In the ever-evolving landscape of legal proceedings, the significance of accurately monitoring and managing cases can hardly be overemphasized. With an array of cases, litigations, and legal matters to handle, law firms and legal departments are always in dire need of an efficient system to streamline their processes. This is where Litigation Tracking Software Systems (LTSS) come into play.

An LTSS is essentially an intricate digital network designed to handle the multifaceted process of litigation management. This software helps legal teams and departments to optimize productivity, increase efficiency, and minimize risks associated with mismanagement or loss of crucial information. It offers an overarching view of the litigation landscape, providing insights into timelines, status updates, and case details.

At its core, LTSS operates on the principles of data analytics, Artificial Intelligence, and Machine Learning. The software is capable of tracking multiple cases simultaneously, updating changes in real-time, and offering predictive analysis based on past data. It essentially automates the monotonous task of manual tracking and allows the legal team to focus on strategic decision-making and client interaction.

The architecture of LTSS can be broadly divided into three tiers: the data tier, application tier, and presentation tier. The data tier is where all the case-related information is stored. This tier effectively functions as the software's memory bank, storing and retrieving vast amounts of data as per the requirements.

The application tier is the processing unit where all the algorithms and calculations take place. This tier uses the data from the data tier and processes it to generate actionable insights. For example, based on the data about a case's progress, the software can predict the likely outcome or suggest the next course of action.

The presentation tier is the user interface where the end-user (legal professionals, in this case) interacts with the software. This tier presents the processed information in an easy-to-understand format, such as graphs, charts, dashboards, and reports.

From an economic perspective, the utilization of LTSS is a cost-effective strategy. Considering the man-hours saved, the efficiency gained, and the improved decision-making abilities, the return on investment is substantial.

Moreover, from a statistical viewpoint, LTSS brings an element of predictability and reduces uncertainty. By analyzing patterns in past data, it uses statistical models to predict future occurrences, thereby helping in effective strategy formulation.

However, there lies a tradeoff between the benefits of LTSS and the concerns over data security. As LTSS deals with sensitive legal information, there is an inherent risk of data breaches and cyber-attacks. Hence, while choosing an LTSS, organizations must ensure that the software adheres to the highest standards of data encryption and cybersecurity protocols.

In conclusion, the advent of Litigation Tracking Software Systems is a testament to the fusion of law and technology. It addresses the challenges associated with the traditional method of litigation tracking and presents a more efficient and accurate alternative. By leveraging the power of data analytics, artificial intelligence, and machine learning, LTSS is set to revolutionize the way legal departments operate, thereby ushering in a new era of legal tech.

However, it is important to remember that the LTSS is simply a tool to aid legal professionals, and the ultimate responsibility of legal decision-making still rests with the human intellect. After all, no software can replace the nuanced understanding, experience, and judgment of a seasoned legal expert.