The effect of playing "home" or "away" and many other determinants, such as shooting percentage, the offensive rebounds, the turnovers and the number of free throws, have been hypothesized as influencing the outcome of major basketball matches. The optimal selection by team coaches during the game is the main unsolved problem. Due to their axiomatic foundation and properties, the convex measures are becoming a powerful tool in performance analysis. In this paper, we will review the fundamental structural concepts of convex performance optimization within the framework of convex analysis. We investigated the ARC optimization program over the coach selection and results found that convex optimization problem fitted optimal under the different game circumstances.
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