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Math Post – Odd Bell Curves

I posted the other day about a mechanic inspired by Target20, a system developed by Daniel Collins:

(d20 + d10) + level + modifiers ? 26

This system assumes the use of descending armor class per older editions of D&D when it comes to combat. So, let's take the case of a 6th level fighter attempting to hit a creature with an Armor Class 5. With this system it would be

(d20 + d10) + 6 + 5 ? 26

Or, you have to roll a 15 or better to hit. The chances of that are 57.5 percent.

In 2e, a similar scenario 6th level Fighter has a THAC0 of 15 requiring an 11 or better with a d20 to hit AC 4. The chance of success is 50 percent.

Not too bad really - I don't mind being a little more generous with combat. But how about lower levels? Let's see:

This scenario is a 2nd level fighter attempting to hit AC2, a tough challenge.

(d20 + d10) + 2 + 2 ? 26

In other words, roll a 22 or better, a 22.5 percent chance of success.

The same scenario in 2e means that the 2nd level fighter has a THAC0 of 19 meaning that he needs a 17 or better to hit. Chance of success is 20 percent.

Saving Throws

When doing saving throws, the basic formula is still the same:

(d20 + d10) + level + modifiers ? 26

This time, though, the modifiers are standard based on the type of Saving Throw: +0 for Spells, +1 for Breath Weapon, +2 for Petrification, +3 for Paralysis and +4 for Death. (At least, this works for Fighters and Clerics)

So, a 6th level Fighter needs to make a Saving Throw against a young dragon's Breath Weapon:

(d20 + d10) + 6 + 1 ? 26

In other words, he has to roll a 19 or better. This provides a 37.5 percent chance of success.

A 6th Level fighter making the same save in 2e has to roll a 13 or greater, a 40 percent chance of success.

Saves in my system are more lethal for higher level characters, but only by a slight margin.

Now because the modifiers are different by class, I would simply put the saves on the character sheet so that a player only needs that reference to roll anything.

Rogue Skills

Doing this take a change in how Rogue skills are handled. Instead of using percentages, skills would have a number that looks an awful lot like a skill rank used in 3e. In other words, Climb Walls wouldn't be listed as 80%, but as +15. Since 2e allows you to start with a base and add points where the player wishes, I'd have to recalculate all new starting points. Climb Walls would start at +11, others would start somewhere between 1 and 5. I haven't worked that out yet.

Anyway, if you have a first level thief with an 80% chance of climbing walls vs a 1st level Thief in Andras with a +15 Climb Walls score...

(d20 + d10) + 1 + 15 ? 26

In other words, he/she would have to roll a 10 or better, an 82 percent chance of success.

More Work to be Done

Still more to be done, obviously. Just a weird idea. Yes, it would be easier to stick to Dan's original idea. His is more tidy in some ways and the formulas don't have this weird 26 all over the place.

Yet, the flat curve works for me. It does some funky things at higher levels that I like. Combat is still not automatic at higher levels, neither are Saving Throws. Maybe it will turn out to be a silly idea after all. As always, we'll see.

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  1. Keith Davies

    The only real downside I see to this compared to the flat d20 roll is that while d20 is ‘very swingy’, it is also very easy to eyeball. Seeing “have to roll a 10 or better, an 82 percent chance of success” confuses me for a moment, until I remember the curve is not linear.

    As much as I like the behavioral characteristics of the bell curve, I have to be honest that analysis and planning are much, much easier with a linear roll.

    • John Payne

      Planning and analysis are much easier with a linear curve. Thinking about Target20 for a second, 5th level characters, are basically going to start with a 20 percent chance of success before any modifiers are put in place. 10th level characters are at 50-50 before any modifiers.

      In actual play, I would have the players refer to the character sheet to determine bonuses and then the GM tells them their target number. For example, a 6th level fighter is making an attack on a creature. The character has a +1 to hit due to a 15 strength. The player knows that they are going to roll d20+d10+6 (combat level)+1 (Strength modifier). Then, the GM applies the Armor Class and other optional modifiers to produce a target number. Assuming the target has an AC of 4 and there are no other modifiers, I gladly tell them that the target number is 15. If the player wants, they can reverse engineer to determine what they believe the Armor Class to be, but the only one doing so-called hard math is me.

      I think I’d also put something on the character sheet that lists the Target Numbers with approximate odds of success. Personally, I don’t want to think in terms of percentage chances of success, I’d rather have an idea that a +2 bonus will have a minor effect, +4 a major effect and a +8 an epic effect. Being surprised when things don’t follow what I’d thought would happen is all part of the challenge for me. Maybe that’s because of some time spent playing Savage Worlds.:)

  2. John Payne


    Leaving this for easy reference later.

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