Imagine this scenario that you might find somewhat relatable:
A father gets his family together to play Pathfinder.
Little Timmy wants to play an half orc barbarian. Dad explains he'll want really high strength to hit things harder, constitution for the health, and dexterity for the initiative and armor. Timmy rolls and ends up with the rolls 13, 14, 12, 13, 14, 12
Timmy is now sad because his physical stats are low for a martial character. Dad tries to make him happier by telling him that with point buy, those are worth a lot of points, but Timmy is still sad.
Timmy's big brother, Charlie, is now up. Charlie had planned to play a magic-focused cleric, but seeing Timmy would need help on the martial side, decides to play a human war cleric. He knows he needs high physical stats for the melee, as well as wisdom for his cleric abilities and charisma for channel energy. He rolls 16, 15, 15, 10, 9 8. Once again decent rolls, however Charlie has a problem. He cannot efficiently cover melee, spellcasting, and healing with those rolls. He now has to decide to focus on, and what the two of them will have to do without.
You yourself may have had a similar experience to this before - skills too spread out or consolidated. But what if I told you there was a way to generate stats that fit your character build more? Well there is... and it's called point buy.
Forgetting everything I am about to write, point buy does solve this problem - you can decide between a consolidated array or a spread out one. But this thread is not about point buy. No, it is about a crazy idea that popped into my head one day. After testing the math, I found it to be only slightly broken. I call it Flexible Stat Rolling, or Flex Rolls.
The process is simple.
Generate a set of 4 stats using the typical 4d6 drop lowest. Do that three times, so you have three sets of 4 stat rolls each. Then, from a set of you choice, take the top two stats. From a different set of your choice, choose the middle two stats. From the last set, choose the lowest two stats.
This is relatively balanced because by taking a high score from one set, you are forced to take medium and low stats from the other sets. I made a computer program that generated the four sets, found all 6 possible selections of stats, and then calculated the one with the highest point buy value (I made up point buys for the numbers below 6 that roughly followed the pattern of increase for going up from 10). Then I had the program do that 10,000 times and calculate the average max point buy value. It was always almost always 23.8 to 24.2, or at least super close to that (I never saw it lower than 23 or higher than 25). I then checked if instead of doing 2 highest - 2 middle - 2 lowest resulted the same average max point buy as 1 high - 2 middle - 3 low or 3 high - 2 middle - 1 low. They were the same. Then I checked all three selection patterns but with rolling 3d6 instead of 4d6 drop lowest, and it was an average of 9 for all of them.
The nice thing about this is that from one collection of rolls, you can select scores in a way that aims for some higher scores by taking a few lower scores as well, or you can select a more balanced selection.