Over the years I've found that sleeper buckets are in a rough geometric progression, or each higher bucket is some multiple of the previous one. But the ratio between two adjacent buckets is not constant and increases slightly as the values of successive buckets increase.
Using the SWC/TE Roomette fares (above) as an example, the ratio between the top two buckets is 1.140 and between successively lower pairs of buckets the ratio slowly decreases down to the two lowest buckets found is where it's 1.111. Finding the nth root of the ratio of highest to lowest buckets found yields the average ratio of those (in this case) seven buckets. The root in this case is 6 because there are 6 steps between those seven known buckets. The 6th root of 1624 ÷ 796 is 1.126 and 796 ÷ 1.126 = 707.
This same method was used to estimate the 6 buckets not found between and high and low bucket FR on the Auto Train, but here the 7th root of 1199 ÷ 530 was used because there are 7 steps between those two buckets. How did I know those two buckets found were the high and low? By comparison with those on the previous chart.
There a a few other other ways of estimating a missing bucket, and they give slightly different and usually higher values. Perhaps (in this case) 796 ÷ 1.111 = 716 is a better estimate, but it's just an estimate of the SWC/TE low bucket Roomette fare. Until somebody finds the actual low bucket being offered we won't know for sure. But does anyone really need to know for sure? I, for one, am not anal enough to waste time looking for it. And for all we know, it may never be offered - ever!
Years ago, Coach fares rose in an arithmetic progression in which the difference between successive buckets was some fairly constant value. But coach fares now also rise in a geometric progression as seen in those for the Palmetto. Didn't analyze it's BC fares.
Hope this helps.
