In an attempt to have players deal with more difficult decisions, I have been considering the idea of making it so that saving throw bonuses don't actually rely on your modifier, but instead use your mod +1 if the attribute is an odd number (effectively making it round up).
For instance, under the current system (RAW): if your Dexterity score is 13, your Dexterity modifier is +1, meaning you add +1 to the d20 roll when you make a Dexterity check (assuming your proficiency bonus is not being added to the specific check). If you are not proficient in Dexterity saving throws, your Dex save modifier is also +1.
Under my proposed system: If your Dex score is 13, your ability score modifier for Dex checks (when prof. bonus is not added) is still +1, as in RAW. However, under my proposed system, your Dexterity saving throw modifier (not including your proficiency bonus) would instead be +2.
The idea here is to make it so that you feel more comfortable spreading out your stats rather than bulking them on individuals.
But I know how big of a deal saving throws are in higher-level play. Would this have a negative effect, and does this address a real concern common to players (or am I just making an assumption)?