Since 3e it didn’t really make a difference if you had an odd ability score, since the most important thing about an ability is its modifier. In some regards it was tried to make odd ability scores kinda useable by using odd number values as prerequisites for feats. But be honest: It wasn’t (and is) not hard to meet those numbers and if they were higher, you simply adapted your build to it. Two-Weapon Fighting needs up to Dex 19? OK, then I’ll go finesse!
But even today people mourn the times pre-3e, when odd numbers in ability scores had their value (at a certain point). And even I, someone who started with 3.0e can acknowledge the usefulness of having an easy and direct bonus to most stuffs, while thinking that the classiness of the 3d6/4d6k3 rolls might be not the best, considering how less the actual attribute says. So I thought: Let’s change it, maybe I might get a nice idea there.
Of course the idea wasn’t either nice nor creative, but simple the expression of common sense. If an odd ability score is halfway to a higher modifier, just increase the modifier-bonus for certain rolls and stats. But it was a bit difficult to settle on the finished rules, since not all traits are equally worth and it should be kept as simple as possible. Sadly, it’s still rather complicated, but since you can track all bonuses on the character sheet, it’s still passable, imo.
Here is the summary. If you have an odd ability score, you increase the following by +1:
- Saving Throws
- STR, DEX or substitute (like the druid’s Shillelagh spell): Weapon Damage
- DEX: Initiative
- CON: Bonus due Hit Die/Dice healing
- INT, WIS, CHA: Spell Attack Modifier
- When (for some reason) your ability score/modifier is halved, round up
If you think it’s not enough, you can even go further, like:
- CON: +1 hit point/2 levels
- +1 to proficiency skills (since you simply know about them more and can utilize the even tiniest improvement better)
- no +1 to spell attacks if you cast a cantrip
And here the details behind the decisions: In the end, an even ability modifier should still be the more valuable option, especially since abilities caps at an even value. So I aimed for lesser bonuses, which would be appreciated, but not as hard valued. If you would grant ability checks (particularly skills) the antedated bonus would be the sorry target of abuse. Stats like AC were a no-go, I really considered the Spell DC, but then the 20 wouldn’t be as powerful as it should be.
The reason why the attack bonus for spells is raised, the bonus for weapons not is the frequency. Weapon-focused classes makes a lot of weapon attacks, since it’s their primary option. But only 23 spells (7 cantrips) are using spell attacks, so many more use a save system.
Saves on the other hands seems absolutely reasonable. Since they varies much more and can’t be abused without a DM, I guessed one of the three most important roles (ability checks, attack rolls, saving throws) could be represented in an odd system.
Initiative is just because. It seems so lonely sometimes…
Maybe some similar rule might appear at the DMG (not that I think it will), but for now, you can consider if some minor boons with odd ability scores is reasonable.