The journey from mere aspiration to the actual realization of a private oasis in the form of a swimming pool is one that necessitates a guided tour through the labyrinth of decision-making processes. As one embarks on this journey, it becomes imperative to understand the criticality of making the right choice of a pool builder, a selection that hinges on a multitude of factors.

A pool builder doesn't merely lay bricks or excavate soil; instead, this individual or company guides the birth of an ecosystem within the contours of your backyard. They shape your dreams into tangible reality, crafting an oasis that mirrors your desires and lifestyle. Therefore, selecting an apt pool builder is a determinative factor that influences the course of this journey.

The first port of call in this voyage is understanding the mosaic of skillsets that a competent pool builder should possess. The pool builder's repertoire should encompass a deep understanding of engineering principles, proficiency with various technologies, and a keen eye for aesthetics. A proficiency in soil mechanics and geology is essential, given that the pool will be a permanent fixture, its foundation deeply rooted in the earth. The builder must be adept at understanding the interaction between the pool, soil, and groundwater to prevent potential structural failures.

Equally important is that the pool builder stays abreast with technological advances in the field. Be it the use of energy-efficient pumps or the application of smart pool systems that can be controlled via smartphone apps, the pool builder must leverage technology to enhance the pool’s functionality and longevity. Furthermore, a keen aesthetic sense is indispensable, given that the pool must seamlessly blend with the overall ambience of the backyard, enhancing its appeal rather than serving as a standalone anomaly.

Having identified the requisite skillsets, the next course of action involves an intensive research phase. According to the laws of economics, perfect information leads to optimal choices. In this context, perfect information involves a comprehensive understanding of the pool builder's portfolio, credentials, and customer reviews.

The portfolio serves as an index of the builder’s aesthetic sensibility and technical proficiency. It provides a glimpse into their methodology, choice of materials, and their ability to customize. A rich and diverse portfolio often signals a greater likelihood of the builder being able to cater to your specific needs.

Credentials act as a seal of assurance, guaranteeing that the builder has met industry-set benchmarks. Recognized certifications, licensing, and affiliations with professional bodies such as the Association of Pool & Spa Professionals (APSP) shed light on the builder's commitment to adherence to industry-set standards and regulations.

Meanwhile, customer reviews offer a candid perspective into the builder's reliability and service quality. Exploring these reviews can provide insights into the builder's commitment to time schedules, adherence to budget, and response to after-sales service requests.

The realm of pool building is not immune to the laws of probability and statistics. Given the multitude of pool builders, it is statistically possible to encounter unscrupulous ones. Thus, it is advisable to scrutinize contracts thoroughly, ensuring that all elements, from materials to aftersales service, are explicitly defined. Additionally, pool builders offering anomalously low quotes might signal potential compromises on quality or adherence to building codes.

Lastly, the choice of a pool builder should echo the principle of ‘ceteris paribus’ or ‘other things equal’ in economics. Your decision should not be swayed by superfluous variables but should hinge solely on the builder's ability to provide the best value, given your budget and requirements.

In conclusion, the selection of a pool builder can be likened to the mathematical theory of optimization – a systematic process to make the best choice from a set of available alternatives. By undertaking diligent research and making informed decisions, one can embark on a fruitful journey towards realizing a dream backyard oasis.