D&D 5E (2014) Is Point Buy Balanced?

[DinoInDisguise]

Balance means balanced results for two players. If one player swings a sword and does 9 damage and another player swings a sword and does 7 damage that is not balanced.

If one has an 8 strength and one has a 20 it is not balanced

If both of them have a 16 strength it still is not balanced.

Giving them equal strength does not make it significantly more likely they will balanced in play.

This is an odd position to take. That's not how balance is defined in any game with randomness. Balance is equality of opportunity and expected outcome, not equality of realized outcomes. If balance required identical results: poker would be unbalanced, chess with time controls would be unbalanced, every RPG ever written would be unbalanced.

By your definition, the concept of balance cannot co-exist with dice. Which would make every balance discussion on these forums moot. Yet we have those discussions, using a different definition of balance. One that works on structural biases.

The same mean or probabilty does not mean the same or a balanced outcome.

You aren't wrong, but it's irrelevant here. Balance has never meant “identical outcomes.” It means:

Same decision > Same expected payoff
Same risk > Same reward
Same competence > Same effectiveness over time

If two characters are mechanically identical, then any difference in outcome is attributable to variance, not the system. That’s exactly what balance is supposed to do. No one is claiming that both characters always do equally well every session. That would be an absurd claim.

The only way to balance a game involving dice is to stop rolling. You are not going to have a balanced game if you are rolling dice for outcomes.

Dice introduce variance, not bias. Balance is about bias. Ability modifiers introduce bias.

Variance = outcomes fluctuate around the mean
Bias = outcomes are consistently shifted in one direction

I don't understand your use of these words.

There are 6 abilities, you are comparing the chance of one character having an 8 and another character having an 18 at that index. The chance of 1 PC rolling an 18 as their best score is 9% (using 4d6d1). The chance of someone rolling an 8 or lower as their best score is 0.00013 or roughly one in 1 million.

This fails in multiple ways. Rare events still matter in design. You dont just ignore outcomes because they are rare. Especially when the system explicitly allows them, your players experience them, and they cause persistent disadvantage.

By this logic critical hits, character death, and TPKs "don't matter" because they are unlikely or rare.

You are also applying the math inconsistently. You claim both that disparity is unlikely, so we can ignore it. And you claim that in-session chance that the weaker will out perform the stronger is "substantially higher."

But even if we accept your premise it fails at all levels. Replace 8 and 18 with 12 and 16, 14 and 18, 15 and 17. These are common and still create consistent bias. That bias is a systemic imbalance.

If you are going to do this though, I will point out that you need to consider the distribution associated with the ability score rolls to begin with. There are 6 abilities, you are comparing the chance of one character having an 8 and another character having an 18 at that index. The chance of 1 PC rolling an 18 as their best score is 9% (using 4d6d1). The chance of someone rolling an 8 or lower as their best score is 0.00013 or roughly one in 1 million.

Assuming both are barbarians and both put strength as their highest stat, the chance the one with the lower 8 in strength will outperform the one with a higher strength in combat during a session is substantially higher than the chance of getting this disparity to begin with.

When you say "will experience more frequent failures" you are discounting extremely unlikely outcomes. This is fine, but it works both ways - if you want to make a statement like this, then the counter would be that condition (one PC with 8 the other with 18) won't exist.

We have two things here. Unbalanced systems and unbalanced outcomes. We can look at them here:

• Unbalanced system: one player is more likely to succeed across the same actions
• Unbalanced outcome: one player happened to roll better tonight

Only the first of those two is a balance issue. Party A has noise, and no player is systemically disadvantaged. Party B has differences that are structural, and one player is structurally disadvantaged.

Saying “they’ll both be unbalanced anyway” is like saying: since weather exists, gravity doesn't matter. Or because people sometimes slip, structural engineering doesn’t matter.

