D20 mods --> GURPS mods...

[GoblynByte]

Am I figuring this correctly? Does the following conversion give more or less the same level or probability between a d20 check and a GURPS check?

d20...GURPS
-10....-7
-9.....-5
-8.....-4
-7.....-3
-6.....-3
-5.....-2
-4.....-2
-3.....-1
-2.....-1
-1.....+0
-0.....+0
+1.....+0
+2.....+1
+3.....+1
+4.....+2
+5.....+2
+6.....+3
+7.....+3
+8.....+4
+9.....+5
+10....+6

I guess this would assume that an 'normal' d20 check would be DC 10 (+0 being an unmodified d20 roll) and would equate in difficulty to an unmodified GURPS skill check (+0 being a GURPS skill of 10). Is that a correct assumption?

[Maz]

You can't really compare the results as D20 is a linear probability while 3d6 is a bell curve.

A +1 on a linear curve is always worth +1. +5% on a D20, to be exact.
A +1 on a bell curve changes in "worth" from a +1,39% to a +12,50%.

[Humabout]

This isn't as clear cut as you may think, because 3d6 produces a bell curve. For instance, take the following example: Rolling against ST 10. At this point, you have the same probability as you do for rolling 1d20 against DC 10.

Now, in GURPS, +1 to your roll means you are rolling against ST 10+1 (11). Now your odds of success are 62.5%. That means you'd be looking at a +2.5 skill bonus on a 1d20 roll. Next, let's look at a +2 to your GURPS roll. ST 10+2 (12) will result in the odds of success equalling 74.1%. That's equivalent to a +4.82 bonus in d20 systems. But remember that a bell curve does not produce a linear trend. Frex, the difference between a +4 bonus and a +5 bonus is less than the 5% that a +1 gets you in d20. You can check out the probability table on BS171 for more details. Remember that a +1 in d20 is 5% worth of penalty/bonus.

Now I'm no statitician, so there are others here that can probably do a better job on this thread than myself, but I"m fairly certain when you start factoring in different skill levels and multiple modifiers, the odds get even screwier in GURPS, but remain pretty stable in d20. My experience in GURPS has led me to believe that this also more accurately depicts RL situations than does d20, where with sufficient skill (about Pickpocket 120), you can steal your own pants off of your own body without noticing that you did it. Surely epic level thieves in 3.5e encountered some rather embarassing situations from time to time....

[Ninjad]

[Anthony]

If we look at odds ratios, which I consider a fairer measure, a +1 on a d20 is anywhere from a x2.11 ratio to a x1.22 ratio, while +1 on 3d6 ranges from a x1.66 ratio to a x2.5 ratio. In general, I'd just divide d20 mods by 2.

[Langy]

First, here's a comparison of a d20 and 3d6 probability spread. This is the probability of that number or lower occuring.

Roll	D20	3d6
1	5%	-
2	10%	-
3	15%	0.5%
4	20%	1.9%
5	25%	4.6%
6	30%	9.3%
7	35%	16.2%
8	40%	25.9%
9	45%	37.5%
10	50%	50%
11	55%	62.5%
12	60%	74.1%
13	65%	83.8%
14	70%	90.7%
15	75%	95.4%
16	80%	98.1%
17	85%	99.5%
18	90%	100%
19	95%	-
20	100%	-

So, with that you can see that a -9 on a d20 is roughly the same as a -5 on 3d6, just like a +9 on d20 is the same as +5 on 3d6. +/- 4 on 3d6 is equal to +/- 8 on d20, 3 with 7 or 6 depending on how you round, 2 with 5, and 1 with 2 or 3, depending on how you round. A +10 on a d20 is the same as somewhere between a +6 and a +8.

[GoblynByte]

Originally Posted by Maz

You can't really compare the results as D20 is a linear probability while 3d6 is a bell curve.

A +1 on a linear curve is always worth +1. +5% on a D20, to be exact.
A +1 on a bell curve changes in "worth" from a +1,39% to a +12,50%.

If you look at my progression, though, the bell curve is represented.

[Maz]

Originally Posted by Langy

So, with that you can see that a -9 on a d20 is roughly the same as a -5 on 3d6, just like a +9 on d20 is the same as +5 on 3d6. +/- 4 on 3d6 is equal to +/- 8 on d20, 3 with 7 or 6 depending on how you round, 2 with 5, and 1 with 2 or 3, depending on how you round. A +10 on a d20 is the same as somewhere between a +6 and a +8.

Heh, I hadn't tried that. Actually that translateds pretty well to just "half modifier", which is actually also close to what GoblynByte had in the first place.

Even with a practical example I think it could work. A level 3 rogue would most likely have +10 to lock picking (+2 Dex, +7 skill, +1 tools).

A GURPS rogue of about 150 pts would very likely have a skill of 14 and +1 from a tool. So -5 puts them in roughly the same ballpark.


You have to remembe rthough that a D20 character rolls an unmodified D20+attribute bonus+other modifiers. So evne a completly untrained average joe D20 character have 50% chance of making a DC:10 roll.
In GURPS you get default penalties on most task unless you have the skill, and with many skill you need to invest at least 2 points to not get a penalty. So on a practical level, DC:10 tasks should probably translate to Easy (+4) tasks in GURPS.

[GoblynByte]

Originally Posted by Langy

First, here's a comparison of a d20 and 3d6 probability spread. This is the probability of that number or lower occuring.

Roll	D20	3d6
1	5%	-
2	10%	-
3	15%	0.5%
4	20%	1.9%
5	25%	4.6%
6	30%	9.3%
7	35%	16.2%
8	40%	25.9%
9	45%	37.5%
10	50%	50%
11	55%	62.5%
12	60%	74.1%
13	65%	83.8%
14	70%	90.7%
15	75%	95.4%
16	80%	98.1%
17	85%	99.5%
18	90%	100%
19	95%	-
20	100%	-

So, with that you can see that a -9 on a d20 is roughly the same as a -5 on 3d6, just like a +9 on d20 is the same as +5 on 3d6. +/- 4 on 3d6 is equal to +/- 8 on d20, 3 with 7 or 6 depending on how you round, 2 with 5, and 1 with 2 or 3, depending on how you round. A +10 on a d20 is the same as somewhere between a +6 and a +8.

Which gives roughly what I came up with.

[Maz]

Originally Posted by GoblynByte

Which gives roughly what I came up with.

YEah, sorry for being a bit hasty. But even if the modifiers "matches" on the base DC:10 Skill:10 assumption they still do not match exactly, because, as I mentioned the +1 varies depending on the actual skill level.

In GURPS a -4 for a Skill:12 person is much worse than -4 for a Skill:16 person.
The first goes from probabilty 74% to 25% (-49%).
The second goes from 98% to 74% (24%).

While in D20, a -8 will always be a -40% reduction.

---


Anyway, I also use D20 material as inspiration for my campaigns. And I use a much rougher guideline.

I jsut say:

DC:10 = +4
DC:15 = +0
DC:20 = -4
DC:25 = -6
DC:30 = -8

I never used anything with higher DC's.

[Langy]

In GURPS you get default penalties on most task unless you have the skill, and with many skill you need to invest at least 2 points to not get a penalty. So on a practical level, DC:10 tasks should probably translate to Easy (+4) tasks in GURPS.

Agree. To get the modifier for GURPS from d20, I'd take the DC, subtract 18, and then divide by two. That winds up working most of the time.