How to create random and balanced ability score arrays

This method allows you to randomly create ability scores while avoiding over-powered or under-powered ability arrays. The total of all six ability scores for a character will add to a fixed, pre-determined number.

1. First, select the minimum and maximum allowed ability score values. For example, we might decide that all ability scores must be between 6 and 18.
2. Next, add the minimum and maximum scores together. Let’s call this number the “pair total” of PT for short. In our example, we add 6 + 18 = 24, so our PT is 24.
3. Create our first ability score using whatever method we like. For example, we can roll 4d6 and keep the highest three. Note that this method could (very rarely) give us a value less than 6, so if we get a value less than 6 we can either re-roll the dice or just use the minimum value of 6.
4. To get our second ability score, we subtract the first ability score value from the PT. For example, if we rolled a 14 for our first ability score, for our second score we’d subtract 24 - 14 = 10, so our second ability score would be 10.
5. Repeat this process two more times so that each time we get a pair of numbers that when added together equal the PT. When we are done, the total of all ability scores added together will equal 3 times the PT. In our example, the total of all generated ability scores would equal 72.

I used a dice roll method 20 years ago.

First, declare your race and class.  Then:

Declare your 'best' stat and roll 1d4+14  (16.5 average)

Declare 2nd best and roll  1d6+12  (15.5 average)

Declare 3rd best and roll 1d8 + 10 (14.5 average) 

Declare 4th best and roll 1d10 +8 (13.5 average)

Declare 5th best and roll 1d12 + 6  (12.5 average)

Declare Worst and roll 3d6  (10.5 average)

I liked this method because you were guaranteed a playable character and there was a chance that your Wizard had an Int 15, and a Str 18.