Since randomness exists, mechanical equality doesn't matter. But that position is very odd. If that was the case:

• Ability scores wouldn’t exist
• Modifiers wouldn’t scale
• Optimization wouldn’t work
• Dump stats wouldn’t hurt

It's almost like expected value governs player experience over time: like entire communities of optimizers exist because bias means something, like the designers didn't waste their time implementing non-sense mechanics.

I'll state my case very clearly:

Balance is not about guaranteeing equal outcomes. Never has been.
Balance is about ensuring the system does not consistently favor one player over another for the same decisions.
Dice introduce variance.
Ability modifiers introduce bias.
Removing bias improves balance even when variance remains.

Claiming otherwise seems to just be tossing the widely accepted definition of game balance in the trash. As any game with variance becomes unable to be balanced. That is a view one can have, I guess. But I don't think it lines up with the reality we observe.

Spoiler: Said another way..

If this is true:

• balance can’t exist if dice exist, and
• mechanical mitigation of randomness is pointless, and
• expected value doesn’t meaningfully affect play

It contradicts:

• probability theory
• game design practice
• decades of observed play
• the existence of the game mechanics being discussed

Spoiler: Oh and this..

If mechanical equality doesn't matter, why are we dropping the lowest of 4d6, and not just running 3d6? But really why have attributes at all? Hm.

 

[Lanefan]

If mechanical equality doesn't matter, why are we dropping the lowest of 4d6, and not just running 3d6? But really why have attributes at all? Hm.

Dropping the lowest of 4d6 provides (in theory) mechanical proficiency, not mechanical equality.

 

[DinoInDisguise]

Dropping the lowest of 4d6 provides (in theory) mechanical proficiency, not mechanical equality.

This only works if mechanics matter. But I was replying to a post where @ECMO3 clearly articulates that the bias given by mechanics doesn't matter when dice are involved. He did this to defend the idea that mechanical equality is irrelevant.

This is clearly argued here;

Assuming both are barbarians and both put strength as their highest stat, the chance the one with the lower 8 in strength will outperform the one with a higher strength in combat during a session is substantially higher than the chance of getting this disparity to begin with.

There isn't much ambiguity in the implication here. That a mechanical bias introduced by attributes is "overwhelmed" by the variance introduced through dice. Such that the mechanical bias is effectively rendered moot. I see no other reading of the quote, or their larger post.

Since you are using dice, the "proficiency" you gain through dropping the lowest is, well, also moot under the above logic. It is useless because the variance from the dice overwhelms it as is clearly implied.

So I assume you agree with me, that the mechanical bias given by higher attributes does matter, and does impact play. And because of that, rolling attributes inherently introduces the risk of mechanical imbalances that also matter. If those imbalances did not matter, there would be no point to dropping the lowest, as your "proficiency" would also not matter.

That's, of course, unless you want to defend the idea that the mechanical biases only matter sometimes. In which case, I'd love to hear that defense as I can't come up with one myself.

 

[Lanefan]

This only works if mechanics matter. But I was replying to a post where @ECMO3 clearly articulates that the bias given by mechanics doesn't matter when dice are involved. He did this to defend the idea that mechanical equality is irrelevant.

This is clearly argued here;



There isn't much ambiguity in the implication here. That a mechanical bias introduced by attributes is "overwhelmed" by the variance introduced through dice. Such that the mechanical bias is effectively rendered moot. I see no other reading of the quote, or his larger post.

Since you are using dice, the "proficiency" you gain through dropping the lowest is, well, also moot under the above logic. It is useless because the variance from the dice overwhelms it as is clearly implied.

So I assume you agree with me, that the mechanical bias given by higher attributes does matter, and does impact play. And because of that, rolling attributes inherently introduces the risk of mechanical imbalances that also matter. If those imbalances did not matter, there would be no point to dropping the lowest, as your "proficiency" would also not matter.

That's, of course, unless you want to defend the idea that the mechanical biases only matter sometimes. In which case, I'd love to hear that defense as I can't come up with one myself.

