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Recent advances in machine learning techniques have made it possible to use high-throughput screening to identify novel materials with specific properties. However, the large number of potential candidates produced by these techniques can make it difficult to select the most promising ones. In this study, we develop the oxidation state probability (OSP) method which evaluates ternary compounds based on the probability (the OSP metric) of each element to adopt the required oxidation states for fulfilling charge neutrality. We compare this model with Roost and the Fourier-transformed crystal properties (FTCP)-based synthesizability score. Among the top 1000 systems with the most database entries in Materials Project (MP), more than 500 systems exhibit an attested compound among the top 3 compositions when ranked by the OSP metric. We find that the OSP method shows promising results for certain classes of ternary systems, especially those containing nonmetals, s-block, or transition metals. When applied to the Cu-In-Te ternary system, an interesting system for thermoelectric applications, the OSP method predicted the synthesizability of CuIn$_3$Te$_5$ without prior knowledge, and we have successfully synthesized CuIn$_3$Te$_5$ in experiment. Our method has the potential to accelerate the discovery of novel compounds by providing a guide for experimentalists to easily select the most synthesizable candidates from an arbitrarily large set of possible chemical compositions., Comment: 11 pages, 3 figures