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- Results ATP and WTA tournament (2009-2013)
Statistical researchThe research design used in this study is derived from Forrest & Mchale (2007). First, for all 37.220 players the odds are turned into winning probabilities, by using the next formula: Winning Probability = 1/odds For example: if Federer has a winning odd of 1,05, the win probability is 1/1.05 = 95%. This is done for all 37.220 players who played a match in ATP and WTA tournaments over the last 5 years. The next step is to divide all the odds in categories based on their probability. The next 20 categories will be used: Table 6: Probability categories
In Forrest & McHale (2007) they use probability categories of 10%, which means this study is more specific by using probability categories of 5%. After the distribution in categories, the mean return per category was calculated. The return will be determined by betting 1 euro per match.
First calculate the standard deviation of every category. Then there will be a T-test for every category. T-statistic = Mean Return Standard Deviation / 
This section will provide the results and findings of the study as described in section 4. More specifically, section 5.1 will presents the results of all ATP and WTA tournaments in the past 5 years (2009-2013). To see if there is a difference in favorite longshot bias between men (ATP) and women (WTA), in section 5.2 the ATP and WTA tournaments are investigated separately. In section 5.3 the trend over the last 5 years is studied. In the last section the results of the influence of surfaces on the favorite longshot bias are presented. In every section a table with the results is presented which contains the probability, the mean return and the standard deviation for every category. In the last column the result of the t-test for every category is calculated. The t-test is significant when it is below -2 or above 2 which means -2 < t < 2 is insignificant. In the analyzing the results, we look at the categories 1 to 7 for the underdogs and categories 15 to 20 for the favorites. When there are many significant t-values we can conclude that there is a favorite longshot bias.
Appendix A shows an overview of all ATP and WTA tournaments in the last 5 years (2009-2013). In total 18.610 matches are played during this tournament. Every player has an odd, so this means that there are 37.220 odds in this study. Below you find the outcomes of all the ATP and WTA tournaments in the last 5 years (2009-2013). Table 7: Results of all ATP and WTA tournaments in the last 5 years (2009-2013)
ATP and WTA tournaments are played at the highest level of professional tennis. The past five years 18.610 matches were played. Those matches were divided in probability categories. Probability category 1 contains the biggest ‘underdogs’ . The betting market gives those players 1 – 5% chance to win the game. The other way around, category 20 (chance: 95-100%) are the most favorite players. In the fifth column ‘Mean return category’, the mean return when betting 1 euro on all the players in the category is given. In every category this contains a negative value, this means that in every category you lose money. What stands out in table 1 is the pattern of the mean return. Lower probability categories contains a more negative return, and higher probability categories a lower negative return. For every betted euro in category 1, the bettor receives €0,53 back. Betting one euro in category 20 will one average give €0,987 back. To make it more clear the graph below is added. Graph 1: Development of the mean return of all ATP and WTA tournaments in the last 5 years (2009-2013) The mean return line gets more to the 0-point on the X-as while the category becomes higher. As said before, every category had a negative return, which means that there is no chance to make a profit on betting on the tennis tournaments. Even though, betting on favorite players will generate the least negative return and is the best strategy possible. Looking at the last column we see a lot of t-values below -2 of above 2 which means a lot of significant results. In category 1 to 7 there are 6 significant values, which is an indication for a favorite longshot bias. However, in the categories 15 to 20 we see also 5 significant values. Based on this you cannot really speak of a bias.
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