Steve Jackson Games Forums - I made a descent formula for ST damage.

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- - I made a descent formula for ST damage. (https://forums.sjgames.com/showthread.php?t=128340)

I made a decent formula for ST damage.

I have through tinkering made a pretty descent formula for ST damage.

After meticulously encoding the mean, maxima and minima for the swing and thrust damage rolls for each ST from 1 through 129, into a spreadsheet; graphing it and then fiddling with parameters for hours, I have found out the following:

Damage scales more steeply until ST 40, then it mellows out. Especially swing damage has an odd sort of hunchback.

To make the mathematics smooth I use what I like to call a damage rating. Damage ratings is a number which can be converted to a dice pool with ease:

Divide the damage rating in seven, and keep the remainder; use twice that many dice.
With the remainder, if above four add another die and subtract four.
Add the rest of the remainder as a bonus.

This method turns a damage rating of 4 into 1d, 6 = 4+2 into 1d+2, 9 = 7+2 becomes 2d+2, 14 = 2*7 becomes 4d, 19 = 2*7+4+1 becomes 5d+1 and so on.

IF the damage rating is below four, use 1d and subtract the difference: 0 -> 1d-4, 1 -> 1d-3, 2 -> 1d-2, 3 -> 1d-1.

The trick is that a damage rating represents the mean of the die roll (favouring more dice.)

Now that we have a neat figure to get our dice pools from we need a formula for working out the damage ratings for swing and thrust.

I have found two good ones:

For thrust:
Divide ST in two, subtract two.
If ST is above 40, subtract the difference divided in five.
Thrust damage rating = ST/2 - 2 - MAX(0, (ST - 40)/5)
For swing:
Divide sevenfold ST in ten, subtract two.
IF ST is above 40, subtract the difference divided in three.
Swing damage rating = 7*ST/10 - 2 - MAX(0, (ST - 40)/3)

These formulas overshoot Swing slightly and undershoot Thrust slightly compared to some of the higher levels of the ST damage table (B. 16).

Q: Why?
A: Because spreadsheets handle lookup tables poorly.

And here is a table for convenience (but bear in mind the values interpolate):

Code:

ST        Thrust        Swing                ST        Thrust        Swing

1        1d-5        1d-5                29        3d+1        5d

2        1d-5        1d-4                30        3d+2        5d+1

3        1d-4        1d-4                31        3d+2        5d+1

4        1d-4        1d-4                32        4d        5d+2

5        1d-4        1d-3                33        4d        6d

6        1d-3        1d-2                34        4d+1        6d

7        1d-3        1d-2                35        4d+1        6d+1

8        1d-2        1d-1                36        4d+2        6d+2

9        1d-2        1d                37        4d+2        6d+2

10        1d-1        1d+1                38        4d+3        6d+3

11        1d-1        1d+1                39        4d+3        7d

12        1d        1d+2                40        5d        7d+1

13        1d        2d                45        5d+1        7d+2

14        1d+1        2d                50        6d        8d+1

15        1d+1        2d+1                55        6d+1        8d+3

16        1d+2        2d+2                60        6d+3        9d+1

17        1d+2        2d+2                65        7d        10d

18        2d        2d+3                70        7d+2        10d+2

19        2d        3d                75        8d        10d+3

20        2d+1        3d+1                80        8d+2        11d+1

21        2d+1        3d+1                85        8d+3        12d

22        2d+2        3d+2                90        9d+1        12d+2

23        2d+2        4d                95        9d+2        13d

24        2d+3        4d                100        10d+1        13d+2

25        2d+3        4d+1                110        11d        14d+2

26        3d        4d+2                120        12d        15d+2

27        3d        4d+2                130        12d+3        16d+3

28        3d+1        4d+3                140        13d+2        17d+2

Re: I made a descent formula for ST damage.

Up to ST 27, a formula giving identical results to RAW is:

Thrust: (ST-5)/8
Swing: (ST-6)/4

Convert fractions as follows:

Up to .125 is discarded.
Up to .375 is +1.
Up to .625 is +2.
Up to .875 is +1d-1.

I never bothered with a formula for the slowdown that RAW provides for, as our games either don't get that high or balancing ST-based damage doesn't matter when they do.

Re: I made a descent formula for ST damage.

Quote:

Originally Posted by Celti (Post 1804228)

That's neat. And yes, not many games get into the ST 40+ range.

Re: I made a decent formula for ST damage.

Quote:

Originally Posted by MagnetoHydroDynamics (Post 1804211)

After meticulously encoding the mean, maxima and minima for the swing and thrust damage rolls for each ST from 1 through 129, into a spreadsheet; graphing it and then fiddling with parameters for hours, I have found out the following:

Damage scales more steeply until ST 40, then it mellows out. Especially swing damage has an odd sort of hunchback.

I have been modelling ST damage as well and I also noticed this pattern. It's actually one progression from ST 10 to 20, then changes slightly between ST 20 and 40 and then it change some more between ST 40 to 100 and after a 100 it stays linear.

Would you mind sharing your spreadsheet? I kinda wanted to see your plots.