Defined as X-ray bright galaxy groups with large differences between the luminosities of their brightest and second brightest galaxies, fossil groups are believed to be some of the oldest galaxy systems in the universe. They have therefore been the subject of much recent research. In this work we present a study of 10 fossil group candidates with an average of 33 spectroscopically confirmed members per group, making this the deepest study of its type to-date. We also use this data to perform an analysis of the luminosity function of our sample of fossil groups. We confirm the high masses previously reported for many of fossil systems, finding values more similar to those of clusters than of groups. We also confirm the high dynamical mass-to-light ratios reported in many previous studies. While our results are consistent with previous studies in many ways, our interpretation is not. This is because we show that, while the luminosities of the BCGs in these systems are consistent with their high dynamical masses, their richnesses (total number of galaxies above some canonical value) are extremely low. This leads us to suggest a new interpretation of fossil systems in which the large differences between the luminosities of their brightest and second brightest galaxies are simply the result the high BCG luminosities and low richnesses, while the high masses and low richnesses also explain the high mass-to-light ratios. Our results therefore suggest that fossil systems can be characterised as cluster-like in their masses and BCG luminosities, but possessing the richnesses and optical luminosities of relatively poor groups. These findings are not predicted by any of the current models for the formation of fossil groups. Therefore, if this picture is confirmed, current ideas about the formation and evolution of fossil systems will need to be reformulated.