When you're creating a brand new character, you have major choices to make that will define how you play your campaign. Choosing your class will take you some of the way towards deciding which ability scores you want to prioritise, and your choice of race will then add bonuses to help you reach your goals.
When you roll or use the standard array to decide your stats, it's likely that you will end up with some odd-numbered ability scores. When you're using the point-buy method, it's sometimes (but not always possible to avoid them). But why would you do this and are there any benefits?
What Are the Drawbacks of Odd-Numbered Ability Scores?
Aside from the fact that everything looks beautifully symmetrical if it's only painted in even numbers, the line of thinking here is related to the way that modifiers are generated. An ability modifier relates to two ability scores rather than just one – so for example, a +1 modifier for an ability comes from a score of either 12 or 13. Point buy is the main character generation method where this becomes a bone of contention – the higher the ability score you buy, the more points from your pool you have to spend on it. You only have 27 points to spend, so when you start getting into the choice between spending 7 points to place a 14 in one of your ability boxes, or spending 9 points to place a 15, that 2 point overspend could cost you when it comes to buying something else. Usually this affects lower scores – it could be the difference between having a score of 8 (-1 modifier) in one of your weaker stats, or keeping things even at 10 (0 modifier).
Not only that, but if you have only one odd-numbered ability score, and it's something you're intending to increase as you level up, you could end up with a spare, floating ability point to drop somewhere else. Ability Score Increases (your first one comes at level 4 if you're not there yet) allow you to increase one stat by 2 points, or 2 stats by 1 point. Eventually, your odd-numbered score could end up at 19 out of your maximum of 20. Disaster! If everything else is even then you then have to waste your final point making another stat odd-numbered, which of course then puts you straight back in the same position – you miss out on increasing your ability modifier. How frustrating!
Example – Gnome vs Tiefling Wizard
Let's imagine two members of a party are creating a Wizard at level 1. One of them decides to go for a Gnome and the other one decides to choose a Tiefling. Intelligence is the most important stat for a Wizard: it governs how easy it is for them to hit with spells and makes those spells harder to resist if they're the type that come with a saving throw. For the purposes of this example, we're only going to look at the Intelligence part of the build, and we'll assume that both characters are using the point buy method of choosing their Ability Scores. Both players want as high an Int score as possible.
The Tiefling player pays 9 points to buy a 15 for their Intelligence. Tieflings (the standard variety – the player has chosen not to go with any variants or choose any of the subraces) get a +1 bonus to Intelligence.
This puts their Intelligence score at 16, which gives them a modifier of +3.
The Gnome player pays 9 points to buy a 15 for their Intelligence. All flavours of Gnome get a +2 bonus to Intelligence.
This puts their Intelligence score at 17, which also gives them a modifier of +3.
As the Intelligence score itself is likely to have no impact at all on the game (the modifier is mostly what we care about apart from the potential for very fringe exceptions depending on how your DM runs the show), the Gnome player gets no advantage from starting with a 17 Int compared to the Tiefling's 16. Both players will have the same Spell Save DC and Spell Attack Modifier. Functionally, despite one having a higher Intelligence score on paper, they are identical with this set-up.
That means that the Gnome player, with their +2 Intelligence bonus could have chosen only to spend 7 points on their Intelligence score, which would get them a 14. After the +2 racial bonus, that still puts them at 16, level with the Tiefling. However, they have now saved 2 points that they can spend elsewhere, such as Constitution or Dexterity, to help their Wizard last a little longer if the going gets tough in combat.
Sounds simple, right? Avoid odd-numbered ability scores at all costs...
But What if There Is a Benefit?
First of all, if you are in a situation where you end up with two odd-numbered scores, it's definitely something that you can easily fix. When you come to your first Ability Score Improvement, you can place one point in each of them and then boom! You've increased two of your modifiers in one fell swoop! That should put a smile on your face!
If you are stuck with a lone odd-number, though, feats may just be your answer. There are plenty of feats that offer you a +1 bonus to an Ability Score alongside the benefit that they grant your character. Resilient is a great example of this, giving you that +1 boost (and solving your problem), and netting you proficiency in the related saving throw along the way. The only catch here is that feats are a variant rule, so you'll need to make good and sure that your DM is allowing them before you start licking your lips at the range of choices available.
In the case of our Gnome and Tiefling players – let's look how things could play out when they hit level 4.
The Tiefling player chooses to use their entire Ability Score Improvement to boost their Intelligence. They increase it by 2 points, giving them a score of 18 and taking their modifier to +4. Happy days!
The Gnome player receives confirmation from their Dungeon Master that feats are permitted. They could choose to increase their Intelligence to 19 by making the same choice as the Tiefling player, as it would give them epic bragging rights! (“Yeah sure we both have a +4 modifier, but my Gnome definitely knows more than your Tiefling does! Read this and weep!”)
Instead, they decide to give themselves an edge in a different way – they take the Gnome racial feat Fade Away (from Xanathar's Guide to Everything). This lets them bump their Int score to 18, granting them that juicy +4 modifier in the process, but it also gives them some added protection in combat. There's nothing like a disappearing Gnome to confuse those bad guys!
As with everything else during character creation, everything is a question of balance and prioritising what you'd like your character to be best at doing. Saving some points, or those big scores on the dice, could be tempting if you're thinking about immediate benefits. However, it's always worth thinking about the long game, and being able to take a feat somewhere down the line could be worth taking into consideration – especially if it helps you to achieve the build you're looking for.