The mechanical biases caused by stat differences only matter* at the very lowest levels, before all the other stuff - magic items, feats, class abilities, level-based bonuses, etc. - comes online and slowly but steadily pushes those stat-based biases far enough into the background that they almost become irrelevant.

We saw this more in 3e: at low level when your only bonus is +2 from a stat it's a big deal, but at high level when that +2 is getting tacked on to +15 from other sources it's just white noise.

* - just how much they matter and-or impact one's enjoyment of play is each person's subjective opinion, of course.

 

[ECMO3]

This is an odd position to take. That's not how balance is defined in any game with randomness. Balance is equality of opportunity and expected outcome, not equality of realized outcomes.

That is balance in a white room it is not balance in play and if imbalance in play causes problems at your table in play, equal ability scores will not minimize or solve it to any degree.

By your definition, the concept of balance cannot co-exist with dice.

It can, although the chance decreases rapidly with every roll.

You aren't wrong, but it's irrelevant here. Balance has never meant “identical outcomes.” It means:

Same decision > Same expected payoff
Same risk > Same reward
Same competence > Same effectiveness over time

Ok so then you are fine if the game is not balanced in play. So am I. I have no problem with this.

When I hear complaints about imbalance in play it is because one player supposedly feels bad or "useless", because another player has more success in play. I say hear about it, because I have never actually seen this personally. But as you note any time there is randomness this will happen.

If two characters are mechanically identical, then any difference in outcome is attributable to variance, not the system.

Yep and that variance will almost always cause imbalance in play. Giving them the same ability scores will not change that.

Variance = outcomes fluctuate around the mean
Bias = outcomes are consistently shifted in one direction

Neither of these are factually true when you are talking about the bonuses from ability scores and random die rolls.

To start with the discussion of Variance is not accurate because the population is not a continuous distribution. It doesn't fluctuate around the mean. A 1st level PC with a 16 strength swinging a longsword against a 16 AC has a mean damage of 3.975, but the most common damage rolled (mode) is 0, not 4 and it does not fluctuate around 3-4. Your chance of doing 0 damage is 50%. Your chance of doing 4 damage is 5.63% and all numbers from 5-11 are slightly more likely than 4 damage even though 4 is already higher than the mean. You have a better chance of doing 19 Damage (0.7%) than you do of doing 3 damage (0%).

Bias also does not mean outcomes are consistently shifted in one direction, it means there is an inclination or prejudice in one direction.

This fails in multiple ways. Rare events still matter in design. You dont just ignore outcomes because they are rare.

Exactly! You are discounting "rare events" that are far more likely to occur when you say: "The player with significantly lower modifiers will experience more frequent failure"

You can't ignore rare events (i.e. the chance the low score character does better).

I agree it is overwhelmingly unlikely the low 8 stat player will be more successful than the high 18 stat player, but in a session it is more likely than getting that disparity in scores you are talking about in the first place. A weak player with an 8 as their highest stat consistently outperforming a player with an 18 as their highest stat is a "rare event" and you can't ignore it or act like it is impossible when you consider it possible to have that disparity in ability scores to begin with.

But even if we accept your premise it fails at all levels. Replace 8 and 18 with 12 and 16, 14 and 18, 15 and 17. These are common and still create consistent bias. That bias is a systemic imbalance.

Replace the 8 and 18 with 12 and 16:

The chance of one player having a high of 12 or lower and another player having a high of 16 or higher is 0.78%. That is not common at all, it is very rare. Not unheard of like 8 and 18, but still rare.

I would say an average combat-heavy session is around 12 rounds of combat. If both PCs are 1st level and fight enemies with a 16AC and have longswords there is a 16% chance the PC with the 12 strength outperforms the PC with the 16 strength in terms of damage over that session. So yes it is more common for a PC with a high of 12 to outperform a PC with a high of 16 than it is to have that disparity in ability scores.

