How much does “Defender Wins Ties” affect challenge rating math?

Question

In my group, we couldn't be bothered in session 1 to look up whether the attacker needed to score equal to or greater than the defender's AC in order to hit. We decided to live in a "defensive" world, and ruled that "Defender wins ties." This goes both ways for PCs and NPCs/monsters alike.

We've played like this for months and I've been wondering:
Just how much, if at all, does this house rule throw off encounter difficulty?

Is there a specific AC threshold that is thrown off by this? Does this favor "horde" encounters or "lone boss" encounters in some way?

(I understand that these are sub-questions, but they are so closely tied to the central question I don't feel they should be separated.)

Answer 1

This has very minimal impact on CR math

The easiest way to evaluate the impact of these changes is to evaluate how they impact CR based on the suggested guidelines for calculating CR for a custom creature.

From the Dungeon Master's Guide, Chapter 9 ("Dungeon Master's Workshop"), subsection "Creating a Monster", the following guideline is given for adjusting the CR of a creature, for Armor Class:

Now look at the Armor Class suggested for a monster of that challenge rating. If your monster's AC is at least two points higher or lower than that number, adjust the challenge rating suggested by its hit points up or down by 1 for every 2 points of difference.

Because every single creature is having its AC increased by 1 with no other changes, this is equivalent to all creatures having their Defensive CR increased by 1/2.

The guidelines for Attack Bonuses are similar:

Now look at the attack bonus suggested for a monster of that challenge rating. If your monster's attack bonus is at least two points higher or lower than that number, adjust the challenge rating suggested by its damage output up or down by 1 for every 2 points of difference.

In the same way, this means the Offensive CR of attack-roll-based creatures has decreased by 1/2. Creatures that depend on Saving Throws for most of their damage won't see an Offensive CR change.

So for all creatures, Defensive CR is being increased by 1/2, and for attack-roll creatures, Offensive CR is being decreased by 1/2, with Saving-Throw creatures seeing no reduction in Offensive CR. For the former creatures, short of especially esoteric situations, the net impact of these changes is not likely to change a creature's overall CR. For the latter, a change of 1/4CR (averaging +1/2 and +0) may be significant at lower levels of play, but is unlikely to impact anything beyond the first few levels of play.

Impact on overall game balance

Battles are going to take slightly longer than usual. All creatures are going to hit with attacks slightly less frequently, which will mean that overall, they take less damage than usual. Healing becomes slightly more powerful under this ruleset, because damage totals are lower, which means healing represents a larger proportion of damage issued during a fight.

Damage will become slightly more swingy, with characters staying at their same level of Hitpoints for longer than usual.

Players (generally) benefit from this system more than hostile creatures

This mostly boils down to the happenstance of how damage sources work. Players are more likely to depend on Spells or Saving-Throw-based Cantrips than hostile creatures are, and Saving Throws are unaffected by these changes (being already "Defender Wins" as written). So those spells will stay at the same power level, whereas weapon attacks and Attack-Roll-based spells (which are more common among hostile creatures) will be negatively affected.

Answer 2

I would say no change to CR.

There is an (approximate) 5% chance that a given roll ties with defender AC. If 5% of attacks DON'T land, for monsters and players alike, I think the game will remain largely the same.

In effect this increases AC of all things by 1, if you were playing "meets beats". Which I don't think is relevant for any single encounter/monster... But a players AC is tested over a larger period of time than one encounter.

A better way to look at this might be "What is the effect of that one extra point of AC, for everything". Looking that up brought me to this post on Reddit. I duplicated the spreadsheet linked within, increased all the armor AC values by 1, and saw that got me. You can try this yourself to look at the differences, but the general results are the same. Enemy hit chance is 5% to 3% lower across basically all levels and AC's, and DPR is slightly lower in all categories as well, but trends are the same across both sheets, leading me to believe that all this has done is make everything, players and monsters alike, a little more durable.

