Monday, April 24, 2006

Fractional Levels in Fudge

Finding difficulty with the Fudge trait scale having only seven levels? Join us as one Fudge Factor author explores some of the possibile ways of handling "in between" levels in Fudge.

A concern that sometimes arises with Fudge is that it is too granular. There are only seven basic levels and in often the upper and lower ends tend to get marginalized. That got me thinking - what about fractional levels? So I did a little analysis and came up with half levels. Of course, as it turns out, most good ideas have already been discovered, and sure enough, someone else came up with the idea before me. Jonathan Benn posted a similar idea on the Fudge List. A recent Fudge Factor article details several options for overcoming the granularity problem. The Fudge Guide also has several ideas for tweaking level granularity. So in the end I can't claim that these ideas were originally mine. But I have tried to summarize the main ideas behind fractional levels and throw in some interesting analysis. If you're looking for a quick and easy way to narrow the gap between Fudge levels, fractional levels just might be for you.

Half Levels

This is one of the simpler methods for adding a little oomph to the Fudge scale. The scale changes to add half levels (+) between the normal levels and becomes

Fair < Fair+ < Good < Good+ < etc.

For resolving the new "plus" levels, a half-die is rolled and added to the normal 4dF. A half-die gives a plus result half of the time (hence the name half-die). A six-sided die can serve as a half-die with a result of 4-6 being treated as a plus and 1-3 as a zero. Or a Fudge Die can be altered to have three plus sides and the rest ignored. Another method is to take a six-sided die and color three sides green and the rest white. There are many possibilities for creating a half-die. Below are some graphs that show how adding the half levels changes resolution results. The first graph shows the chance of success for a non-opposed action, or the probability of rolling above a certain level. For example, when a player character with a Fair skill level rolls 4dF, he/she will get a Fair result or better 62% of the time, a Good result or better 38% of the time, and so on. I've centered the results at the Fair difficulty level, but the results can be shifted around any task resolution level. I.e., a Mediocre+ skill attempt of a Mediocre task has the same probability of success as a Fair+ skill attempt of a Fair task. As the plot shows, and already mentioned, a character with a Fair trait level (dark blue line) will roll a Fair result or better 62% of the time, while a character with a Good trait level will roll a Fair result or better about 81% of the time. There is almost a 20% success rate between the two trait levels for a task with Fair difficulty. The Fair+ level fits nicely in between the Fair and Good levels to give a 72% chance of rolling a Fair result or better. The difference between the closest levels for Fair task resolution now shrinks to 10%, rather than being 20%. As seen on the graphs, the success rate differences between adjacent levels decrease as harder (Good, Great, etc.) or easier (Poor, Mediocre, etc.) tasks are attempted, but the plus levels still nicely fill the gap between the basic levels.

When two characters with the same trait level attempt opposed rolls against each other, each will win 50% of the time (assuming ties are re-rolled). The second graph below shows the results of resolving an opposed action when one of the characters has a Fair trait level. A Good trait will beat a Fair trait 69% of the time. A Fair+ trait however will beat a Fair trait only 60% of the time. Again the gap is narrowed so that a higher level character need not dominate a lower level character. The plus levels decrease the spread so that adjacent levels have only about a 10% winning percentage between them. This can make a big difference if you want one character to be slightly better than another character, or you would like to implement a skill progression system that doesn't allow characters to become overly powerful too quickly. The half level system is a fairly simple method, but does require introduction of a new type of die, which may not be right for your campaign. Below I describe the third level method, which is a little crunchier than the half level method, but has the advantage of using existing Fudge Dice.

Third Levels

Implementation of third levels is very similar to the method of half levels. The Fudge scale now becomes

Fair < Fair+ < Fair++ < Good < Good+ < Good++ < etc.

There are two ways to implement the third levels. The first method involves only rolling one extra die. If you have a + level, only count the extra Fudge Die if a plus is rolled. If you have ++ level, count a roll of plus or zero as a plus on the extra die. The second method involves rolling one extra die for each + level. So a character with a + level would roll one extra Fudge Die, while two extra Fudge Die for a ++ level. The extra Fudge dice are only counted when pluses are rolled. Analysis shows the two methods to give nearly identical results, so I will assume use of the second method in the following graphs.

