GURP Action 2 introduced Basic Abstract Difficulty (BAD) which is basically a generic task difficulty modifier. The specific details don’t matter for today. What does matter is that GURPS Action often suggests using 10 + absolute value of BAD as opposing NPCs skill level/resistance. I figured that simply using unopposed rolls with a penalty equal to BAD would be simpler and avoid an extra roll. I knew the numbers wouldn’t be exactly the same, but I never got around to doing the calculations.

That changed after Kalzazz, Mailanka and I had a conversation about psychic resistance in Psi-Wars. Kalzazz’s character in Undercity Noir, Anastasia Siberiana, has Will 12 which is above average but not sufficient to provide much protection against psychic maledictions. I mentioned that I assumed Will 12 when determining my character’s effectiveness against mooks. Mailanka mentioned that he would generally apply BAD as a penalty not not bother with a resistance roll. I mentioned that using BAD instead of Quick Contests would have different numbers but that a penalized roll would be simpler than doing a proper resistance roll. Due to a miscommunication, Mailanka thought I meant that it would be easier to put mooks to sleep. Thus, I decided to do the calculations I had been putting off.

With that context out of the way, here are my results. In full disclosure, I didn’t feel like doing proper probabilities. Determining exact probabilities with all of the corner cases would take more effort than I was willing to exert. Instead, I created a simulator that handled the corner cases and ran the following scenarios 100000 times. I did not even use a cryptographically secure RNG. I figured a regular RNG would be sufficient. I also rounded to four digits of precision because raw floating point numbers aren’t particularly useful and because four digits should look nice in the tables.

Success Chance by Skill Level and BAD

This is the character’s skill level against BAD. I didn’t label my axes since I don’t know how to do that nicely in Markdown and because it is obvious.

  0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
10 0.5012 0.3775 0.2613 0.1609 0.0923 0.0466 0.0180 0.0046 0.0000 0.0000 0.0000
11 0.6242 0.5017 0.3748 0.2606 0.1613 0.0928 0.0459 0.0185 0.0047 0.0000 0.0000
12 0.7414 0.6217 0.5007 0.3751 0.2596 0.1638 0.0927 0.0463 0.0178 0.0047 0.0000
13 0.8360 0.7406 0.6249 0.4976 0.3771 0.2595 0.1627 0.0911 0.0467 0.0186 0.0048
14 0.9074 0.8354 0.7416 0.6256 0.5019 0.3755 0.2597 0.1618 0.0939 0.0468 0.0181
15 0.9535 0.9058 0.8364 0.7422 0.6246 0.4994 0.3759 0.2622 0.1610 0.0910 0.0463
16 0.9824 0.9543 0.9086 0.8377 0.7398 0.6242 0.5019 0.3754 0.2604 0.1624 0.0928
17 0.9815 0.9812 0.9536 0.9039 0.8372 0.7386 0.6258 0.5013 0.3745 0.2600 0.1629
18 0.9810 0.9818 0.9819 0.9537 0.9070 0.8386 0.7399 0.6270 0.5007 0.3740 0.2586
19 0.9813 0.9820 0.9812 0.9818 0.9533 0.9083 0.8378 0.7382 0.6257 0.5002 0.3754
20 0.9813 0.9816 0.9815 0.9813 0.9810 0.9528 0.9078 0.8397 0.7407 0.6231 0.5007

It is clear from this that 100000 simulations does give some error, but the results are close.

QC Success Chance by Skill Level and BAD Skill Level

This table shows the PC skill level vs NPC skill level with ties rerolled. This is for generic skill quick contests that are not resisted. Probabilities are of PC winning.

