Transposon insertion site sequencing (TIS) is a powerful tool that has significantly advanced our knowledge of functional genomics. For example, TIS has been used to identify essential genes of Saccharomyces cerevisiae, screen for antibiotic resistance genes in Klebsiella pneumoniae and determine the set of genes required for virulence of Mycobacterium tuberculosis. While providing valuable insights, these applications of TIS focus on (conditional) gene essentiality and neglect possibly interesting but subtle differences in the importance of genes for fitness. Notably, it has been demonstrated that data obtained from TIS experiments can be used for fitness quantification and the construction of genetic interaction maps, but this potential is only sporadically exploited. Here, we present a method to quantify the fitness of gene disruption mutants using data obtained from a TIS screen developed for the yeast Saccharomyces cerevisiae called SATAY. We show that the mean read count per transposon insertion site provides a metric for fitness that is robust across biological and technical replicate experiments. Importantly, the ability to resolve differences between gene disruption mutants with low fitness depends crucially on the inclusion of insertion sites that are not observed in the sequencing data to estimate the mean. While our method provides reproducible results between replicate SATAY datasets, the obtained fitness distribution differs substantially from those obtained using other techniques. It is currently unclear whether these inconsistencies are due to biological or technical differences between the methods. We end with suggestions for modifications of the SATAY procedure that could improve the resolution of the fitness estimates. Our analysis indicates that increasing the sequencing depth does very little to reduce the uncertainty in the estimates, while replacing the PCR amplification with methods that avoid or reduce the number of amplification cycles will likely be most effective in reducing noise.