In management games the participants can win prizes and they have to pay a fee to take part in the competition. Typically, in these games both the skill of the participants and random factors influence the game results. Therefore, a logical question is: do management games classify as games of chance according to the Gaming Act? Skill can be applied by carefully studying the competition to which the management game is related in order to make a good estimate of the expected scores of all potential team elements. Data from the past, from related competitions can be used for this purpose. However, no matter how
well one is prepared, one never knows whether all predictions will come true.
The uncertainty about the results of the real sports events can be interpreted as the random factor in the management game. In contrast to casino games, in a management game there is no objectively defined randomization process from which one can derive information about the probabilities. Therefore, we have to adapt the methods from chapter 2 slightly, before we can apply them to a management game in order to determine if it should be classified as a game of chance or as a game of skill.
We list the characteristics of a management game that are important for our analysis:
• the game consists of several comparable rounds of play;
• in each round the participants earn points and the scores of participants do not (or hardly) influence the scores of other participants;
• the bets (or participation fees) are the same for all participants;
• the distribution of prizes is based on the comparison of the scores of all participants: a participant’s gains (prizes) in the management game depend on his own score, but also on the scores of the other participants;
• the game has at least a few thousand participants.
For games with these characteristics it is possible to determine the relative skill level, based on realized scores of players, the prize schedule and other game specific information about possibilities for team formation. This is done by estimating probabilities from the available game data. Clearly, this analysis can only be carried out after the game has ended. However, it is definitely reasonable to use the results of such an analysis to draw conclusions about management games that will be organized in the future, if these games show a large extent of similarity with the game for which the analysis was carried out.
Since the bets are the same for all participants, we do not have to take them into account in our analysis. This influences neither the learning effect nor the random effect, so the relative skill level is also not affected. Therefore, in the remainder of this chapter, game results can be interpreted both as gains and as (the monetary value of) prizes.
The analysis is based on estimates of the game results of the three player types beginner, advanced player and fictive player. In the analysis of this practical situation, the advanced player takes the role of the optimal player, as discussed in section 2.3.2.
Since the game has a large number of participants, it is reasonable to as-sume that there will be both beginners and advanced players among them.
Beginners will reach low scores, while the advanced players will attain high scores that bring them close to the top of the ranking. We assume that the population of advanced players will be smaller than the population of begin-ners. Therefore, we fix the score of the type beginner at the average of the lowest five percent of the scores in the final ranking of the management game.
The score of the type advanced player is defined as the average score of the top ten of the same ranking. This is a modification of the analysis of chapter 2:
instead of taking expectations with respect to the probabilities determined by a given randomization process, we take the averages of groups of comparable participants.
The scores of the players are influenced by the uncertain events in the sports competition. Therefore, we make a statistical model of the scores of all participants in each round of play. In this model the player influence on the score is a systematic component, while the fluctuations around this component are attributed to the uncertain events. Our estimation of the model is based on the realized scores of the participants. The scoring possibilities in the management game are directly determined by the events that occur in the underlying sports competition. They can vary over rounds. In the example of GPM 2003, a round of play corresponds to a Grand Prix race. In a race with many crashing cars there are less (positive) scoring possibilities than in races in which almost all cars reach the finish. This difference will have a systematic effect on the scores for the corresponding round of play in the management game. So, in our statistical model we have to take into account this variation.
Therefore, we use a two-way analysis of variance (ANOVA) with player in-fluence and round inin-fluence as explanatory factors to estimate the distribution of the scores of all participants. The fit of this model turns out to be good.
Using the given prize schedule of the game, these estimated distributions also lead to the expected game results of the player types beginner and advanced player. For the fictive player we do not use the statistical model. His game
result can be derived from the game data. The fictive player knows in advance the result of all uncertain events: he knows which team elements score well in each round. He can use this information to set up a “perfect team”, leading to the maximum game result that is achievable.
In section 3.3 we present the details of this analysis of skill for the case of GPM 2003.