Transcription factors (TFs) regulate gene expression by binding to specific binding sites (TFBSs) in gene promoters. TFBS motifs may contain one or more variable positions. Although the prevailing assumption is that nucleotide variants at such positions are functionally equivalent, there is increasing evidence that such variants play a role in regulation of gene expression. In this article, we propose a method for studying the relationship between the expression of target genes and nucleotide variants in TFBS motifs at a genome-wide scale in Saccharomyces cerevisiae, especially the combinatorial effects of variants at two positions. Our analysis shows that nucleotide variations in more than one-third of variable positions and in 20% of dependent position pairs are highly correlated to gene expression. We define such positions as 'functional'. However, some positions are only functional as dependent pairs, but not individually. In addition, a significant proportion of the functional positions have been well conserved across all yeast-related species studied. We also find that some positions require the presence of co-occurring TFs, while others maintain their functionality in the absence of a co-occurring TF. Our analysis supports the importance of nucleotide variants at variable positions of TFBSs in gene regulation.