Dice Rolls and Modifiers

Roll20 handles all of this, and that's a double edged sword. For those of you that want to better understand how rolls, attacks, and damage are calculated, and the Player's Handbook just isn't cutting it, I've tried to break down the more common scenarios in the sections below.
First, let's start with values that modify your dice rolls, as they form the foundation of your character's strengths and weaknesses.

Modifiers:

At Their Core: A modifier is a single number that impacts rolls regarding a certain action. There are two such modifiers you will see often; your Ability Score Modifier, and Proficiency Modifier.
Ability Score Modifiers: Your ability scores are the six core stats that determine how your character performs. They are the Strength, Dexterity, Constitution, Intelligence, Wisdom, and Charisma values, converted from their scale of 0 to 20 into a range of -5 to +5.  Note that the scale does continue to increase beyond 21.

Proficiency Modifier: Proficiency is determined by your Class, Background, Race, and Feats. Often represented by a checkmark next to a skill or saving throw. Proficiency in something allows the proficiency bonus modifier to be added to the roll, along with the ability score modifier. Your proficiency bonus is determined by your level.

These two values are then applied to rolls in the calculations below.

Calculations:

At Their Core: There are five situations where you will find yourself rolling, three that share a formula; Skill Checks, Saving Throws, and Attacks. We’ll cover damage and initiative after, as they are a bit different.

Final Value = 1d20 + Ability Score Modifier + Proficiency Bonus

Skill Checks and Saving Throws Each skill has a primary ability associated with it, as listed on your character sheet. For example, Athletics is associated with Strength. This means that when you roll Athletics, the ability score modifier you include is your Strength’s Ability Score Modifier. If you are proficient in the skill or saving throw (indicated usually by a checkmark on the character sheet), you will also add your proficiency bonus to the roll. Some feats, abilities, and class features (like the Bard/Rogues “Expertise”, can manipulate this calculation.

Example: When Fork rolls for Stealth, which is associated with Dexterity, his d20 roll is modified by his +3 Dex Modifier, and +2 for being proficient in it. Meaning whatever he rolls, he adds a total of 5 to the dice roll.

Attack Rolls Attack Rolls are done to determine whether your attack will hit. Two things differentiate attack rolls from skill checks. The ability score modifier you apply is determined by how you’re attacking, and whether you are proficient is determined by what you’re attacking with.

• Melee Attacks: Strength Ability Score Modifier (Dexterity can be used in certain situations, like if the weapon has the “Finesse” Property)
• Ranged Attacks: Dexterity Ability Score Modifier
• Ranged Spell Attacks: The modifier is determined by your class, either Wisdom, Intelligence, or Charisma. Vita’s is Wisdom, while Bulgey and Tilly utilize Charisma.

The proficiency bonus modifier is applied if the attacker is proficient with the weapon they are using. Spellcasters are always proficient for spell attacks.

Example: When Bulgey attacks with a Rapier, which has the “Finesse” property, he chooses to add his Dexterity modifier of +2 to the roll, and another +2 for being proficient with Rapiers. So when he rolls to attack with it, he adds a total of 4 to the dice roll.

Initiative Rolls Initiative Rolls are done to determine turn order at the start of combat. The roll is modified by your Dexterity Ability Score Modifier, and in the case of a tie, the character with a higher dexterity score goes first. This is why, in Roll20, you see decimal values associated with each roll, it automatically prioritizes the higher dexterity roll when the whole numbers are tied.

Example: When Brian rolls initiative, his Dexterity Modifier is +2 for a Dexterity Score of 14. This means, in Roll20, whatever he rolls will have 2.14 added to it.

Damage Rolls Spell Damage Rolls are often dictated by the wording of the spell, and cannot easily be summed up by a catch-all formula. However, spells that involve a Ranged Spell Attack roll can crit, and in those situations follow the same logic as the below calculations. Non-Spell Damage Rolls are comprised of two groups; the dice and the modifiers.
The Dice: The dice roll is determined by the weapon being used; each weapon is defined as having a certain dice associated with it; be it a 1d4, 1d6, 1d8, 2d6, 1d10, or 1d12. Some skills, feats, and abilities may add additional dice to this group, such as the rogue ability “Sneak Attack”.
The Modifiers: The modifier that impacts damage is determined the same way as the attack roll’s damage modifier. The big difference with damage is that you do not apply any proficiency bonus.
Critical Hits: When the attack roll’s d20 lands on 20 (or 19 for certain classes and abilities), the attack is considered a critical hit. Modifiers are not considered when considering if an attack is a critical hit. Once determined to be a crit, all die rolls associated with that attack’s damage are doubled. So if you were going to roll a 1d8 for damage, you now roll 2d8. The modifiers are NOT doubled.

Example: Brian attacks an enemy (with Armor Class 12) with his shortswords. With his first swing, he rolls a d20, adds his strength modifier (+2), and adds his proficiency (+2). He rolls a 16, which gives him a total attack of 20, which hits. He then rolls the damage die for a shortsword (a 1d6), and adds his strength modifier (+2). Rolling a 4, +2, would be 6 damage.

With his offhand, he rolls a d20 to attack, and rolls a 20. The modifiers don’t matter, a natural 20 roll on a d20 hits, and crits. He then rolls double the damage die (so 2d6 now), and adds his strength modifier (+2). Rolling a 3 and a 5, +2, would be 10 damage.