Increasingly, visual signals such as images, videos and point clouds are being captured solely for the purpose of automated analysis by computer vision models. Applications include traffic monitoring, robotics, autonomous driving, smart home, and many others. This trend has led to the need to develop compression strategies for these signals for the purpose of analysis rather than reconstruction, an area often referred to as "coding for machines." By drawing parallels with lossy coding of a discrete memoryless source, in this paper we derive rate-accuracy bounds on several popular problems in visual coding for machines, and compare these with state-of-the-art results from the literature. The comparison shows that the current results are at least an order of magnitude -- and in some cases two or three orders of magnitude -- away from the theoretical bounds in terms of the bitrate needed to achieve a certain level of accuracy. This, in turn, means that there is much room for improvement in the current methods for visual coding for machines.