Bell Curve

Home

1d6

All Combinations

Number Occurs

Roll Succeeds

2d6

All Combinations

Number Occurs

Roll Succeeds

3d6

All Combinations

Number Occurs

Roll Succeeds

End

 RPG Math

Home

2d6

3d6

Bell Curve

 Gaming

Home

RPG / Dice Math

Philosophy

Reality Fault

Referee

Systems

Dragonquest

Hero System

Magic: The Gathering

New Inquisition

Neopets

Runequest

Star Fleet Battles

Traveller

 Bob's Page

Home

Fannish

Gaming

Humor

Issues

Projects

Quotes

Rants

Technosphere

Miscellaneous

Personal

Daily Goodies

 Planet Ten

 Gaming Material

## Final Notes

Well, that's about it. At this point you should have some idea of how often certain numbers appear during a game, and why.

Hopefully, it's a little clearer now why your In Nomine character with Savoir Faire on a 5- succeeds only about a third of the time and why it's more important your Hero character uses a level on OCV when your chance to hit is 11- than when your chance is already 15-.

Some of the implications for GMs may not be obvious, though. Here's one of my favorites: In Hero System, there are only four useful numbers in any game for your Combat Value (CV), whether it's Offensive CV (OCV) or Defensive (DCV). Which numbers are useful are different for each game, though.

### Friendly Fire

Let's use an example to illustrate. If two characters (Lee and Chris) with the same Combat Value (CV) throw water balloons at each other, they have the same chances to hit each other: 11+OCV-DCV. From our table, we can see they have a 62.5% chance to hit each other. (Not 50%, as many folks assume.) Note that it doesn't matter if their CVs are 3 or 30. The formula is the same.

If Lee has a one point CV advantage on Chris, this changes dramatically. Lee now hits Chris on [ 11+(OCV+1)-DCV ] a 12-, hitting 74% of the time. Not only does Lee hit Chris much more easily, but Chris has a harder time hitting Lee. Chris succeeds on [ 11+OCV-(DCV+1) ] a 10-, only 50% of the time.

If Lee has a two point CV advantage on Chris, it only gets worse. Lee now hits Chris on [ 11+(OCV+2)-DCV ] a 13-, hitting 84% of the time. Chris only hits Lee on [ 11+OCV-(DCV+2) ] a 9-, only 38% of the time. Lee is now twice as likely to hit Chris as be hit.

Here's a score card for different Combat Values:

CV Lee Chris
Same
 Hits on | 10 throws 11- (62%) | 6 hits
 Hits on | 10 throws 11- (62%) | 6 hits
+1
 Hits on | 10 throws 12- (74%) | 7 hits
 Hits on | 10 throws 10- (50%) | 5 hits
+2
 Hits on | 10 throws 13- (84%) | 8 hits
 Hits on | 10 throws 9- (38%) | 4 hits
+3
 Hits on | 10 throws 14- (91%) | 9 hits
 Hits on | 10 throws 8- (26%) | 3 hits
+4
 Hits on | 10 throws 15- (95%) | 10 hits
 Hits on | 10 throws 7- (16%) | 2 hits

By the time we get to a CV difference of +4, Chris is soaked and really, really wants to buy a level with water balloons. Chris is hit five times for every water balloon that hits Lee.

In general, if two characters are in combat with each other and one has an advantage of four (or more) points of CV on the other... they win, all else being equal. Period. No save.

### Creating Acceptable CV Ranges

When you're setting up a game, or creating a character to play, it's important to determine the acceptable range of CVs. If all the characters are supposed to be generally useful in the same combat situations, all the character's CVs should be within three or four of each other, including all bonuses, levels, etc. It is useful to set a maximum and minimum CV, and stick to it.

If one character can generate a CV higher than the maximum, you can either require they reduce the item or feature that goes over the limit or allow them to have the capability, but simply use the maximum during play. If the nominal maximum CV is set at 10, and a character can generate a CV of 11 or more, simply use a CV of 10.

An interesting side effect of using a fixed maximum is that a character who should be more "combat savvy" than others can be allowed the ability to generate a CV above the useful maximum, but it will only become important when they suffer penalties during play. Frex, if the combat expert could generate a CV of 11 in a campaign where the maximum is 8, they could still have a CV of 8 with a penalty of 3 to CV for darkness, where other characters do not.

In general, for any group of characters (PC or NPC) you want to be "in the ball park" with each other, their CVs must be within three of each other. This includes all maneuvers, levels, martial arts, bonuses for weapons, and let's not forget you can spread an Energy Blast for extra levels, too.

If normal humans (CV 3) are supposed to be able to affect the PCs, this means the highest PC CV should be no more than 7. If normal humans are supposed to be no threat, than minimum PC CVs should be at least 10 or 11.