After writing that last sentence I wasn't satisfied so I went searching for DPR tables for players and found this gem. Repeating the same "increase all enemy AC by 1" trick I did with the last sheet and checking results, I noticed that changes in KPR and DPR were no more significant, but did change trends between sheets slightly, although I would be hard pressed to break that down for you in a way has a concrete answer. Looks like KPR for all classes and breakdowns in that table dropped somewhere from 1% - 4%... Except Sword and Board Barbarian, which stayed exactly the same.

Which means everything is harder to kill, and has a harder time killing everything else. Except S&B Barbs. Do you have one in your party?

Answer 3

The lower your chance to hit with your attacks/abilities, the more this hurts you.

Consider an extreme example: suppose we have a high-level, well-protected fighter facing off against a horde of weak monsters. Assume ACs and bonuses are such that under RAW, the fighter could hit with a roll of 11-20 (10 pips on the die) and each of the monsters can only hit on 19-20 (2 pips on the die).

This change means that the fighter now hits on a 12-20 (9 pips on the die) and monsters hit only on a 20 (1 pip on the die). So the fighter's hit chance & hence damage output has decreased by 10%, but the horde's has decreased by 50%. Effectively the fighter has become 80% stronger relative to the horde, in terms of how often they hit.

If both sides have disadvantage, the discrepancy is even larger: the fighter's damage output drops by 19% (from 100/400 to 81/400 chance to hit) but the horde's drops by 75% (4/400 to 1/400). Now the fighter has become 224% stronger relative to the horde.

As this answer points out, abilities that don't rely on an attack roll aren't penalised at all, so they benefit most of all.

Answer 4

“Defender Wins” hurts players over the course of the game, without significantly impacting any single encounter.

Run this rule if you want to subtly increase the overall lethality of your campaign.

Defender wins does not have a significant impact on any single encounter when analyzed inside a vacuum. It becomes problematic when taken holistically in the context of multiple encounters over the course of a dungeon crawl.

Monster packs, as a general rule, roll more attacks against players than players roll against monsters. Think of it like attacks per round (APR). A level 5 party, with a Fighter, Rogue, Wizard and Cleric, has 5 attacks per round. An appropriate pack of 10x orcs (CR Medium), has 10 attacks per round. This means the attacks per round is a 5:10 ratio during the first turn of combat.

The orcs will overcome the effective +1 to AC more quickly than the players will (they are rolling more attacks). A missed hit from the players penalizes the PC’s more heavily than the orcs as the players fewer hits deal more damage.

Defender wins, means that 1 out of every 20 attacks that would have hit – now miss. The first group to reach 21 attacks effectively overcomes the +1 to AC on each side. It should also be noted that this house rule does not alter or change potential damage per attack. This means if a monster gets an extra attack against a hero it otherwise shouldn’t (because it could be killed already), potential damage – and thus average damage – increases.

Using the 10:5 ratio of Party VS Orcs, each orc should take on average 2 hits to kill. This means at a minimum, the combat will need 4 rounds. (4 rounds x 5 attacks = 20). But with the AC adjustment, 1 of those attacks will now miss. Meaning one of the orcs, at some point during those 4 rounds, did not die when it should have under the normal rules. If it doesn’t happen until turn 4 – then the orc gets one additional attack. If it happened sometime around turn 2 or 3 – that orc will get an additional 2-3 attacks against the players it otherwise wouldn’t have.

Isolating the practical effect of +1 AC

Scenario 1 – Players hit every attack, but miss one attack every 20th attack roll.

In this scenario, we assume the party can kill 2.5 orcs per round (Half an orc, is an alive orc). So the number of orcs on the field per round would be: 8,6,3,1 (Combat is over after round 4) Monsters have a total potential damage output of 171 damage (18x9).

If the missed hit happens sometime around 1, 2, or 3, then the numbers look like this, 8,6,4,2. Monsters now have a total potential damage output of 180. An increase of 9% total potential damage. This overcomes the 5% drop in chance to hit.