The other examples you cited:
14 and 18:
Chance for this disparity - 2% (rare)
Chance 14 Strength PC doing more damage during session than 18 strength PC - 16% (uncommon)

15 and 17:
Chance for disparity - 13% (uncommon)
Chance of 15 strength PC doing more damage during session 17 Strength PC - 31% (common)

In all of these cases the low scores are less likely to result in poor performance for the low score player than they are to even exist in the first place.

We have two things here. Unbalanced systems and unbalanced outcomes. We can look at them here:

• Unbalanced system: one player is more likely to succeed across the same actions
• Unbalanced outcome: one player happened to roll better tonight

Only the first of those two is a balance issue.

I don't think either of them are a problem, but only one of those actually happens at the table.

• expected value doesn’t meaningfully affect play

I never said this. I said multiple times on this post that ability scores do matter and do affect play.

I said they will not make gameplay more balanced, or to use your verbiage (which I do like by the way) - they will not lead to balanced outcomes.

 

[CreamCloud0]

I stopped following this thread about 20 page ago, but I just had some thoughts on the Intimidation sub-discussion.

Typically, we think of Intimidation in terms of fear, but what if, instead, it was reframed in terms of dominance? I was thinking about the Ghosts of Saltmarsh ship officer rules, where the First Mate uses Intimidation to get the crew to do stuff. Now, sure, you can interpret that as a pirate threatening bodily harm (and have a reputation for dealing it out), but the rules could work just as well for any sort of military commands, and I think the latter is the intent. Barking orders is Intimidation. Not (necessarily) due to fear, but due to exerting dominance to get someone to take action.

You might get along swimmingly with your commanding officer, and he might value and respect his subordinates. But in the heat of battle, when commands need to be followed immediately, it's how well you can present your dominance to those subordinates that matters more than whether you can sit down over tea and come to an agreement (Persuasion).

And the great thing, is this already works well with the all the current assumptions of fear-based Intimidation also. They use a form of dominance, and my idea is just to expand it to other forms of dominance, and make it the "giving orders" skill (amongst other things).

so like, reorient intimidation as your capability to exert authority?

 

[AlViking]

This is an odd position to take. That's not how balance is defined in any game with randomness. Balance is equality of opportunity and expected outcome, not equality of realized outcomes. If balance required identical results: poker would be unbalanced, chess with time controls would be unbalanced, every RPG ever written would be unbalanced.

By your definition, the concept of balance cannot co-exist with dice. Which would make every balance discussion on these forums moot. Yet we have those discussions, using a different definition of balance. One that works on structural biases.



You aren't wrong, but it's irrelevant here. Balance has never meant “identical outcomes.” It means:

Same decision > Same expected payoff
Same risk > Same reward
Same competence > Same effectiveness over time

If two characters are mechanically identical, then any difference in outcome is attributable to variance, not the system. That’s exactly what balance is supposed to do. No one is claiming that both characters always do equally well every session. That would be an absurd claim.



Dice introduce variance, not bias. Balance is about bias. Ability modifiers introduce bias.

Variance = outcomes fluctuate around the mean
Bias = outcomes are consistently shifted in one direction

I don't understand your use of these words.



This fails in multiple ways. Rare events still matter in design. You dont just ignore outcomes because they are rare. Especially when the system explicitly allows them, your players experience them, and they cause persistent disadvantage.

By this logic critical hits, character death, and TPKs "don't matter" because they are unlikely or rare.

You are also applying the math inconsistently. You claim both that disparity is unlikely, so we can ignore it. And you claim that in-session chance that the weaker will out perform the stronger is "substantially higher."

But even if we accept your premise it fails at all levels. Replace 8 and 18 with 12 and 16, 14 and 18, 15 and 17. These are common and still create consistent bias. That bias is a systemic imbalance.



We have two things here. Unbalanced systems and unbalanced outcomes. We can look at them here:

• Unbalanced system: one player is more likely to succeed across the same actions
• Unbalanced outcome: one player happened to roll better tonight

Only the first of those two is a balance issue. Party A has noise, and no player is systemically disadvantaged. Party B has differences that are structural, and one player is structurally disadvantaged.

