From D&D Wiki
|This material is published under the OGL 1.0a.|
If static modifiers for attack rolls, checks, and other d20 rolls has made the game too predictable, you can try using variable modifiers instead.
Essentially, the variable modifier system replaces any modifier higher than +1 or lower than -1 with one or more additional dice added to or subtracted from the basic d20 roll.
For example, at 1st level a half-orc barbarian normally has an attack bonus of +4 when swinging his dwarven waraxe. Instead of rolling 1d20+4 to determine the attack’s success, the player would roll 1d20+1d8. The actual modifier added to the 1d20 roll might then be any value from 1 to 8, making the final result less predictable, even though the average would remain virtually the same.
Effectively, for every point of bonus or penalty beyond 1, the “die size” of the variable modifier increases by one step, as shown on the tables below.
Starting at a modifier of +11 or -11, the pattern simply repeats every 10 points. A +13 bonus is the same as a +10 bonus (+1d20) added to a +3 bonus (+1d6), and thus the character would roll 1d20 and add 1d20 + 1d6. Similarly, a -15 penalty would be the same as a -10 penalty (-1d20) and a -5 penalty (-1d10) added together. When the Variable Penalties table gives a penalty such as “-(1d20 + 1d10),” it means add together the rolls of the dice inside the parentheses and treat the total as a penalty on the check.
Use variable modifiers only when adjusting the roll of a d20. Don’t apply them to damage rolls, hit point rolls, percentile rolls, or any other roll that does not involve a d20.
Behind the Curtain: Variable Modifiers
On average, variable modifiers are about 1/2 point higher or lower than static modifiers—in other words, an average result on a check with a variable bonus is about 1/2 point higher than the same check with a static bonus, while an average result on a check with a variable penalty is abou 1/2 point lower. Since the majority of checks made by player characters have a bonus rather than a penalty, this system is slightly advantageous to player characters. However, it also increases the randomness of the result, and randomness tends to favor monsters over PCs.
If you use this variant, don’t allow players to choose between using variable modifiers and static modifiers on a case-by-case basis. Instead, all d20 rolls should use the variable modifier system. It’s possible to allow some characters to use the variable modifiers while other use static modifiers, but doing this runs the risk of creating a perception of inequality between characters.
Taking 10 And Taking 20
Avoid using variable modifiers when a character takes 10 or takes 20 on a skill check. Since those two rules rely on a certain level of predictability, a character who takes 10 or takes 20 should apply the normal static modifier to his roll rather than using the less predictable variable modifier. Otherwise, even simple tasks can become unnecessarily dangerous.
|Static Bonus||Dice||Average Bonus|
|+11||+1d20 + 1||+11.5|
|+12||+1d20 + 1d4||+13|
|+13||+1d20 + 1d6||+14|
|+14||+1d20 + 1d8||+15|
|+15||+1d20 + 1d10||+16|
|+16||+1d20 + 1d12||+17|
|+17||+1d20 + 2d6||+17.5|
|+18||+1d20 + 3d4||+18|
|+19||+1d20 + 2d8||+19.5|
|… and so on.|
|Static Penalty||Dice||Average Penalty|
|-11||-(1d20 + 1)||-11.5|
|-12||-(1d20 + 1d4)||-13|
|-13||-(1d20 + 1d6)||-14|
|-14||-(1d20 + 1d8)||-15|
|-15||-(1d20 + 1d10)||-16|
|-16||-(1d20 + 1d12)||-17|
|-17||-(1d20 + 2d6)||-17.5|
|-18||-(1d20 + 3d4)||-18|
|-19||-(1d20 + 2d8)||-19.5|
|… and so on.|