In this paper, we present the performance evaluation of haptic compression methods for networked teleoperation systems or haptic interfaces in virtual environments. Haptic data, which include position, velocity, and force data exchanged through the communication channel, are considered by various compression methods based on down-sampling. We introduce the operational rate-distortion performance measure that evaluates not only the compression ratio, but also the quality of reconstructed haptic data. The deadband method, also known as a perception-based haptic compression method, is categorized as an adaptive down-sampling method and compared with a fixed rate down-sampling method. In the case of force data compression, we propose the modified deadband method, which adopts a force predictor, a quantizer, and a contact force detector. Experiments are performed by using a haptic device incorporated with a virtual teleoperator. The performance evaluation and comparison of the fixed rate down-sampling, deadband, prediction-based deadband, and modified deadband methods are provided. The results show that the proposed method achieves improvement in the compression ratio and quality measurement compared to other methods.