  10 11 12 13 14 15 16 17 18 19 20
10 0.4975 0.4005 0.3042 0.2235 0.1541 0.1033 0.0641 0.0362 0.0234 0.0157 0.0118
11 0.5996 0.5005 0.4012 0.3038 0.2207 0.1554 0.1017 0.0648 0.0413 0.0264 0.0185
12 0.6946 0.5992 0.4999 0.4006 0.3053 0.2231 0.1551 0.1014 0.0679 0.0429 0.0286
13 0.7751 0.6938 0.5988 0.5024 0.4002 0.3057 0.2243 0.1546 0.1036 0.0701 0.0448
14 0.8456 0.7789 0.6941 0.5995 0.4995 0.3974 0.3049 0.2248 0.1565 0.1057 0.0691
15 0.8974 0.8468 0.7791 0.6945 0.6021 0.4979 0.4010 0.3034 0.2257 0.1565 0.1067
16 0.9367 0.8975 0.8450 0.7767 0.6965 0.5986 0.5030 0.4000 0.3045 0.2234 0.1578
17 0.9604 0.9354 0.8988 0.8448 0.7748 0.6939 0.5994 0.4976 0.3999 0.3083 0.2228
18 0.9760 0.9596 0.9325 0.8954 0.8422 0.7753 0.6930 0.6018 0.4999 0.3999 0.3055
19 0.9840 0.9736 0.9571 0.9306 0.8940 0.8408 0.7765 0.6927 0.6003 0.4996 0.3964
20 0.9879 0.9821 0.9707 0.9546 0.9294 0.8923 0.8424 0.7768 0.6922 0.6016 0.4986

QC Success Chance by Skill Level and BAD Skill Level (Resistance and Rule of 16)

This table is PC skill vs NPC’s resistance. The PC must succeed and win the contest to be counted as a success. Probabilities are for PC success.

  10 11 12 13 14 15 16 17 18 19 20
10 0.2997 0.2428 0.1855 0.1362 0.0930 0.0589 0.0376 0.0232 0.0162 0.0120 0.0099
11 0.3994 0.3317 0.2628 0.1950 0.1411 0.0968 0.0632 0.0389 0.0251 0.0177 0.0135
12 0.5030 0.4275 0.3498 0.2739 0.2038 0.1444 0.0974 0.0636 0.0413 0.0276 0.0193
13 0.6072 0.5286 0.4453 0.3628 0.2781 0.2046 0.1453 0.0994 0.0672 0.0449 0.0299
14 0.6991 0.6244 0.5412 0.4525 0.3602 0.2797 0.2100 0.1459 0.1001 0.0680 0.0464
15 0.7837 0.7133 0.6325 0.5447 0.4527 0.3603 0.2807 0.2082 0.1494 0.1026 0.0702
16 0.8525 0.7908 0.7185 0.6348 0.5448 0.4529 0.3604 0.2820 0.2085 0.1490 0.1034
17 0.8481 0.7921 0.7207 0.6351 0.5444 0.4532 0.3640 0.3647 0.2794 0.2091 0.1462
18 0.8520 0.7900 0.7166 0.6369 0.5473 0.4534 0.3631 0.3623 0.3619 0.2814 0.2084
19 0.8534 0.7922 0.7186 0.6376 0.5456 0.4524 0.3625 0.3629 0.3619 0.3639 0.2801
20 0.8511 0.7941 0.7201 0.6373 0.5459 0.4536 0.3647 0.3637 0.3649 0.3636 0.3640

As expected, success with resisted malediction type attacks tends to be less successful than straight Quick Contests.

Success Chance by Skill Level and BAD - QC Success Chance by Skill Level and BAD Skill Level

This table is the first table - the second table. The column headers are BAD which isn’t so bad since the skill levels for the second table are based on BAD.

