D&D 5E No ascending bonuses: A mathematical framework for 5e

[Hassassin]

So we need a system that maintains the illusion of danger well above the actual threat of death.

Assuming you want this, I think it basically means that the probability to be knocked unconscious is significant, but the chance of 1) bleeding to death and 2) everyone going down are still small.

 

[KarinsDad]

While I agree with the sentiment, we have to face facts. If you're going to face dozens of lethal encounters, you're either going to get really, really consistently lucky or die.

If every encounter is 20-to-1, in the party's favor, they only have 50-50 odds of winning a dozen fights in a row.

So we need a system that maintains the illusion of danger well above the actual threat of death.

The question is, where are you pulling out these numbers?

Very few people today play against lower level encounters because they are too easy. Making lower level encounters a bit tougher in 5E just means that more DMs will sometimes throw in lower level encounters.

Making higher level encounters a bit easier means that the DM can sometimes go a bit higher than he normally would.

In 4E, one of our groups went from 1st level to 17th and another went from 1st level to 18th (although that group skipped some levels). We had no TPKs and I cannot remember a death, but I'm sure one or two happened. I don't remember ever running away either. That's not a dozen fights in a row. That's over 250 fights.

There are just too many synergies and options in 4E for the base math to lead you to a conclusion of "sooner or later, you all die". The players have just too many ways to heal and to buff and to debuff.

Flatting out hit points and damage per attack doesn't change that. It might change it if the concept of minions were dropped for the concept of lower level foes, but the Pandora's box of minions has been opened and I doubt you'll ever see it go away. If you get a few dozen much lower level mooks attacking the PCs, most of them will never hit and many will die when the Wizard drops a Wall of Fire on their butts.

I just don't see where this concern that every group of PCs will eventually lose comes from. Maybe you could explain it with a more mathematical example.

 

[KarinsDad]

Good review, though if we are looking at core dnd stats then healing should be factored in.

Traditionally Pcs have not only gotten more hitpoints but also access to more healing.

I have always said that healing is the one factor that allows the game to work at all. If PCs couldn't heal (or find some way to heavily mitigate damage), or NPCs could often heal, then PCs would never make it to 4th level.

Once the game designers get the core offensive and defensive 5E mechanics in place, they then should come up with a healing system that works for that math. But, that healing has to take into account the strength of the PC's attacks (not just damage, but the strength of all effects) and the strength of the NPC's attacks.

From what I can tell, WotC really didn't do that for 4E. They did not come up with a consistent offensive and defensive mathematical framework, nor did they take into account the strength of effects or the strength of NPC's attacks.

Sitting down and doing the math (and there is a ton of it) for every game element is the most important thing that the game designers can do this time around. The game is much better if it just works at all levels. Healing is just a small part of that, but a crucial and necessary one for the PCs.

And one thing that NPCs should have as a tool is healing. Not as powerful and often as the PCs, but without it, NPCs seem like cardboard cutouts. The most powerful and intelligent BBEGs should realize right away that the reason that the PCs keep winning is because they heal themselves in combat. 4E doesn't have enough NPC healing IMO. It should be a bit more frequent than it is, especially in boss fights.

 

[mmadsen]

The question is, where are you pulling out these numbers?

I pulled the 20-to-1 odds number out of my bag of holding. It's supposed to be a ridiculously high number.

I then calculated the probability of winning over and over at those odds. With 20-to-1 odds, each fight, by definition, has just over a 95-percent chance (20/21 = 95.2%) of going the party's way.

Winning a dozen such fights in a row happens roughly half the time (95.2%^12 = 56%).

If the party actually engaged in fair fights, they would only expect to win half the time, so winning even the first fight would be impressive, and getting to a dozen would be effectively impossible.

Even at 3-to-1 odds, the party will generally win just one or two in a row.

 

[KarinsDad]

I think what tends to break the game (or did particularly in 3E) is not the level inputs but the enhancement bonuses. When you add magic armor, a ring of protection, a DEX boost, an amulet of natural armor, etc, to AC and they all stack, the math breaks pretty quickly (across all scores, generally except HP). To make the system work we either need to eliminate enhancements, or keep them to a reasonable number. Perhaps no stacking at all (only the best enhancement that improves AC counts, for example), or limit stacking to a total -- no more than +5 can be applied to any score or roll from any enhancements.

It's a very tough question.

Magic items introduce a lot of chaos into any system. In all versions of D&D that I can recall, if the PCs didn't eventually get magic items, they were screwed. And players like magic items.

So, one possible solution might be as follows:

You design the mathematical framework of the game such that the PCs and NPCs are using the same basic math, but the NPCs might be one level below the curve (i.e. 4th level NPCs fight as 3rd level PCs) in some way. In other words, the NPCs might have a slightly harder chance to hit and might be hit a bit easier, but they might have some extra hit points and do a bit more damage than the average PC (this is the 4E model, there are other options, but typically, monsters of the same level are a little bit weaker than the PCs).

Once you determine the mathematical framework, you limit your magical items.

