Understanding how different aspects of basketball performance translate into overall team efficiency is central to analysis and strategy. This paper derives a mathematical expression that presents team offensive, defensive, and net ratings directly in terms of a team's four factors and shooting percentages. The resulting formula captures the full nonlinear structure of how shooting, turnovers, rebounding, and free throws jointly interact to determine team efficiency. Using this relationship, we introduce a Shapley value-based framework that decomposes team net rating into a sum of contributions from individual factors. This way, different facets of the game are made commensurable. The decomposition requires only standard box-score statistics and a single parameter $μ$, which represents the relative frequency of possession-ending free throws and remains constant for a given league and season. Consequently, it can be applied equally to individual games, full seasons, or league-wide trends. Moreover, it is immediately applicable to box-score statistics from any league or competition level by a simple change of reference point and the estimation of league- and season-specific parameter $μ$. Empirical analyses using NBA data from 2000 to 2025 validate the offensive ratings produced by the formula against exact play-by-play data, showing a nearly perfect correlation ($r = 0.999$) and a low Mean Absolute Error of $0.188$ points per 100 possessions. These analyses further illustrate how the proposed framework can be used to quantify how teams achieve success in different ways or to explain the results of individual games.

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