  0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
10 0.0037 -0.0230 -0.0429 -0.0625 -0.0618 -0.0567 -0.0461 -0.0317 -0.0234 -0.0157 -0.0118
11 0.0246 0.0012 -0.0265 -0.0433 -0.0594 -0.0625 -0.0558 -0.0463 -0.0366 -0.0264 -0.0185
12 0.0468 0.0225 0.0008 -0.0255 -0.0458 -0.0593 -0.0624 -0.0551 -0.0501 -0.0383 -0.0286
13 0.0610 0.0469 0.0260 -0.0048 -0.0232 -0.0462 -0.0616 -0.0635 -0.0568 -0.0515 -0.0400
14 0.0618 0.0565 0.0475 0.0261 0.0024 -0.0219 -0.0452 -0.0629 -0.0626 -0.0589 -0.0510
15 0.0562 0.0590 0.0573 0.0478 0.0225 0.0015 -0.0251 -0.0412 -0.0648 -0.0655 -0.0604
16 0.0457 0.0568 0.0636 0.0610 0.0433 0.0255 -0.0011 -0.0246 -0.0441 -0.0610 -0.0650
17 0.0211 0.0458 0.0548 0.0591 0.0624 0.0446 0.0263 0.0037 -0.0254 -0.0483 -0.0600
18 0.0051 0.0222 0.0494 0.0582 0.0648 0.0633 0.0469 0.0252 0.0008 -0.0259 -0.0468
19 -0.0027 0.0084 0.0240 0.0512 0.0593 0.0675 0.0614 0.0456 0.0255 0.0006 -0.0210
20 -0.0066 -0.0006 0.0108 0.0267 0.0515 0.0605 0.0654 0.0628 0.0485 0.0215 0.0021

These are fairly close. Are they close enough to ignore the second roll for things like stealth against active observation, interrogations, influence skills, etc. against non-specific NPCs? That is for you to decide, but it seems reasonable to me.

Success Chance by Skill Level and BAD - QC Success Chance by Skill Level and BAD Skill Level (Resistance and Rule of 16)

This is the first table - the third table.

  0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
10 0.2015 0.1346 0.0758 0.0247 -0.0008 -0.0123 -0.0197 -0.0186 -0.0162 -0.0120 -0.0099
11 0.2249 0.1700 0.1120 0.0655 0.0202 -0.0040 -0.0173 -0.0204 -0.0204 -0.0177 -0.0135
12 0.2384 0.1943 0.1509 0.1012 0.0558 0.0194 -0.0047 -0.0173 -0.0234 -0.0229 -0.0193
13 0.2288 0.2120 0.1796 0.1349 0.0990 0.0549 0.0174 -0.0083 -0.0205 -0.0263 -0.0251
14 0.2083 0.2110 0.2004 0.1731 0.1417 0.0957 0.0496 0.0160 -0.0063 -0.0213 -0.0283
15 0.1698 0.1925 0.2039 0.1975 0.1719 0.1391 0.0952 0.0540 0.0116 -0.0116 -0.0239
16 0.1299 0.1636 0.1901 0.2029 0.1950 0.1713 0.1415 0.0934 0.0519 0.0134 -0.0106
17 0.1334 0.1892 0.2329 0.2688 0.2928 0.2853 0.2618 0.1367 0.0951 0.0509 0.0167
18 0.1290 0.1918 0.2653 0.3168 0.3596 0.3852 0.3768 0.2647 0.1388 0.0926 0.0502
19 0.1280 0.1897 0.2625 0.3442 0.4076 0.4560 0.4754 0.3754 0.2638 0.1363 0.0953
20 0.1303 0.1875 0.2614 0.3440 0.4351 0.4992 0.5431 0.4760 0.3758 0.2596 0.1367

According to my simulations, using BAD penalized success rolls for maledictions against mooks seems to favor the PCs significantly. Is this a problem? I don’t see why it would be in a game where a single point of penetrating damage is sufficient to defeat a mook. Any NPC with a name will still get a proper resistance roll.

Final Thoughts

I know that I did not generate probabilities using “proper” mathematics. Also, subtracting the values of the tables isn’t a “great” way to present the data (although I am being honest about my presentation which puts this ahead of much of the dishonest “proper” presentation), but doing the math and statistics “properly” is too much work. I merely wanted to get some quick numbers that were “good enough.” I will leave proper math and statistics to someone else.