Characteristics!

So your Sudowoodo is 'proud of its power', and you're wondering what that means...

This is your Pokémon's characteristic, you can find it on their Summary, right over what flavor of berry they like to eat. It serves as an indicator of which of your Pokémon's Individual Values is the highest, and knowing what each means can be a priceless breeding tool.

These characteristics represent a top IV in HP:
'Often dozes off' can be: 1, 6, 11, 16, 21, 26, 31
'Loves to eat' can be: 0, 5, 10, 15, 20, 25, 30
'Likes to relax' can be: 4, 9, 14, 19, 24, 29
'Scatters things often' can be: 3, 8, 13, 18, 23, 28
'Often scatters things' can be: 2, 7, 12, 17, 22, 27

These represent a top IV in ATTACK:
'Likes to thrash about' can be: 1, 6, 11, 16, 21, 26, 31
'Proud of its power' can be: 0, 5, 10, 15, 20, 25, 30
'Quick tempered' can be: 4, 9, 14, 19, 24, 29
'Likes to fight' can be: 3, 8, 13, 18, 23, 28
'A little quick tempered' can be: 2, 7, 12, 17, 22, 27

These mean you have a top IV in DEFENSE:
'Capable of taking hits' can be: 1, 6, 11, 16, 21, 26, 31
'Sturdy body' can be: 0, 5, 10, 15, 20, 25, 30
'Good perseverance' can be: 4, 9, 14, 19, 24, 29
'Good endurance' can be: 3, 8, 13, 18, 23, 28
'Highly persistent' can be: 2, 7, 12, 17, 22, 27

These indicate a top IV in SPECIAL ATTACK:
'Mischievous' can be: 1, 6, 11, 16, 21, 26, 31
'Highly curious' can be: 0, 5, 10, 15, 20, 25, 30
'Very finicky' can be: 4, 9, 14, 19, 24, 29
'Often lost in thought' can be: 3, 8, 13, 18, 23, 28
'Thoroughly cunning' can be: 2, 7, 12, 17, 22, 27

These represent a top IV in SPECIAL DEFENSE:
'Somewhat vain' can be: 1, 6, 11, 16, 21, 26, 31
'Strong willed' can be: 0, 5, 10, 15, 20, 25, 30
'Somewhat stubborn' can be: 4, 9, 14, 19, 24, 29
'Hates to lose' can be: 3, 8, 13, 18, 23, 28
'Strongly defiant' can be: 2, 7, 12, 17, 22, 27

These ones mean you have a top IV in SPEED:
'Alert to sounds' can be: 1, 6, 11, 16, 21, 26, 31
'Likes to run' can be: 0, 5, 10, 15, 20, 25, 30
'Quick to flee' can be: 4, 9, 14, 19, 24, 29
'Somewhat of a clown' can be: 3, 8, 13, 18, 23, 28
'Impetuous and silly' can be: 2, 7, 12, 17, 22, 27

If two of your Pokémon's IVs are tied for highest, the characteristic represents a random stat. So if you have a 31 in Speed and Attack, it may say 'Likes to thrash about' OR 'Alert to sounds'.

When breeding, I check every Pokémon that has not only the characteristics indicating the IVs I'm looking for, but also any characteristic indicating a 31 IV. For example, I was breeding for HP and Special Attack in a Pokémon, when I hatched a baby who was 'Alert to Sounds', possibly meaning it had a 31 in Speed. When I checked his stats, on a whim, I realized he had 31 IVs in HP, Special Attack AND Speed, which is incredibly rare. So never toss a Pokémon aside because it doesn't appear to have what you're looking for.

Ideally, you should check every Pokémon. When hunting for 31s, you may pass up checking a Pokémon with a 'sturdy body'... and that Pokémon may turn out to have straight 30 IVs in every stat. Certainly a keeper!

Don't let the often boring task of making and hatching eggs make you forget to pay attention to the tiny details.