Strategic behavior across gender:
A comparison of female and male expert chess players
By Patrik Gränsmark
With the tremendous development of the database softwares in the last decade, chess has become one of the most documented games or sports in the world. To have access to such a rich database is a dream for any scientist whose research relies on statistics. Scientists are not only interested in the data per se but also in the fact that expert chess players constitute a very interesting group of people, not least because chess is associated with intelligence and expertise. One field of research analyzing chess data is economics where concepts as risk behavior and strategic aggressiveness are studied.
When we compete in sports, games or the working life, we try to increase our winning probabilities by adopting suitable strategies. In tennis, football, poker and chess, to mention but a few, certain situations require certain degree of aggressiveness. This also applies to a wage bargaining situation where we must find an optimal level of aggressiveness. If we demand too low a wage we signal that our skills are not particularly high. On the other hand, if we ask for a wage far above the market wage, we signal that we are not very realistic. In tennis, for instance, we can choose to adopt a more aggressive style which will lead to more forced wins but also to more unforced errors. Whether it is better to adopt a cautious strategy with few unforced errors or a more aggressive but also riskier strategy depends on the situation and particularly, on the characteristics of the opponent. It is clear that people differ in their preference for risk as some people like to “gamble” while others prefer to play “safe”. The concept of risk preferences has become a hot issue in economics, not least because our risk behavior directly affects how we choose to invest our savings. Should we choose a safe bank account with a low interest rate or invest in the stock market with higher expected payoff but to a higher risk of losing?
One of the most debated topics within the study of risk behavior is if there are gender differences in risk preferences. More specifically, the question is whether men take more risks than women. If there are differences in risk preferences between men and women, this would affect, for example, savings for retirement which would lead to different future pensions for men and women. The current consensus within economics is that men do prefer more risk than women. However, whether these differences are cultural or genetic remains to be shown.
In a recent study, carried out at the Swedish Institute for Social Research at Stockholm University, chess data is being used to address the question of whether there are gender differences in risk behavior and strategic aggressiveness. The study employs data from Chessbase 10 with one and a half million chess games, performed by players with an Elo of 2000 or more. The data set covers games played between 1997 and 2007 and includes chess games from 140 countries. The purpose of the research is to study risk behavior and aggressiveness among expert chess players with focus on potential gender differences. It investigates whether the aggressive behavior changes depending on the gender of the opponent and whether such potential changes are rational or not.
Why is chess data relevant?
Strategic aspects involved in playing chess have become an established analytical tool in cognitive psychology. The process of finding the best move in a chess position is perfect for studying search processes and problem solving. For example, one result obtained from chess research is that it takes about ten years of intense learning and hard work to become an expert, a time frame that also fits with arts, sports, science, and the professions.
When comparing group differences in the social sciences, as for instance gender or ethnic differences, it is important to take into account that there may be underlying differences in skills or productivity. For instance, an individual that has spent one year in unemployment will probably demand a lower wage than an individual that has been head-hunted from a current employment. Chess data offers some very useful information on this matter, namely the Elo rating, which measures playing strength. The Elo rating can be used to account for such differences in productivity. Having access to such a measure, researchers can compare players of equal playing strength. The database softwares contain information also on age, gender, nationality and number of games played for each player. This means that we can compare players of the same age, nationality and other factors to make sure that the results are not driven by hidden group differences.
In some professions and sports, physical strength is an advantage and therefore men and women can not be compared on an equal basis. Chess does not require any physical strength and for this reason it is easier to compare male and female performance and even more so since men and women engage in direct competition. Moreover, the rules of chess are the same around the world which makes it straight forward to compare the data across countries. Such luxury is not very common within the social sciences.
One objection that can be raised against studying chess players is that they are not representative of the whole society. This point of critique is probably valid and for this reason expert chess players are often compared to people in intellectually demanding professions and high-status positions as they, as well as chess players, are associated with intelligence and expertise.
Measuring risk behavior and aggressiveness in chess
The first question to solve is of a methodological nature. How can we measure risk behavior and aggressiveness in chess on a metric scale? The solution was based on the fact that the chess openings have been classified into Eco codes. The categorization into 500 Eco codes allows a further classification of the character of the openings. Eight chess players with Elo rates ranging from 2000 to 2600 were asked to give their opinion on the character of the 500 Eco codes. In more detail, the eight judges were instructed to define each opening as either aggressive or solid. Consecutively, the opinions of the judges were used to declare each Eco code as either aggressive or solid if at least six out of eight judges defined it as aggressive or solid, respectively. In cases when there were five or fewer votes for either aggressive or solid, the opening was considered to be neutral.
The figure displays how the judges reasoned when labeling an opening as either aggressive or solid.
The figure shows two examples: the French Defense and the Sicilian Defense. After the first move for each side (1.e4 and 1...e6/1…c5), it is too early to classify the opening as being solid or aggressive. In later moves, however, it is often possible to choose a move that leads to an aggressive or solid position. For instance, in the French defense, white can grab space with 3.e5, the Advance variation, which will be used for an attack later on or play the French Exchange variation with a symmetric position. The Advance variation is considered to be an aggressive opening while the Exchange variation is a solid choice. The Advance variation typically incurs a permanent weakness on d4 but as compensation white has more space. In the Exchange variation white has no permanent weakness in the pawn structure but neither is there any space advantage. White has to rely only on the first-mover advantage. All in all, the Advance variation is a riskier choice with higher winning/losing probabilities, while the Exchange variation is more solid with higher drawing probabilities. In the second example, white chooses between the Alapin variation or the Morra gambit against the Sicilian defense. Here, the Morra gambit is a riskier choice while the Alapin is more solid.
