Chances of success in Hero System

Hero System uses a 3d6 roll to determine success. You try to roll below your skill level (plus any modifiers) or less.

But a 3d6 roll has a bell-curve distribution, which means modifiers affect effective success chances rather differently to resultion systems like d20 or d100, which have flat distribution curves. In a d20 system, a +2 modifier is always equivalent to a 10% greater chance of success - but in Hero System (or GURPS, which also uses a 3d6 resolution system), it varies depending on the starting success chance. The effect of modifiers is greater the closer the target number is to 10 or 11, and has a decreasing effect the further away from this average the starting success chance is.

Despite this, it's pretty easy to calculate the chances of success once base skill level and any modifiers are taken into account. Let's call base + modifiers the Effective Skill Level.

Effective skill Chance of success
3- 0.46%
4- 1.85%
5- 4.62%
6- 9.25%
7- 16.2%
8- 25.92%
9- 37.5%
10- 50.0%
11- 62.5%
12- 74.07%
13- 83.79%
14- 90.74%
15- 95.37%
16- 98.14%
17- 99.53%

An effective roll of 18- would be a 100% success chance, but in Hero System, a roll of 18 always fails (and a roll of 3 always succeeds) no matter what the effective skill level, so you never have a success chance greater than 99.53%.

Success in Combat

Hero System uses a simple comparative method for hitting things. The basic success roll in combat is 11 or lower, but this is modified by bot hthe attacker's offensive combat value (OCV) and the defender's defensive combat value (DCV), to the final target number is 11 + OCV - DCV (Hero System 6e describes this slightly differently, but the formula remains the same).

As a result, it's crucial to balance values for Combat Values properly in Hero System. It matters little how high the values are, so long as they're well balanced to the challenges PCs are likely to face. Because this is Hero System, it's not too bad to present weaker opponents in the early stages of a mission, so long as significant fights are challenging.

Hero System uses 3d6 rolls, which follow a bell curve distribution, so an an advantage of a point or two can make a significant difference to whether a character succeeds or fails in an attack.

OCV-DCV 3d6 roll required Chance of success
-6 5- 4.62%
-5 6- 9.25%
-4 7- 16.2%
-3 8- 25.92%
-2 9- 37.50%
-1 10- 50.0%
0 11- 62.5%
+1 12- 74.07%
+2 13- 83.79%
+3 14- 90.74%
+4 15- 95.37%
+5 16- 98.14%
+6 17- 99.53%

For example, a character with OCV and DCV of 6 facing a character of OCV and DCV 5 will hit his opponent about 3/4 of the time and be hit about half the time. A character with CVs of 7 will hit a character with CVs of 5 about 5/6 of the time and be hit about 2/5 of the time.

Now consider multiple opponents. A character with a CV advantage of +1 in both attack and defence fighting two opponents will be hit by both opponents about 1/4 of the time, and hit by one opponent about half of the time. The advantage lies with the pair at in the early stages of the fight, and with the singleton once one of the opponents is downed, assuing she hasn;t been too badly damaged until then. All other things being equal, that's a fair fight - remember, though, that a series of fair fights actually puts a PC at a disadvantage, as they're likely to be in all those fights, whereas an NPC is likely only in one. This would make this battle a fairly challenging one.

These odds, of course, assume the characters are simply standing and swinging at each other with simple strikes. A clever fighter will look for advantages in manoeuvres or in her environment. The greater the advantage a character has over her opponent, the less risk she'll face by picking aggressive manoeuvres which reduce her defence.

Since this is Hero System, and characters are supposed to be significantly better than average, it's no real problem that an Average Joe with CVs of 3 doesn't stand up too well against a slightly better PC with CVs 4 or 5, but it is worth bearing in mind when trying to put up a challenge for PCs.