Saying “they’ll both be unbalanced anyway” is like saying: since weather exists, gravity doesn't matter. Or because people sometimes slip, structural engineering doesn’t matter.

Since randomness exists, mechanical equality doesn't matter. But that position is very odd. If that was the case:

• Ability scores wouldn’t exist
• Modifiers wouldn’t scale
• Optimization wouldn’t work
• Dump stats wouldn’t hurt

It's almost like expected value governs player experience over time: like entire communities of optimizers exist because bias means something, like the designers didn't waste their time implementing non-sense mechanics.

I'll state my case very clearly:

Balance is not about guaranteeing equal outcomes. Never has been.
Balance is about ensuring the system does not consistently favor one player over another for the same decisions.
Dice introduce variance.
Ability modifiers introduce bias.
Removing bias improves balance even when variance remains.

Claiming otherwise seems to just be tossing the widely accepted definition of game balance in the trash. As any game with variance becomes unable to be balanced. That is a view one can have, I guess. But I don't think it lines up with the reality we observe.

Spoiler: Said another way..

If this is true:

• balance can’t exist if dice exist, and
• mechanical mitigation of randomness is pointless, and
• expected value doesn’t meaningfully affect play

It contradicts:

• probability theory
• game design practice
• decades of observed play
• the existence of the game mechanics being discussed

Spoiler: Oh and this..

If mechanical equality doesn't matter, why are we dropping the lowest of 4d6, and not just running 3d6? But really why have attributes at all? Hm.

Well said, better than what I had started. Unfortunately it's not going to change anything, we'll just get more counter-factual responses on why ability scores don't matter because of reasons that simply don't add up.

 

[AlViking]

The mechanical biases caused by stat differences only matter* at the very lowest levels, before all the other stuff - magic items, feats, class abilities, level-based bonuses, etc. - comes online and slowly but steadily pushes those stat-based biases far enough into the background that they almost become irrelevant.

We saw this more in 3e: at low level when your only bonus is +2 from a stat it's a big deal, but at high level when that +2 is getting tacked on to +15 from other sources it's just white noise.

* - just how much they matter and-or impact one's enjoyment of play is each person's subjective opinion, of course.

If the magic items, feats, class abilities, level-based bonuses are applied equally (in 5e they will not be*) then it's just raising the bar for everyone. In addition, I'm not really concerned about previous editions and 5e has a much flatter approach - the bonuses don't get so ridiculous as they did in 3e. No matter which edition we're talking about the difference still persists, going from a +n to a +y doesn't change the difference between the two characters. As I showed in my spreadsheet calculations, some aspects (DPR for the fighter) balance out but other (HP - 60 vs 100 HP at 8th lvl) don't because the person with the high score never needed to invest in DPR. For the barbarian comparison there's no way for the player with poor stats to ever catch up in any aspect of the player with high stats. They're just too far behind.

*They can't be because someone with a high score will max out their primary ability more quickly. At that point there is no trade-off between increasing that ability score and taking feats.

 

[DinoInDisguise]

Balance means balanced results for two players.

Your argument redefines balance into meaninglessness, and is inconsistent with basic probability theory, basic game design principles, and decades of both observed play and RPG design practice. And it does this with self-defeating claims like "dice make balance impossible" and "rare outcomes don't matter."

Given these issues, I have nothing further to add.

The mechanical biases caused by stat differences only matter* at the very lowest levels,

Ah but so does your "proficiency" under that logic. Also, just admitting that they matter at all is agreeing with me.

Well said, better than what I had started. Unfortunately it's not going to change anything, we'll just get more counter-factual responses on why ability scores don't matter because of reasons that simply don't add up.

Come on Alviking. We’re being asked to accept that mechanics both matter and don’t matter at the same time. And every game with variance is impossible to balance.

Can't wait to spring these concepts during the next caster-martial divide debate. I learn so much in some of these threads.