In a private project I did a re-editing and translation of RM 2nd Ed. to German, using LaTeX, giving me the "Director's Cut" RM rulebook I am using for my campaigns, with all the options decided upon, massaged into the main ruling text. (Yes, I am a bit mad that way. Mr. Charlton of I.C.E. told me as much in so many words when I told him of my work, asking him if there was a chance to get this greenlit for publishing. Sadly, the answer was no. ;-) )
This required me to transfer the Arms Law / Spell Law tables to LaTeX, a task I was not at all keen to do all manually. So I had a look at some way to "compress" the data in some way, and came up with a functional shorthand I could type with one hand on the numpad and one hand to mark my position in the table. (Using Perl scripts to turn the shorthand into readily-formatted LaTeX source at a later point.) Allow me to quickly explain the shorthand.
Each AT column gets "translated" into three lines of numbers:
- Crit Severty (0: None, 1: A, 2: B, 3: C, 4: D, 5: E)
- Crit Type (indexing a pre-defined array -- 1: Puncture, 2: Slash and so on)
Each line starts with the initial value (at 150), with following numbers indicating how many lines there were with that number / index. I used
* <val1> <val2> <count> to indicate
<count> groups of two alternating values (crit types),
- <val1> <val2> <val3> <count> to indicate
<count> groups of three alternating values (crit types), and
/ to indicate an end to decreasing / alternating numbers, the rest being verbatim values written out.
Taking the Shortsword table, for the AT 20 column, we get this:
5 25 24 24 24 9
3 3 4 9
3 13 / 1 3 2
For the Sling table, we get this at AT 20:
10 10 10 10 10 9 10 10 10 10 9
5 3 3 5 5 10
You see some further regularities in this which might be compressed even further (the four "10" / one "9" grouping for Sling damage), strongly hinting that the tables have been created based on some mathematic formula.
But having literally seen all the tables written down in this shorthand, I can also tell you that there are most likely several formulas at work here (so I did not bother trying to come up with an even more compressed shorthand than I already had). Note, for example, the "weird" tapering off of crit types in the Shortsword table, with puncture crits strewn in among the crush crits. Other tables do other kinds of "changing crits", or otherwise "break sequence" somewhere down the column.
I have never seen the formulas documented anywhere, even given the various "easier" combat resolution tables / systems provided by I.C.E. directly. None of those systems gives the exact results of the original AL / SL tables.
And that is after fixing some outright mistakes where it is obvious that 2nd edition Arms Law / Spell Law did not always list the numbers / criticals it was supposed to at some points (breaking otherwise obvious sequences). In that way, my Director's Cut may even be "more correct" than the original rules.