## 4 Discussion  
In this paper, a common approach of modeling Markovian sports which relies on the assumption of identical and independent point distribution (iid) was challenged by introducing match dynamics in the form of short- and long-term sports momentums. Mathematical formulations for those two concepts were proposed and the influence of short-term and long-term sport momentums on the prediction of certain characteristics in volleyball matches was studied, most notably the total number of points that will be played in the matches and handicap. The method was tested on a real dataset and the results confirmed the initial assumption--by introducing dynamics into the simulation of volleyball matches, it is possible to more accurately simulate the real flow of a match and consequently obtain significantly better results when predicting the aforementioned characteristics of the volleyball match compared to the widely used iid assumption. Significant improvement is particularly evident in the last five groups of matches. When predicting the total number of points that will be played in those groups of matches, the simulation error when using the approach that combines short- and long-term sports momentums is on average 20% smaller compared to the iid approach. Even greater improvement is evident when using the _evolving probability_ approach to predict the handicap. The simulation error, in this case, is on average 25% smaller compared to the iid approach. It is important to note that in the first two groups of matches, using only the long-term momentum parameter shows better results when predicting the total number of points compared to the _evolving probability method_. Such results were expected and they support the hypothesis that the short-term momentum loses its impact when there is a significant difference in team strength ratios. It needs to be emphasized once again that the method proposed in this paper is an interpretable simulation method, and the method can very easily be incorporated into expert systems to gain insight into possible match score sequences that may arise under  
different circumstances. Experts in the sports domain can use the simulations to identify, understand and optimize player performance. The method is very flexible and can be easily upgraded by defining other parameters such as psychological pressure and fatigue. A secondary part of this paper, but still necessary for the result demonstration, was the profiling part. Due to the limitations of the dataset used in this research, this paper proposes a profiling method that was adapted to work on heterogeneous datasets. In future work, a dataset that would have more information about the historical matches of each team will be collected. This will allow to focus on the profiling step, and to build much more detailed profiles at the team level rather than the match level. It would be interesting to explore how much it would contribute to the improvement of the results of the proposed predictive model. The paper focuses on examining the assumption of independent point distribution. By introducing the short-term momentum formulation, the paper proved that the assumption of independent point distribution is not necessarily adequate when predicting different characteristics of a sports match--volleyball matches in particular. To examine the quality of the identical distribution of points in the prediction of certain characteristics of the volleyball match, in future work, the idea is to test the influence of the decisive points on the psychology of the team and embed this feature in the model proposed in this paper. The future research will also focus on applying the proposed model to other discrete sports, especially tennis, which is usually a sport of particular interest in sports data mining. A.S.: Software, Data Curation, Formal Analysis, Investigation, Writing--Original Draft, Visualization. D.P. : Validation, Investigation, Supervision, Writing--Review and Editing, Funding Acquisition. M.V.