The graphs are similar to the ones presented above. Again, third levels basically split the spread between adjacent levels into third increments. A roll with a Fair trait has a 62% chance of rolling a Fair result. For rolling a Fair result, a Fair+ trait has a 68% chance of success, a Fair++ a 74% chance of success, and a Good trait has an 82% chance of success. The margin between adjacent levels drops to around 6% from 20%. For opposed actions, a Fair trait will beat a Fair trait 50% of the time, while a Fair+ trait 56%, Fair++ 62%, and Good 69%. The trait level scale thus becomes smoother.

Other Fractional Levels

Besides the two above-mentioned fractional levels, other methods are certainly possible. A Fudge scale involving one sixth levels, one fourth levels, and so on could be used. A very smooth skill system may improve in one fourth increments (1/4, 1/2, 3/4) or one sixth increments (1/6, 1/3, 1/2, 2/3, 5/6). Fractional levels also need not be additive. A Fair- level is certainly possible whereby an extra die is rolled and gives a minus result one third of the time.

Other potential uses

Damage Spiral

If you'd like to make the wound track a little friendlier and take the sting off damage, then fractional levels may just do the trick. Rather than giving a -1 to any results for a Hurt character, give the character a minus half (-) level, or minus third (--). The character simply rolls a half die (or third die) that adds a negative result to the final roll one half (or one third) of the time. The Very Hurt level can also be adjusted appropriately. If this method isn't to your liking, you still may want to consider implementing a Tough advantage. With this advantage, a character only takes minus half (or minus third) levels for Hurt results.

Attribute Bonuses

Fractional levels allow a nice way for skills to be linked to attributes. Letting skills default to the associated attribute makes characters very powerful. Instead, a high attribute gives a fractional die bonus to the appropriate skill. A Good attribute may give a half (or third) bonus die, while a Great attribute may give a full +1 (or two-thirds die). Players may now feel that being a brawny strong-arm makes an important, though not overwhelming, difference on the outcome of their Arm Wrestling skill resolution.

One-time Bonuses

Maybe the players came up with a decent plan and the gamemaster would like to give them a bonus when they implement it. A bonus of +1 may seem rather large, but the players still deserve a reward. As a GM, you could give them a bonus half die for their efforts. Or a character is on higher ground in the middle of an intense sword fight. The elevation advantage may warrant a half die bonus, which doesn't totally swing the outcome in favor of the elevated character.


Fractional levels are a great way to add just enough extra crunchiness to a game without it becoming too overly complicated. With the extra levels, granularity issues become more manageable, as do issues of the damage spiral. If you're looking for a way to allow steady character advancement, this system may also help. Characters acquire better skills more gradually as their skills move up in level. Overall, fractional levels are a very useful option for the Fudge gamer. Below are tables summarizing the analysis presented above.

Half-Die Success Rates: Non-Opposed Rolls
Trait Levels
Opposed Task Level Fair Fair+ Good Good+ Great
Terrible 99 99 100 100 100
Poor 94 96 99 99 100
Mediocre 81 88 94 96 99
Fair 62 72 81 88 94
Good 38 50 62 72 81
Great 19 28 38 50 62
Superb 6 12 19 28 38
Legendary 1 4 6 12 19
Half-Die Success Rates:
Opposed Rolls versus Fair Trait Level
Higher Trait Level  
Fair 50
Fair+ 60
Good 69
Good+ 77
Great 84
Third-Die Success Rates: Non-Opposed Rolls
Trait Levels
Opposed Task Level Fair Fair+ Fair++ Good Good+ Good++ Great
Terrible 99 99 99 100 100 100 100
Poor 94 95 97 99 99 99 100
Mediocre 81 86 89 94 95 97 99
Fair 62 68 74 81 86 89 94
Good 38 46 53 62 68 74 81
Great 19 25 32 38 46 53 62
Superb 6 10 15 19 25 32 38
Legendary 1 3 5 6 10 15 19
Third-Die Success Rates:
Opposed Rolls versus Fair Trait Level
Higher Trait Level  
Fair 50
Fair+ 56
Fair++ 62
Good 69
Good+ 74
Good++ 79
Great 84