# Mathematical Algorithm for Risk Assessment of Police Officer in VR Training Simulation
## 1 Introduction  
The widely developed fields of application of virtual reality (VR) technology are mainly medicine, education, and entertainment, but also selected elements of manufacturing processes, robotics, and data visualization [1]. Particularly noteworthy is training simulated in a 3D environment [2], and it covers a wide range of activities [3; 4; 5; 6]. Conducting training in virtual reality (VR) is a flexible and effective method of improving and acquiring skills. The VR technology solutions are also used in the field of emergency response. The high potential of the technology enables conducting training activities related, for example, to fire fighting. Studies carried out have shown the need to continue work to determine the methods of transferring skills acquired in VR training to real incident scenarios and to assess the potential risks associated with frequent training in an engaging and physiologically-simulating virtual environment [7]. VR technology allows you to create infinitely large and complex training scenarios, enabling you to take actions that would require vast hardware, financial, and human resources in real life. At the same time, the quality of the training does not differ from that of traditional training [8]. The results of studies based on both methods showed that trainees preferred 3D visual instruction in virtual reality, while a comparison of the level of training in both groups did not show any difference. Other studies have shown that virtual reality and augmented reality courses have delivered bettereducational results than traditional training in terms of speed of action, as well as in the number of errors made. It has been found that emergency medical service workers who participated in training increased their skills, in terms of the speed of performance of tasks, by 29% [9]. The use of the VR-based method for training is particularly applicable in areas where cooperation of human teams in different fields is required, which is associated with high economic costs and a high risk. Particularly noteworthy is the VR training used in responding to natural and construction disasters and fires [10]. The use of these methods enables the user's immersion, building subconscious patterns to be used in the event of crisis situations [11; 12; 13; 14]. Such arrangements are described in relation to, i.a., the tasks carried out in an accident environment [15], as well as in relation to the education and training systems implemented by the military sector. [16; 17] Another user group is customs and police, who are involved in high-risk events [18; 19]. A strong sense of presence and effective immersion into virtual reality ensure that training is delivered in a secure and controlled environment. Trainees have the ability to prepare and \"practice\" various topics and sequences, before they take action in real world conditions. This leads to a significant increase in skills, while, at the same time, they take action more confidently and use tools more effectively, enhancing their practical efficiency and reducing possible material or time losses. However, it is the responsibility of the trainer to educate trainees effectively, without neglecting areas that pose the biggest difficulties when it comes to actions taken. It is particularly important to include elements in the simulation representing threats that the user will encounter in real life, and to assess the risk of their actions depending on the presented threats. A virtual evaluation system that takes the complexity of training in a simulated 3D environment into account is proving to be helpful in assessing learning outcomes. The following training proposal is aimed primarily at the students of police specialist courses and provides an assessment of the risk of actions taken on the site of a traffic incident, based on a mathematical algorithm implemented for VR training technology.