In 1E and 2E, there were +4 and +5 weapons, but I saw very few DMs hand them out. DMs who handed out a Sword of Sharpness or a Vorpal blade tended to regret it sooner or later. The vast majority of weapons handed out were +1, there were some +1 but +x in a specific situation, a few +2s and a very rare +3. 3E came along and decided that +4 and +5 weapons should be a major part of the game system and even +6 weapons showed up in some later splat books (or possibly the Epic Level Handbook) as artifact level.

4E went straight to +6.

The same mostly applies to other items. The powerful 1E and 2E Staffs of Power and such got weaker, the magic armor and weapons got stronger (in the straight up sense, not for other effects of the items) and were expected to be handed out.


So, what if we limit magic items to +3? PCs in a normal magic campaign are expected to get a +1 weapon, armor, and (if they still exist) neck item eventually per tier (if tiers still exist).

This limits the "Christmas tree effect" somewhat because a lot fewer (of what players consider necessary) items will be handed out.


To offset this effectiveness increase on the side of the PCs, monsters have special abilities that are used or not used dependent on how many magical items the DM hands out.

For example:

A Paragon level Elite monster has his normal stat block. In addition, the monster has a section in the stat block if the DM is following the normal magic distribution rules:

Aura: When allies of the monster are within 5 squares of him, they gain +2 to their defenses (the aura does not have to be buffs or debuffs, it could be anything beneficial to the NPCs or harmful to the PCs).

If the DM is not using those distribution rules, then he ignores this Aura. The monster could even have an aura regardless, but with slightly different power levels:

Aura:

Low magic: xxxx
Medium magic: xxxx
High magic: xxxx

The DM decides the power level of this ability.

Instead of an Aura, the monster could have an additional encounter power, or one of his Encounter powers could become At Will (which makes the monster quite a bit tougher). There are a lot of optional abilities that the game system could give to the monsters to make them weaker or tougher.

The stat block could be color coded to quickly show a DM which options are which.

And, this works great for the DM. He doesn't have to use these optional abilities, just to offset magic items. He could use them if he wants to give a given set of monsters a bit more umph, or to make a given set of monsters a bit weaker.

DM: "I want to use a Mountain Troll, but it is just too tough for my players."

Problem solved. Use the weakest version of the Mountain Troll, ignore it's optional abilities, and the players are taking on a Mountain Troll.

 

[KarinsDad]

I pulled the 20-to-1 odds number out of my bag of holding. It's supposed to be a ridiculously high number.

I then calculated the probability of winning over and over at those odds. With 20-to-1 odds, each fight, by definition, has just over a 95-percent chance (20/21 = 95.2%) of going the party's way.

Winning a dozen such fights in a row happens roughly half the time (95.2%^12 = 56%).

If the party actually engaged in fair fights, they would only expect to win half the time, so winning even the first fight would be impressive, and getting to a dozen would be effectively impossible.

Even at 3-to-1 odds, the party will generally win just one or two in a row.

And if there wasn't magic in the game system and monsters had all of the abilities of PCs, this math might mean something.

My proof for this is 4E.

Fights aren't fair. Ever. PCs always have a huge advantage.

If one carefully looks at most above same level 4E encounters, they'll notice something. The NPCs often get the upper hand in the first few rounds. A few PCs are bloodied. Multiple PCs have effects on them. Things look dire. But slowly, the PCs start evening the odds and eventually, they start ripping through the encounter. Why is this if the PCs are losing in round one, that they win in round six?

Action Economy.

Although one or sometimes even two PCs might be knocked unconscious in an encounter (although most encounters, no PCs are knocked unconscious), they almost always get back up. The monsters almost never get back up.

The three things that cause this to happen are:

1) Options. PCs tend to have a lot of options. Monsters have only a few. Each player can decide in each situation whether to pull out a big gun, or if a lesser gun will work. Monsters don't have this option too much. They might get one or two Encounter (read Daily cause the monster is not coming back) powers, but once their wad is shot, they're done.

2) Healing. PCs often have quite a bit of this. Parties without Leaders aren't completely screwed (they still have #1 and #3), but parties with Leaders just wipe through encounters. Not at the start of the encounter, but part way through. Monsters rarely have healing, so once a monster is down, it typically stays down forever.

3) Action Points. PCs already have a "get out of jail card" free option. They get to focus an additional attack when needed. The vast majority of monsters do not have action points.

So if the PCs get 5 attacks in round one and the NPCs get 5 attacks in round one, the PCs are still doing 5 attacks in round six whereas the monsters are done to 1 or 2 attacks at that point.

By definition, the PCs win. This is how the game is designed to work so that PCs can be heroes that get past level 3. These are the reasons that PCs can take on an encounter 4 levels higher than the group and win. But when an encounter gets to 5 levels or 6 levels higher, it starts becoming really dicey (and even 4 levels higher is often a real challenge).


So, I opine that the rationale for adding more "get out of jail free" abilities to the game system is flawed. It's not a straight up math problem. PCs have healing and PCs have many more options than monsters, hence, they win. They don't need even more ways to win. The 4E game system is already extremely easy unless the PCs have run out of Daily resources (powers and/or healing surges).

