Ability Score Rolling Redux (5e Variant Rule)
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Ability Score Rolling Redux
So the normal range for ability scores when you roll for them with the rules of the 5e PHB is 3-18. If you want a higher but still fair and random system for your players rolling ability scores for their characters, I've got you covered. Roll 7d4 and take the highest 5 for each score. This gives you a new random range of 5-20, leaving a small window to have a powerful character or a very weak one, but not quite as weak as a 3 ability score would give.
DM Note: It's worth noting that a low level party usually doesn't get a 20 ability score without building the character specifically to do so, so it leaves room for more powerful characters (If slightly); and since 20's the highest natural maximum, it means that a character that starts with this score couldn't improve in that area, so keep this in mind. It may not be viable for long running games, but might be well suited to shorter ones where the opportunities to improve your characters are rarer or even non-existent (As is the case with one-offs).