Digital Avatar of a Tennis Player.

A Digital Avatar of a Tennis Player (DATP) includes gameplay parameters and Technique Element Clips (TEC). Gameplay parameters are determined by streaming coefficients such as "alpha," "beta," "gamma," and "timing." TECs contain video fragments showcasing the execution of tennis strokes in typical situational gameplay states.

About Virtual and Quasi-Virtual Tennis Players.

• Phygital tennis offers a unique opportunity for everyone to experience the game of tennis. "Phygital tennis" is just a figure of speech—a term for a new, alternative version of tennis. However, phygital tennis implies a Tennis Game System (TGS), whose distinctive feature is the unique integration of a tennis player's digital image (digital avatar or DA) and the mathematical model of the sport.
• The TGS is concretely described by three stochastic differential Kolmogorov equations. This system serves as the primary algorithm guiding the Bot Administrator (BA) in organizing and conducting virtual tournaments.
• Once registered in the phygital tennis system, enthusiasts and fans of the game automatically acquire the status of a quasi-virtual tennis player (QVT). This opens up exciting opportunities to participate in virtual tournaments. Moreover, players can enhance their DA through training on real tennis courts if they wish.
• Why "Quasi-Virtual" Tennis Player? The BA initially does not know the technical level of a QVT. This could be someone who has never held a tennis racket. Nonetheless, the BA registers the player in its database, assigning them the lowest gameplay rating.

Digital Transformation of Sports.

The digital transformation of sports is characterized by an exceptionally high social impact. This is evidenced by the widespread popularity of eSports games and numerous sports project competitions, where categories like "Transformation in Sports" feature a variety of original sports innovations.

Phygital Tennis and the Tennis Metaverse.

Phygital tennis is based on the concept of uniting randomness and determinism. The digital image of a tennis player and the model of the "Tennis" sports system form a unified stochastic representation of virtual competitions.

This operational scheme of the virtual tennis system aligns closely with the current metaverse concept, which we propose to call the "Tennis Metaverse" (TMV). In the future, the uniqueness of a tennis player’s digital image will be authenticated through NFT tokens (NFTs are unique tokens representing digital assets on blockchain networks, confirming ownership of original digital objects).

Metaverses and Their Popularity.

Metaverses have become one of the most popular concepts of the early 2020s. The combination of virtual reality and monetization has made this segment of the internet highly sought after.

Tennis Metaverse is a new form of organization of tennis as a digital-physical hybrid ecosystem, in which real sports skills are objectively measured, certified and transformed into autonomous digital entities (NFT avatars) capable of existing, interacting and competing in a virtual environment through stochastic game models.

A tennis player's NFT avatar is a structured collection of data that includes identification cryptographic parameters, certified game characteristics of a real athlete, a mathematical model of behavior based on a stochastic process, and operational mechanisms of functioning placed in a non-interchangeable token format for autonomous participation in digital matches of a hybrid sports metaverse.

📌The meaningful role of the NFT avatar as a digital twin
NFT avatar:

• represents a real tennis player in a virtual environment;
• inherits its game qualities obtained objectively;
• capable of autonomous gaming activity without human intervention;
• is the legal and technological bearer of the identity of the player in the metaverse;
• acts as a unit of interaction in esports competitions;
• maintains consistency and verifiability of data through NFT structure
• provides the hybridity of sports by connecting physical results and digital play.

Cyber tennis is an alternative form of tennis implemented in the Tennis Metaverse, the essence of which is in autonomous competitions of NFT avatars, where the outcome of matches is determined by emulation based on an a priori stochastic model (Markov process), the parameters of which are the real playing qualities of tennis players.

✅Thus, Cyber Tennis is a subsystem of the Tennis Metaverse ecosystem. From the standpoint of system analysis CYBER TENNIS is an autonomous virtual gaming subsystem operating within the Tennis Metaverse ecosystem and designed for simulated competition between digital doubles of tennis players represented as NFT avatars.
Cyber tennis is a formalized stochastic model of sporting activity in which:

• elements of the system are digital avatars of players containing parametric models formed according to the data of real certification of tennis players;
• system dynamics is implemented as a stochastic Markov process, where the probabilities of transitions between game states are determined by objectively measured game qualities of real athletes;
• interaction processes are completely autonomous, do not require physical human participation and are unfolding in the digital environment of the metaverse;
• the result of game activity (the outcome of the match, the quality of game actions, the dynamics of the set and the draw) is due to computational emulation of sports behavior, and not the physical actions of athletes;
• the control system (Tennis Metaverse) provides the infrastructure: game regulations, virtual courts, rating mechanisms, synchronization rules and interpretation of results.

📌 Smart tennis hub and its functional features.

Smart tennis hub is a technological complex for objective certification of tennis players and the formation of parameters of their NFT avatars, in which:

• a robotic tennis gun controlled by artificial intelligence is used as a reference opponent;
• machine vision system records and analyzes game indicators in real time;
• in the course of standardized tests, formalized parameters (activity, stability, errors) are measured, which form the basis of the tennis player's digital double.

The hub functions as a portal to the Tennis Metaverse, transforming real sports skills into certified data for esports activities.