## 2011-02-26

### Super Saturday: MSH Rank Numbers

From 1984 into the 1990's, TSR produced the Marvel Super Heroes game. It's well-known for its standard list of character abilities (FASERIP), and for having ability and power ranks measured with descriptive names (Remarkable, Incredible, Amazing, etc.) that have associated numbers.

Consider those rank numbers: Overall they have a geometric look to them, with the increment between ranks generally increasing upwards. But there are places that definitely rub me the wrong way, like the long "flat spot" in the middle, where the numbers increase uniformly by 10 points per step (Good to Amazing: scores 10, 20, 30, 40, 50). So, the MSH rank numbers were not really systematically chosen; see the chart above and the table below for specifics.

In the Basic Rules, there's one additional, separate rank called "Class 1000" for cosmic-level entities. In the Advanced Rules, the table is further extended to add Shift Y (200), Shift Z (500), Class 1000, Class 3000, Class 5000, and also "Beyond" (i.e., Infinite; for the Beyonder from the Secret Wars miniseries; see here). As a thought experiment, if we wanted to "smooth out" those numbers, what could we do?

Option One: Exponential Trendline

The most standard way of resolving this would be to use a "line of best fit", in this case an exponential curve which runs closest to the data points. I used the OpenOffice Calc spreadsheet program for this, and the resulting curve is shown in the chart at the top. The curve of best fit here is f(x) = 1.19*1.52^x (where x equals the order of the rank, i.e., Sh0=1, Fb=2, Pr=3, etc.) and the resulting correlation coefficient is R^2 = 0.98 (measures fitness of curve on scale 0 to 1; i.e., this is a 98% quality match).

If we use this function to compute new rank numbers, and round off to the first 1 or 2 significant digits, then we get the following:

Pretty close, but you can see in the middle of the chart that the Remarkable rank is fully 10 points off where it ideally should be. And, as you can see in the graph at the top, the "flat spot" causes what we might call a "slingshot" effect inwards, thereby missing the values for Unearthly and Shift X.

A sub-option here would be to prioritize anchoring the curve on the endpoints, i.e., temporarily take out the "flat spot" and then interpolate what should go in that region. If we do so, then we get a trendline of f(x) = 1.08*1.51^x, and an improved correlation coefficient of 99%. The rounded numbers then come out as follows:

Option Two: Renard Numbers

In industrial design there is the concept of "preferred numbers" from a logarithmic scale, chosen to conveniently divide into powers of 10, and also to maximize the chance of finding compatible parts of different sizes. One common international standard is called "Renard Numbers", the simplest of which increases by a factor of 10 over 5 steps (and is so called "R5"; i.e., at each step multiply by the 5th root of 10, approximately 1.58, similar to the base in the exponential function above). See here for more detail.

Interestingly, when rounded off to a single significant digit, the R5 series starts off with the numbers 1, 2, 3, 4..., which is the same as the "flat spot" in the middle of the MSH rank numbers. Thus, we might consider using this series for our basis. However, in order to do so we really need to delete the "Amazing" rank (the "flat spot" really is too flat for too long), and add another rank at the low end that I'll call "Anemic" (between Feeble and Poor); then we can use the R5 numbers directly, rounded to one significant digit:

I like this kind of thing because, in theory, we can extend it indefinitely by just remembering the initial sequence of digits {1, 2, 3, 4, 6, 10}. Or, if we want to add a bit more precision to the ranks after Unearthly (as per the ISO-3 rounding standard for R5), then we can get the extended ranks of Shift X (150), Shift Y (250), Shift Z (400), Class 600, Class 1000, Class 2000, Class 3000, etc.

Conclusion

Will I use either of these modifications? No; although I'm partial to the R5-series fix, the values shown in MSH are probably "close enough" for a comic book game, and the burden of changing all the pre-published material outweighs the benefit we'd get from this. However, similar analyses can be made of other irregular quantifications in the game that fail to convert or scale well, such as: Strength lifting capacity, Endurance breath-holding duration, Intensities from heat and cold, etc. -- and by far the most broken of all, Resource rank levels. So, I think it's interesting to think about.

Addendum: Hey, I'm Unearthly! This blog just ticked over the 100-follower count in the last day or so. I really immensely appreciate all of you who take the time to read here, and your thoughtful comments, ideas, and feedback. More to come!

1. I never paid much attention to the rank numbers, but I suppose it might just be because my GMs seldom mentioned how they used them in resolving things.

2. I loved the Rank Numbers and how they worked. At the time the Marvel game was being published, it worked almost perfectly while thinking in game mechanics while reading the comics.

For arbitrary numbers, they certainly modeled things in Marvel very well at that time.

3. Looking at my TORG stuff last night, and, thanks to this blog post, I recognized that the scaling of the Value Chart was R5:
Value Measure
0 1
1 1.5
2 2.5
3 4
4 6
5 10
6 15
7 25
etc.

4. Michael, nice catch!

5. Love MSH, though I'm up to like version 6.15 of my house rules. Still, there's so much material out there for it, it was almost irresistible to clean up the rules a bit and start running it. But then again, I prefer playing "obsolete" games than dropping \$40 bucks for a single book in a "new and improved" system... that'll just wind up needing a lot of fixes of its own.