Conversational grounding, vital for building dependable dialog systems, involves ensuring a mutual understanding of shared information. Despite its importance, there has been limited research on this aspect of conversation in recent years, especially after the advent of Large Language Models (LLMs). Previous studies have highlighted the shortcomings of pre-trained language models in conversational grounding. However, most testing for conversational grounding capabilities involves human evaluations that are costly and time-consuming. This has led to a lack of testing across multiple models of varying sizes, a critical need given the rapid rate of new model releases. This gap in research becomes more significant considering recent advances in language models, which have led to new emergent capabilities. In this paper, we aim to evaluate the performance of LLMs in various aspects of conversational grounding and analyze why some models perform better than others. We demonstrate a direct correlation between the size of the pre-training data and conversational grounding abilities, meaning that they have independently acquired a specific form of pragmatic capabilities from larger pre-training datasets. Finally, we propose ways to enhance the capabilities of the models that lag in this aspect.