This doesn't mean that all the characters in every game can only have CVs in a four point range. For example, if you've decided your average town guard (CV 4) with some sword training (WF: Sword) using a broadsword (OCV +1) and a shield (DCV +1) are supposed to be a credible threat to the PCs, you need to make sure that the average PC CV (counting level, equipment, etc.) isn't any more than three points higher: a CV of 8.

### Examples In Play

Let's examine an example or two from the GM's perspective.

If the difference between a CV of super-hero character and the CV of your "average" agent is four, our charts show us that the super-hero will hit the agent five times for every one time the agent hits the hero. Nominally, a group of five agents should hit the hero as many times as the hero hits them. A group of five agents, with attacks and defenses comparable to the hero's, is probably a plausible threat.

If the difference in CV is only two, our chart shows that the agents are hitting the hero four times out of ten, while the hero is hitting the agents eight times out of ten. The hero is hitting twice as often as the agents, so a reasonable challenge for the hero is probably closer to two agents.

These comparisons are contingent on the agents attacks being able to harm the hero. If the attacks and defenses of the agents and heros are not almost the same, the calculation gets more complicated, but the "hits per agent" calculations are still useful.

#### Baker's Dozen

For example, let's assume our hero is hitting the agents five times for each time the hero is hit. Also, the hero's attacks are putting twenty-five points of STUN on the agents, over and above their defenses. (10d vs DEF 10, for example) On average, it will take one shot to knock out an agent.

If there are twelve agents, our hero will need to hit a total of twelve times: twelve agents, one shot each. In the time it takes the hero to land twelve shots, the agents will probably get about three shots each. If they only hit one time in five, they'll hit the hero seven (maybe six) times. If the agent's weapons are putting 5 STUN on the hero, past defenses, that's 30 points of STUN before all the agents are out. The hero will be winded, and a bit groggy, but is in no real danger here.

If the agent's weapons are putting 10 points of STUN through the hero's defenses (perhaps they have weapons that affect the hero's Vulnerability) that's a total of 60 or 70 STUN. Perhaps the player will do a quick bit of math and have The Avenging Dark Wrath Wraith perform a tactical retreat, to fight another day. I'll also note that the hero's CON in this example had better be 15 or more, or there is a good chance they will be Stunned at least once. If that happens, the hero is down for the count early in the combat.

Doing this type of analysis before you run a game is quite helpful when you're trying to put in scene where the heros are outnumbered, but not out-classed. There is nothing more embarrassing than the PCs being wiped out by what was supposed to be a "push over" group of thugs. ...and vice versa. Knowing how often you can expect a character to hit and be hit in combat can help a lot when planning a scenario, or when deciding if Dark Wrath Wraith should run away.

#### It's just one level... or two

A second example of where these tables can be of use would be the allocation of experience. If a player wants to buy "just one or two levels" or "a new martial maneuver and a level" you can use these tables to help you decide how that will affect your game. One of the features of the HSR is the synergies that different type of skills and powers have, and the various ways that they can be combined. The drawback (everything's a trade-off) is that it is easy for creative players to "hide" expenditures of points that can be stacked to create extreme effects.

One level with swords, and one level with a Martial Arts style doesn't seem too extreme -- until they stack those levels with the +2 OCV magic sword, the +1 Accuracy spell mage cast, the -3 DCV for darkness they can ignore with Night Vision, and so on. Suddenly, they have a 8 point CV advantage on the opponents. If you're not familiar with what that might mean, it can cause no end of problems in a campaign.

For example, if the character that raises their CV outside the normal range is one of your front-line fighters, opponents that challenge them will make mincemeat out of the other PCs. If you don't put in something that can take on the front-line fighter, the combat becomes quite one-sided.

Understanding the relationship between CV and success can help you avoid letting the PCs stats get too far out of sync, and help them understand why you want to do this.

#### Expanding The Range

On the other hand, you may want to make the distinctions between different types of characters more pronounced. If front-line fighters in your game should to be markedly better than the rest of the group, you now know that their CVs should be three to four points higher than the back-up or non-fighters in the group. Given that structure, you can define a much broader range of acceptable CVs:

Type Class CV
Front-line Fighter, Cleric 6-9
Backup Cleric, Thief 4-7
Non-combat Mage, Healer, Town Guard 2-5
Untrained Butcher, Baker, Chandler 2-3

### Conclusion

Math is your friend when you run or play in a role-playing game, and a powerful tool in helping to make sure things stay fun. I hope this article has made some of these things easier to use in your gaming. So... just don't sit there... go run something! Shoo! :-)

 << prev | next >>

Last updated: 2001 Nov 29