We study scaling convolutional neural networks (CNNs), specifically targeting Residual neural networks (ResNet), for analyzing electrocardiograms (ECGs). Although ECG signals are time-series data, CNN-based models have been shown to outperform other neural networks with different architectures in ECG analysis. However, most previous studies in ECG analysis have overlooked the importance of network scaling optimization, which significantly improves performance. We explored and demonstrated an efficient approach to scale ResNet by examining the effects of crucial parameters, including layer depth, the number of channels, and the convolution kernel size. Through extensive experiments, we found that a shallower network, a larger number of channels, and smaller kernel sizes result in better performance for ECG classifications. The optimal network scale might differ depending on the target task, but our findings provide insight into obtaining more efficient and accurate models with fewer computing resources or less time. In practice, we demonstrate that a narrower search space based on our findings leads to higher performance.