Strength has consistently been one of the best ability scores in every version of Dungeons and Dragons, so it makes sense that it has finally fallen from grace to be a common dump stat. Even for melee characters, Dexterity is a better choice to focus on since it provides a bonus to your AC, is used to determine initiative, is the most common saving throw made in the game, and, like Strength, is added to attack and damage rolls. So, how can Strength be made more like Dexterity? Try adding one or two of the following variants:
Bonus Hit Points
Strength and Constitution are fairly similar in their descriptions, so it stands to reason that they could provide similar bonus as the other. While this may be better presented as a feat, it is really only overpowered when being used with multiple of the options below. You could allow characters with a Strength score of 14 or higher to gain +1 hit points per level and characters with a Strength score of 18 or higher to gain +2 hit points per level. This is essentially a bonus to hit points equal to half of the character’s Strength modifier rounded down with a minimum of 0. This bonus to hit points still won’t downplay the importance of Constitution, but it will still provide an added source to survivability from Strength.
Bonus Melee Damage
Since Strength is a measure of ones pure physical power, it makes sense that Strength provides a higher bonus to damage than Dexterity. Instead of Strength granting a +1 bonus to damage per modifier, have Strength grant a +2 bonus to damage per modifier. In other words, double a character’s Strength modifier to damage.
Another option would be to allow Power Attack functionality to affect Strength-based attacks. Basically, allow players to trade their attack roll bonus for bonus damage. Players should not be allowed to trade in more than their Strength modifier. The penalty the player suffers to their attack roll and the bonus damage gained last until the start of their next turn, meaning this also affects attacks made with an Extra Attack feature and attacks of opportunity.
This is a fairly powerful variant that might be better suited to a feat than as a base function of Strength. Characters that have a positive Strength modifier (score of 12 or above) can use their reaction to make a Strength check DC either 15 or half of the damage taken, whichever is higher. On a success, the player gains resistance to whatever types of damage the attack dealt. This cannot be used against damaging effects that already require the player to make a saving throw.
Since initiative is more of a measure of a character’s combat readiness, players should have the option of using either their Strength or Dexterity modifier when rolling initiative.
While a minor benefit to Strength is the impact it has on your character’s ability to jump, this is often overlooked by players and DM’s in favor of just making an athletics check. Athletics checks should only be made under dire circumstances or of the players wants to try a physical activity beyond what their character would normally be capable of (ie. making a standing long or high jump).
In the PHB, we are given defined values for each jump type. Make the following modifications to those:
When moving at least 10 feet before jumping, you can cover a distance of your Strength score + 5 feet.
When moving at least 10 feet before jumping, you leap into the air a number of feet equal to 5 + your Strength modifier.