It has been well accepted that the folding energy landscape may resemble a funnel according to the theory of protein folding. This theory of "folding funnel" has been extensively studied and thought to play an important role in guiding the sampling process of the protein folding and refinement in protein structure prediction. Here, we have investigated the relationship between the "funnel likeness" of protein folding and the size/structure of the proteins based on a set of non-homologous proteins we have recently evaluated using a statistical mechanics-based scoring function ITScorePro. It was found that larger proteins that consist of more helix/sheet structures tend to have a higher score-Root Mean Square Deviation (RMSD) correlation (or a more funnel like energy landscape). Another measurement in protein folding, Z-score, has also shown some correlation with the size of the proteins. As expected, proteins with a better "olding funnel likeness" (or score-RMSD correlation) tend to have a better-predicted conformation with a lower RMSD from their native structures. These findings can be extremely valuable for the development and improvement of sampling and scoring algorithms for protein structure prediction.