This assumes the players hit with every attack. If they only have a 50% chance to hit, the numbers change quite a bit. The orcs now only die at a rate of 1.25 per round (.25 orcs per attack). This changes the numbers quite a bit. 8, 7, 6, 5, 3, 2, 1. This is 7 rounds of combat, or 35 player attacks. In this same match, the orcs have 32 total attacks – for a total potential damage output of 288.

Now add in the 1 miss out of 20 (from the +1 ac). The First miss happens on or before round 4. And there is a 75% chance of a 2nd miss sometime in the second half of combat. This means an extra orc will be alive for certain in rounds 4, 5, 6, and 7. Or 4 additional attacks. Somewhere around round 6 or 7, a second miss should happen, and for simplicity, we will add one additional attack, and one additional combat round – for a final total of 37 attacks and 8 combat rounds. Bringing our raw damage potential up to 333. This is an increase of 8.6% damage. Again, this overcomes the -5% chance to hit.

When you increase raw damage potential, you necessarily increase overall damage when calculating average damage. A 9% damage increase compared to a 5% chance to hit means a 4% overall increase in final damage against the party.

This may not seem like a lot, but over the course of a long dungeon crawl it adds up. Assuming 3-4 encounters in-between long rests or the “Final Fight”, the party will have taken 12-14% more damage compared to the standard AC rule.

The extra 1 or 2 combat rounds per encounter also encourages players to expend more limited resources (spells, healing, hit dice, abilities). Meaning they will be weaker on their next encounter down the chain – forcing more frequent Long Rests or risking lethal combat. This is most noticeable at lower levels where players have very few hit points, and 1 or two extra attacks can mean the difference between a live wizard, and a very dead wizard.

Also consider what the extra round of combat means for Big Evil monsters. It’s a full extra round of breath weapons, or spells, or multi-attack. One extra round against dragon is up to 3-4 attacks, and they have high to-hit and high damage output (easily overcoming the +1 ac bonus). An evil wizard with frontline minions is going to get off one more AOE or save or death throw during the encounter than it otherwise should.

The rule favors Optimized and Min/Maxed Characters and Spell Casters. Penalized non-optimized or support Characters.

This rule also heavily penalizes Multiple Attribute Dependent classes (Monk, Paladin, and Druid), multi-class builds, or feat intensive builds. These builds tend to not have a maxed or near maxed primary attack stat, or have to delay their ASI until much later in their careers. A 5th level Min/Maxed fighter/wizard with an attack rating of +8 can more easily absorb the +1 to AC, than the support bard with a total of only +5 or +6 to their attack roll.

As mentioned in other answers, the effect this rule has on any single encounter will be marginal. But taken in the context of multiple encounters over the course of your campaign, will result in a lot of extra damage an expenditures of resources against the players.

Player hit points and resources are persistent in-between encounters. Monsters usually have full HP and resources whenever initiative is rolled. Most parties that run this rule and don’t see any noticeable effect are usually pretty liberal with the +1 and +2 weapons – counteracting the to hit nerf against monsters and ends up being a bonus AC to the players.

If you run things as intended, you will see your players subtly struggling harder than they should over the long course of a campaign and they get ground down through multiple encounters.

At low levels, this rule variant is especially lethal (where one single attack can outright kill most player classes).

In Summary

For any single combat encounter, the “Defender Wins” rule doesn’t have a huge impact on game balance. But over the course of a dungeon crawl, and in fringe cases (Huge Hoard, High AC Monster, Spell Caster Monsters), it has a noticeable long term effect. Players are taking monsters off the field less frequently, increasing damage dice exposure, and increasing the number of combat rounds per encounter. This causes players to have overall fewer hit points and resources at the end of an encounter run or dungeon crawl, making the campaign more difficult.

Run this rule if you want to subtly increase the overall lethality of your campaign.