The ratio of asymmetric vs. symmetric molecules of heavy ozone, r50 = <16O16O18O>/<16O18O16O>, or similarly r49 for 17O-containing ozone, is an essential feature of the unusual oxygen isotope effect in ozone formation. Whereas information on r49 is sparse and of limited accuracy, precision in laboratory measurements of r50 has recently been improved. The two most recent experiments, however, disagree on whether there is a preference for the formation of asymmetric over symmetric molecules or not (r50 > 2 versus r50 = 2). To throw light on this discrepancy, the temperature dependence of r50 has been derived from a reanalysis of existing measurements: r50 is found to decrease from 2.13 at 360 K to about 2.00 at 170 K. Kinetic model calculations show that the discrepancy between the two measurements disappears when temperature conditions for ozone formation are accounted for. The reanalysis confirms that the isotope enrichment in atmospheric 16O218O predominantly but not exclusively resides in the asymmetric molecule, with the preference for asymmetric molecules becoming smaller at low-temperature conditions. The enrichment $E_{50}^{a}$ of 16O16O18O which likely characterizes the source strength of ozone to transfer heavy oxygen (18O) into other atmospheric molecules is quantified as a function of temperature and in relation to the overall enrichment of heavy ozone. This information can now be used in atmospheric models that simulate isotope transfer effects.