We consider a new measure for the quality of on-line algorithms, the relative worst order ratio, using ideas from the Max/Max ratio [Ben-David,Borodin 94] and from the Random Order Ratio [Kenyon 96] The new ratio is used to compare on-line algorithms directly by taking the ratio of their performances on their respective worst orderings of a worst-case sequence. Two variants of the bin packing problem are considered: the Classical Bin Packing Problem and the Dual Bin Packing Problem. Standard algorithms are compared using this new measure. For the Classical Bin Packing Problem, all algorithms considered can be linearly ordered by this measure. For the Dual Bin Packing problem some algorithms are found to be incomparable under this new measure, i.e., there are sequences where the one algorithm does better and sequences where the other does better. Many results obtained are consistent with those previously obtained with the competitive ratio or the competitive ratio on accommodating sequences, but new separations and easier results are also shown to be possible with the relative worst order ratio.