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That goes up against (in the case of simply swinging a sword) the targets AC. E.g if your attack roll bonus total is 10 and the target has an AC of 20 then to hit it you have to make D20+10 = 20. That is a 50% chance close enough.
Different types of attack go up against different types of defences (for example a fireball goes up against reflex saving throws and fire resistance) but the principle is always the same.
It follows that to improve your chance of hitting the target you try to improve your attack roll bonus because this shifts the D20 roll in your favour. The list of things to look at are listed in that formula above. For example your cleric can cast Bless on the party (an enchantment) which IIRC grants them a +1 to attack rolls. A +1 on a D20 roll = +5% chance to hit. That's why Bless is considered a kick arse spell.
If you study the combat log and expand the details of any one swing you will see the calculation set out, how exactly your attack roll bonuses were added up. Obviously knowing all this is very important when picking level up options and choosing your gear.
When you attack, there are (up to) 3 dice rolls.
You roll to see if you hit, this is based on your primary stat which only effects hit chances (eg.. charisma, intelligence...), but is ALSO reduced by enemy armor, so rather than actual armor, armor is more like a dodge chance.
You roll for damage if you hit.
The enemy rolls to resist statuses if the attack has them (saving throw), the stat they use for the roll is mentioned on the ability tooltip.
Basically just dice rolls all the way down, there is little way you can plan for any of it, except to pump as many points into your primary stat, I guess.
Much more frustrating than just a basic 95% hitchance against most enemies, with armor and stats only effecting damage and not making you miss all the time.
https://roll20.net/compendium/dnd5e/Rules:Combat?expansion=0#toc_31
Your primary stat is obviously important but that's just one part of it, there are many other ways to improve your attack rolls. That's what the game is about, it's a bout manipulation the D20 rolls in your favour, loading the dice so to speak.
It's like backgammon. Bad backgammon players think they lose 'cos they get unlucky rolls. Good backgammon players pocket their money and politely enquire if their victim would like another game.
Taking damage is the worst possible outcome and it is very lethal.
By default, the hit rate is 50% (you need to score a 10 on a d20 to hit) then each bonus point in attack equals +5% and each point in AC over 10 for the defender translate to -5%.
So it does go down very fast, and you need you stack attack bonuses to keep it up.
It is broken down into sub cathegories.
Bonus from stats (strenght, dex...)
Proficiency bonus
Bonus from magic weapon
Roll bonus
wait... What is a "roll bonus"?
Edit: I think it is from being Blessed by an Elixir of Heroism. Does that mean that the duration for the Bless is until the next long rest, even if the Blessed icon is only present for 10 rounds?