To ensure a satisfactory QoE (Quality of Experience) and facilitate system design in speech recognition services, it is essential to establish a method that can be used to efficiently investigate recognition performance in different noise environments. Previously, we proposed a performance estimation method using the PESQ (Perceptual Evaluation of Speech Quality) as a spectral distortion measure. However, there is the problem that the relationship between the recognition performance and the distortion value differs depending on the noise reduction algorithm used. To solve this problem, we propose a novel performance estimation method that uses an estimator defined as a function of the distortion value and the SNR (Signal to Noise Ratio) of noise-reduced speech. The estimator is applicable to different noise reduction algorithms without any modification. We confirmed the effectiveness of the proposed method by experiments using the AURORA-2J connected digit recognition task and four different noise reduction algorithms.