Math of D&D

The balancing of Dungeons and Dragons has meant that it is easier make encounters for players.  But the understanding is a little harder too.  Groups have been set to a four person standard.  Four players encounter their level challenges and it is a challenge, five player groups can defeat their level plus one challenges and six players their level plus two challenges.  Meaning that it is okay to throw larger groups against harder challenges and expect them to survive.  Like when five characters fought a troll and won and when a group of second levels took on an encounter that was two levels higher than them.  

The Dungeon Master's Guide, has some interesting tables for creating monsters.  They suggest that you start with hit points and move to armour class.  Then to look at maximum damage and then attack bonus.  

The defense side suggests how long the battle will last.  Mor hit points means more hits needed to defeat and this is a mathematical number.  If every character causes 7 points damage per hit that means that a creature with 70 hit points needs to be hit 10 times.  Armour class means how much percentage that they need to hit.  We assume that everyone has a +2 to hit because of stat, and +2 because of proficiency, so an AC of 11 is 70% likely to be hit.  Every AC point higher reduces the chance by 5%.  So when my players faced off against a foe with 42 hit points and and AC of 21, they were only 20% likely to hit and therefore, required 6x5 attacks to kill that one encounter character.  There were 6 characters so fighting this creature would require an average of 5 rounds of combat.  If it were just a sword fight.  And the fighter could use second wind to heal one and a half hits so, potentially 6 rounds of combat.  There was two other NPCs in that encounter, they had three hits worth of hit points and a 30% chance of being hit and could heal on hit worth of HPs so that means 4 hits.  One character got a lucky hit and killed one right away.  So that means there were expected to be in combat 8 rounds.  They were not, because that was just a rough count and did not include critical hits.  

If the NPCs AC was lower, say 15 then they would be hit 50% of the time and that would mean 14 hits would require 28 attacks, or five rounds of combat.  If they had a AC of 10, it would mean 75% success on hits so 18 attacks or three rounds of attack.  

There is the difference of armour class.

Offensive power is how likely is the monster likely to kill the characters.  The average it is measured in maximal damage and hit bonus.  In eight rounds the NPCs are going to do 8hp damage every hit.  The hit bonus was 5, this means that they had a 50% chance to hit AC 16, and in 8 rounds they would each get  nine attacks.  So an expected 9 hits for 72 points damage.  But the characters put the well armoured characters up first and that meant that the hitting chance dropped to about 25% so 18/4 or 4.5 hits or 36 points of damage.  

This is what happened.  

The def CR of the NPCs was 7 and 6, but the off CR was lower at about 1, so the average CR was 4 and 3 which means that it was a tough encounter.  

If there had been less players there, say 4, then the combat would have lasted longer, instead of 8, it would be 12.  So the NPCs would have got 13 hits apiece, and a 6.5 hits for 52 hp damage.  Likely two players would have died before the end of the combat and then maybe the other two.  Because less attacks mean less hits on them and more on them.

It was a tough encounter but with six players it was a lot easier.

5e D&D is about math