 

[mmadsen]

We essentially have four scores under discussion, two offensive (Attack bonus and damage) and two defensive (AC (or other Defense, for 4E model) and hit points).

Yes, and those four value compound, so that a character who hits twice as often for twice as much damage, and who gets hit half as often and can take twice as much damage, ends up 16 times as powerful -- which is actually powerful enough to take on four times as many enemies (via Lanchester's Square Law).

I think what tends to break the game (or did particularly in 3E) is not the level inputs but the enhancement bonuses. When you add magic armor, a ring of protection, a DEX boost, an amulet of natural armor, etc, to AC and they all stack, the math breaks pretty quickly (across all scores, generally except HP). To make the system work we either need to eliminate enhancements, or keep them to a reasonable number. Perhaps no stacking at all (only the best enhancement that improves AC counts, for example), or limit stacking to a total -- no more than +5 can be applied to any score or roll from any enhancements.

Agreed. It's the many stacking bonuses that add up to a problem. Keeping only the largest bonus makes the math work, but it leads to "worthless" +1 items, hand-me-down amulets, etc.

Now, as I've already mentioned, big bonuses have different effects at different points along the d20 range. Near the middle of the range, each plus or minus one involves a factor of roughly 1.1. Near one end of the range, a plus or minus one involves a factor of 2 (hitting or getting hit only on a 20 vs. 19 or 20); on the other, a factor of 1.06 (hitting or getting hit on a 3-20 vs. 2-20).

 

[mmadsen]

DMs who handed out a Sword of Sharpness or a Vorpal blade tended to regret it sooner or later.

A sword of sharpness or a vorpal weapon is much, much scarier to another PC than to a typical monster. Automatically killing (or crippling) your enemy on a natural-20 to-hit roll makes roughly 10 percent of your attacks lethal (or disabling), which isn't a big deal if you expect to finish off your opponent in fewer than 10 hits, and it has no healing power.

The vast majority of weapons handed out were +1, there were some +1 but +x in a specific situation, a few +2s and a very rare +3. 3E came along and decided that +4 and +5 weapons should be a major part of the game system and even +6 weapons showed up in some later splat books (or possibly the Epic Level Handbook) as artifact level.

4E went straight to +6.

Also, D&D weapons have a history of adding their bonus to the to-hit roll and the damage roll, so a +5 sword might allow you to hit 1.5 times as often for twice as much damage, or three times the damage per round.

 

[KarinsDad]

Also, D&D weapons have a history of adding their bonus to the to-hit roll and the damage roll, so a +5 sword might allow you to hit 1.5 times as often for twice as much damage, or three times the damage per round.

I think 5E should continue that model of bonus to hit and bonus to damage. It's a sacred cow. But, it's a lot less problematic of a model if we stop at +3.

Players will grumble about being limited to +3 weapons for a while, but if other magic items became a bit more useful (a lot of 4E items are, for the most part, worthless mostly because they are too specialized), not just in combat, but in other situations, players will come around to a +3 max model and a +1 item, even without additional abilities, will become quite a bit more special.

+1 to hit and +1 to damage where it is not required to make the main math model work (like in 4E) combined in a system of less damage and fewer hit points (possibly where monsters have optional abilities to stay in sync) will be worth a lot more than it is today.


I think 5E should get away from specialized magical items and move more towards generic useful items that more PCs can find useful. It's a pain for a DM to go out of his way to often hand out items specifically designed for the group of PCs he has. That doesn't make the DM's job easier.

 

[mmadsen]

Fights aren't fair. Ever. PCs always have a huge advantage.

Yes, that was my point. Even remotely fair fights would catch up to the PCs very, very quickly.

So, I opine that the rationale for adding more "get out of jail free" abilities to the game system is flawed. It's not a straight up math problem. PCs have healing and PCs have many more options than monsters, hence, they win. They don't need even more ways to win. The 4E game system is already extremely easy unless the PCs have run out of Daily resources (powers and/or healing surges).

I don't think the goal is to add more "get out of jail free" abilities; rather, it's to shift what kind of "get out of jail free" abilities the PCs have.

For instance, if we increase ACs but reduce hit points, we haven't given PCs more defenses, just different ones.

If we reduce saves, or increase the severity of failures, but we allow hit points to add to saving throws, we haven't given PCs more defenses, just different ones.

+1 to hit and +1 to damage where it is not required to make the main math model work (like in 4E) combined in a system of less damage and fewer hit points (possibly where monsters have optional abilities to stay in sync) will be worth a lot more than it is today.

If characters have higher defenses and lower hit points, then +1 to-hit and +1 to damage becomes much more effective.

In fact, a +6 weapon in 4E might not be that powerful, considering the easy to-hits and high hit points.

I think 5E should get away from specialized magical items and move more towards generic useful items that more PCs can find useful. It's a pain for a DM to go out of his way to often hand out items specifically designed for the group of PCs he has. That doesn't make the DM's job easier.

I believe the move toward specialized magic items was a reaction to 3E's "Christmas tree" of "mandatory" magic items that granted generally useful bonuses.