An aggressive opening strategy always involves a higher level of risk, as launching an attack on one part of the board implies that you neglect another. Typically, in such positions every move tends to be of utmost importance. Solid play avoids many possible weaknesses but at the cost of fewer attacking possibilities. Usually, one slip in a solid position will not lose the game.
To obtain viable results to the research question the measure of risk and aggressiveness that resulted from the judges’ classification was engaged in a statistical regression analysis. Rigorous statistical techniques were used as it is important to account for the fact that female players have lower Elo ratings at the upper end (only players above 2000 in Elo are considered). The women in the sample are also considerably younger on average than men. As already stated, one of the greatest assets of the Chessbase data is that it is possible to account for these gender differences to isolate the effect of the risk behavior.
Turning to the results, they unveil some interesting pattern by showing that male chess players choose more aggressive openings than women in general. The difference between men and women in this aspect is about 2 percentage points. The implication is that male chess players, although equally strong (and old), choose to play more of, for example, the Advance French and Sicilian Morra gambit relative to the Exchange and Alapin variation compared to their female counterparts. Furthermore, similar gender differences are seen regardless of the Elo levels, that is, the pattern is found for both amateurs and professionals. However, the most striking result is that male players, when playing against female opponents, choose about 1 percentage point more aggressive openings compared to when playing against male opponents even when the playing strength and degree of aggressiveness are the same for the male and female opponents. That is, the results presented here emerge even after controlling for the fact that women on average play less aggressively, that is, they are not driven by the general gender difference in risk behavior and aggressiveness.
The first question to ask is why male players choose more aggressive openings against female opponents. Could it be that such a strategy for some reason is more efficient when facing a female opponent? To obtain an answer to this question, an analysis of the performance was carried out. The result is that male players actually perform about 1 percentage point worse when adopting a more aggressive strategy. Expressed differently, it is irrational to choose a more aggressive opening when playing against a female opponent, given that other characteristics are accounted for. This implies that male players that behave more aggressively against female opponents could improve their performance by choosing less aggressive openings.
As one might expect the study also finds that younger players in the sample choose more aggressive opening strategies than older players. This coincides with the common view that younger players (should) choose more active openings to develop their chess skills and to optimize their performance. A similar pattern is seen at different Elo levels where players with higher Elo ratings prefer to adopt more solid openings in general. Nevertheless, the gender difference in risk and aggressiveness persists regardless of the Elo level.
What about the reliability of these results? Can they be trusted or may there be other hidden explanations behind the findings? From a statistical point of view, the results are rather strong. It is clear that the results are not driven by gender differences in age, nationality or playing strength. The fact that the players in the data set can be studied over time makes the findings even stronger as it allows accounting for differences that are constant over time as for instance cultural and religious differences. As in most research there may be explanations that have been overlooked but from a statistical point of view the results are quite convincing with high levels of significance.
A final word
The fact that male players take more risks than their female counterparts goes hand in hand with earlier findings within economic research. Thanks to the richness of the chess data, the present study also presents a novel result: that men behave even more aggressively when playing against a female opponent. The implication is that female chess players do not compete under the same conditions as male players do. An elevated aggressiveness could very well discourage women from competing in chess. A similar pattern could be present in the labor market as for instance at a job interview. If male recruiters treat female job applicants more aggressively than male applicants then women could be discouraged from applying for or accepting such jobs. It is interesting to note that men on average could gain from lowering their degree of aggressiveness against women as they could increase their performance by about 1 percentage point. A parallel reasoning could perhaps be applied to the job market, meaning that recruiters could find a better employee on average, if treating male and female applicants in a similar manner (given that they are similar).
It should be stressed that the objectives of the study is not to criticize male chess players but rather to inform about the findings and show that chess data are contributing to research progress. It is possible and perhaps even likely that chess players are unaware of this behavior and that it is rather some kind of instinctive behavior. Highly rational chess players would probably not be willing to pay a price (in the shape of lower performance) to be able to treat women differently, if they were aware of this behavior. However, this question lies outside the scope of this research paper.
Finally, the chess data can also be used to study other research questions. An ongoing project is studying gender differences in chess game duration measured as the number of moves. Some players are more impatient and prefer to end the games earlier while other do not mind waiting (too) patiently for a better moment. The preliminary results reveal that there are indeed gender differences. There are also gender differences in performance around the 40th move time control suggesting that the probability to end up in time trouble differs across gender.
Downloadable working paper
Title of the study: Strategic Behavior Across Gender – a Comparison of Female and Male Expert Chess Players. Published in: Labour Economics (2010). Authors: Christer Gerdes, Patrik Gränsmark, Swedish Institute for Social Research, Stockholm University.
 The evaluators were three female and five male chess players. The two Grandmasters Pia Cramling and Evgenij Agrest were the highest rated players.
 See the complete research paper for further explanations of the statistical methods and sensitivity analysis. Click on the link at the end of this article to download a version of the research paper.
 Although it might be of limited value outside the chess world, it would also be possible to calculate how each chess opening have performed when taking into consideration the Elo rating, age and other factors of the player in focus as well as the corresponding variables of the opponent. Moreover, it would be straight forward to calculate how different openings have performed against inferior and superior opponents.