Is it better to take the array and be Joe Average, or to roll for the odds of getting on average better scores?

I am new to D&D. I was looking at character creation for D&D 5th edition. There were a few ways one could generate ability scores. I assumed the optional method of taking the numbers 15,14,13,12,10,8 would be at least as good as the default chance method (roll 4d6, drop lowest die), and more likely, just a bit better than chance.

However, with the above method, the summed ability scores is 72, which is just a bit shy of the summed average one would obtain by rolling dice: the average ability score generated by dice should be 12.2446, which means the sum of the average ability scores is 73.4676.

What the 15,14,13,12,10,8 method accomplishes is to give some moderately high scores, but no exceptional ones, without giving any terrible scores (dice rolling typically gives at least one score of seven or less). To my mind that suggests that the rationale is that many players may find that “joe just-below-average” across the board is better than Achilles, who is amazing in some ways, but has that crazy heel weakness. He is also maybe better than “Joe Exactly-average” who has no high scores and no low ones?

Are those rationales good, i.e. is it actually better to have Joe Just-below-average-with-some-bright-spots than Joe Completely-average or Achilles?


Correction: The odds of rolling all ability scores at 8 or above are 70%, so I misspoke when I said usually one will roll one score below an 8. In fact, usually one does not, but not in a strong sense. It is no more unlikely to get a score below 8 than two coin flips coming up tails. It happens.

I provide a quick chart at the end, which makes the statistics easy to generate. As I generated the numbers quickly, I confess the possibility of error. For the 1296 possible rolls of four dice here are the number of ways you can obtain each value as the sum of the best three.

Sum of best three | Number of possible rolls that give that sum of best 3 --------------------------------------------   3                     1   4                     4   5                    10   6                    21   7                    38   8                    62   9                    91   10                  122   11                  148   12                  167   13                  172   14                  160   15                  131   16                   94   17                   54   18                   21