# "3d4 Array" Score Rolling

There are several methods of generating ability scores when creating new Dungeons & Dragons 5e characters. Those that offer a great deal of random variance can all too often leave a character starting off much weaker or stronger than the rest of the party. More balanced methods don't allow the variance between players' scores that helps differentiate characters at the start of the game. It's a surprisingly difficult challenge to reconcile these shortcomings and create a system that appeals to all players.

### Argument Against Other Methods
* **4d6 keep 3** and other highly variable methods frequently produce a drastic difference in power between characters. While it can be enjoyable to roleplay low stats, it’s not fun to be constantly ineffectual or outshined by another player character.

* **Point Buy** and **Standard Array** are well balanced, but less dynamic in their results. Characters can feel *"samey"*, especially at low levels. This also removes the thrill of rolling stats at character creation in favour of a  much more sterile-feeling system. 

* The **[Colville Method](https://blog.dwgill.com/matt-colville-rollout/)** is very enjoyable, but doesn’t fit every style of game. Players generally have an idea of what class or subclass they want to play, and this rarely accommodates such planning. However, this method is a step in the right direction and a good way to *discover* your character, not just build it.

### Argument For the 3d4 Array
Using the method I've named "3d4 Array" produces the balanced start of Point Buy and Standard Array, wile still allowing for some variance and providing an opportunity to roll some dice. It is a compromise, plain and simple, but an effective one.
>##### Average Values
> Over a sampling of 1 million sets of rolls, the average scores of characters created with this method came out to **12.16**, and the average total modifier came out to **5.00**. According to a reddit post (https://redd.it/75ixng), here's how it stacks up against other methods:
>
> |Method|Avgerage Score|Average Modifier|
> |:-:|:-:|:-:|
> |Std. Array|12.00|5.00|
> |Point Buy|12.03|5.08|
> |Mr. Seti|12.16|5.00|
> |4d6k3|12.25|5.90|
> |Colville ("v1")|13.04|8.06|

## The Method
The 3d4 Array method uses a simple set of pre-defined tables to generate a pseudo-random result from three d4 rolls. A player rolls **1d4** for **Tables A**, **B**, and **C** to generate their ability scores. Roll **1d4** for **Table A**, and noting down the two values the dice roll corresponded with. Do the same for **Table B** and **Table C**. At this point, an array of 6 scores has been produced. Assign the values to your character's attributes in whatever order you like. 

##### Mr. Seti's Score Tables
<div style='margin-top:10px'></div>

<div style='column-count:3'>
|1d4|Scores A |
|:-:|:-------:|
|1  |10, 10   |
|2  |9, 11    |
|3  |8, 12    |
|4  |7, 14    |

|1d4|Scores B |
|:-:|:-------:|
|1  |11, 12   |
|2  |10, 13   |
|3  |9, 14    |
|4  |7, 16    |

|1d4|Scores C |
|:-:|:-------:|
|1  |14, 15   |
|2  |13, 16   |
|3  |11, 17   |
|4  |9, 18    |

</div>


The tables are balanced so that the overall power of a character (all scores summed) will be comparable for each player, but they may have quite different individual scores to choose from. Specialized characters with especially high individual scores have lower overall scores as a counterweight, while more rounded characters will pull a higher overall stat pool to make up for their less definied individual strengths.

#####  

Rolling three ones with the d4s would produce a very well rounded character, while three fours would end up with a character very strong at several things, while being much weaker at others. No matter the result of the dice rolls though, the overall total of the scores added together will be very close, giving players a balanced start to the game.

#####  





<div class='descriptive'>
##### Example

As a player, say you rolled three sequential d4, and got the results 3, 1, and 4. The scores you'd use from the tables would be "8, 12" (Table A), "11, 12" (B), and "9, 18" (C). The dice you rolled had higher face values and thus your scores will have a more deviation, as the more varied scores are at the lower portions of the tables. Having a starting attribute with a score of 18 would make your character very strong in some way, but you'll have to balance it out with the much lower score of 9 it was paired with.
</div>

<img src='https://i0.wp.com/triangularroom.com/wp-content/uploads/2015/05/Dice-Small.png' style='position:absolute;bottom:50px;right:30px;width:280px' />

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<div class='footnote'>3D4 ARRAY v1.1 2020-03-01</div>