidence
both from the lab and the field that women are more risk averse than men. Although
strategy within tennis is hard to measure, Paserman finds that women adopt a more
conservative playing strategy and take fewer risks (Paserman, 2007).
Therefore, under break point in women’s tennis, we would expect the server (knowing they
are likely to make more unforced errors) to adopt a less risky strategy. The returner’s
chance of winning the point therefore will increase. The less risky strategy adopted by the
server at this point, compromising of a slower serve (Paserman, 2007), combined with the
un-balanced of levels of pressure both players are experiencing because the expectation to
hold serve and lose return remains, would therefore see a switch of expectation at this
crucial break point.
The returners expectation could now change, and thus will expect to win this break point on
return given they have the knowledge that the server is under more pressure to hold their
serve and plays a less risky strategy. The women’s salient reference point therefore is now
to win the break point on return, and losing such a point is framed as a loss. This would be
consistent with Koszegi and Rabin’s (2006) suggestion that rational expectations might
serve as the point of reference for reference-dependent choices. Women adopt a new
reference point and expect to now also win the return game, consistent with our rational
behavior.
When compared against men’s tennis, we can conclude that these factors would have less
impact in ATP matches. We hypothesize that men are able to play closer to iid, therefore
less likely to be influenced by importance of point or pressure, and less likely to make
unforced errors. Their nature is to play a consistent aggressive strategy, which to maximize
their chances of winning the match, is viewed as rational behavior. However, where rational
behavior would continue to suggest men play points on serve and return equally, we
observe men adopt a loss averse strategy of gameplay to hold their serve as per the
18
expectations set. We could theorize that women also attempt to hold this loss averse
strategy. However, because they react differently under pressure and given the nature of
their gameplay, the returner changes their expectation on important points to win more
break points on return compared to the average performance on return for the match.
To test further whether the explanation for our results for women’s tennis is down to
pressure on the server and a change of expectations for the returner, we could collect data
on break points, and of how many of these break points were down to forced and unforced
errors. This would give us a clearer picture as to the reason behind winning the point, to try
and accurately document the reasons behind the win and losses of break points. With more
time and resources, this would provide an ideal route for further research to provide more
in depth analysis to support this paper.
Furthermore, we could compare the type of break points, as an avenue of further research
to more accurately document loss aversion and importance of point. Further research will
also complement the work by Paserman (2007) to look at performance under pressure
between game point and set point. We could also single out other important points such as
match point and position in the tournament to offer more insight as to the degree of loss
aversion tennis player’s experience.
It is clear that, although loss aversion is a dominant factor in men’s tennis, it is not the only
driving factor to influence their behavior under break point conditions facing immediate loss.
In women’s tennis, a change of the reference point and expectations is the product of a
reaction to increased pressure suffered by the opponent, with women making more
unforced errors. It is therefore suggestive that under break point conditions, the server
continues to adopt the expectation to hold their serve whilst the returner changes their
reference point and expectation to hold the return. Therefore although loss aversion still
may exist in the women’s game, it is difficult to prove without considering the many other
factors that may be influencing their behavior.
B. Alternative Explanations
We should also take into consideration the differences of game structure between
competitors within a single match. Bois and Heyndels (2009) find that the structure of
women’s tennis competitions leads to less balanced games than is the case for men. As a
general rule, men’s tennis is more competitively balanced than women’s tennis. (Bois,
Heyndels, 2009).
19
Physiological differences between men and women may offer further support on our
findings. From the documentation of average serve speed, we know that male players have
a lot more power and explosive style of play leading to a much faster game compared to
women. The world record of fastest service speed is in the name of Samuel Groth with
163.7 mph, (ATP World Tour, 2012) while Venus Williams holds the record for female
players with 129 mph (WTA Tennis, 2014). These physiological differences are of course
inherent to gender difference, and clearly affect the gameplay between men and women,
but the extent to which they influence the degree of loss aversion is unknown.
We should be aware that technological changes e.g. lighter tennis rackets might
compensate for the differences in size and strength (Galeson, 1995), but the extent to
which these influence is not documented and may be an avenue for further research.
Finally, work of Lallemand et al (2008) also examines how female tennis players react to
prize incentives and heterogeneity in ex ante player’s abilities. They find that the outcomes
of tennis matches are determined more by differences in abilities than by financial
incentives. Men’s tennis is examined in Gilsdorf and Sukhatme (2008) who finds that
increases in prize money differentials have a positive effect on the probability that the
higher ranked player wins the match. Both studies confirm that financial incentives can be
used as an instrument to change competitive balance and could influence the degree of loss
aversion.
V. Conclusion
Our results demonstrate that loss aversion, a fundamental bias, continues to persist in a
highly competitive market, the ATP singles tournaments. We find that experienced agents
systematically exhibit this bias and that it is not only pervasive, but also costly.
In our study, we clearly define the expectation tennis players are given to hold players
serve, and to violate this expectation is seen as a loss. Furthermore, breaking an
opponent’s serve is viewed as a gain, with the reference point being players holding their
service. We demonstrate that professional male tennis players play break points on their
return game less accurately than they play otherwise similar service games.
Furthermore, the results show that women initially display the opposite effect. Their
performance is significantly lower on serve break point than on their return. We investigate
further into the nature of men and women’s tennis matches and uncover differences in
competitiveness between men and women. By considering the factors affecting a players
performance, we theorize a change reference point and expectation in women’s tennis,
20
concluding that with knowledge of the opponents behavior under the pressure of an
important point, they change their expectation to see losing a return a loss under these
circumstances.
Our findings are consistent with Prospect Theory (Kahneman and Tversky 1979). Rather
than broadly bracketing across all points within a match, players narrowly bracket and
adopt the salient reference point of holding serve within each game. Although tennis players
should strive to play each game as competitively as possible, players lose more break points
on return (in the domain of “gains”) in comparison to break points on their service (in the
domain of losses”).
Further analysis on the various factors influencing a player’s performance could be
completed to provide further insight into women’s behavior. It could be suggested that the
returner in women’s tennis play the sport of tennis in a closer fashion to the rational tennis
player. Our analysis of gender differences in tennis performance further supports our
findings that male tennis players are more competitive and display a more defined example
of loss aversion than women. More insight however is needed to clarify the key driving
factors other than loss aversion within women’s tennis.
Although we find a persistent bias among experienced professionals in a high-stakes
setting, we cannot directly generalize our findings in tennis to other domains, such as
financial advising, real estate and public policy. Our results, however, are suggestive. If
male tennis players exhibit loss aversion when playing throughout the Majors, judgment
biases may be more pervasive than prior research suggests.
21
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