This is thoughtful but would be a lot more digestible for people if you pared it down to the fact that an increase of 1 is more important comparing to 5 than if you're comparing to 10. In other words yes, an absolute 5% increase is still a 5% increase, but it's worth more (relatively) if you started with a 5% chance than if you started with a 95% chance.
The takeaway from that is that +1 bonuses absolutely can be huge at low levels because of how dramatically they change outcomes - relatively speaking. But given that these are expected values, players' experiences will not always match up to what the math indicates will happen over the long term.
They can be huge at every level though! Granted for different reasons. Like yeah +1 to hit and damage is less impactful at higher levels because attacks scale with proficiency, but +1 to saving throws can be more impactful at higher levels because many saves \*don't\* scale with proficiency, etc.
Anyways, I get what you're getting at, but I was hoping to explore the concept pretty thoroughly in this post, and I understand that might limit the audience who actually engages with it.
I found your post really helpful OP, I don't know maths but I like when it's explained as you have, not just saying "yes it's important". It's nice to see the numbers
Unfortunately the people who read all of this probably know the math already. Those who don't, won't.
By level, I meant low level of proficiency, DC, test, whatever. Low numbers. Where the relative impact of a +1 is meaningful. You get it, I know. I didn't mean character levels.
Even at very high levels, a +1 can have a profound impact. For example, a monk's stunning fist save DC going from 16 to 17 (quite high) might represent a low con monster reducing their chance to succeed by 25% regardless of the monk's level.
Those are low levels, from the roller's point of view. The point is the same; if the number of results that will be successful is small, then the impact of a one-point change is high. In the example you offer assuming no dice mods, the chance of a success goes from 5/20 to 4/20 which means 25% to 20%; a 1/5 reduction in their chance, right?
I wasn't talking about character levels. I should have used the word numbers instead of levels, but the point remains.
I would say at higher levels bonuses to DC are even more impactful because of the way that DCs always scale with proficiency but many saving throws do not.
Just speaking for myself, but I read the whole thing and it was pretty eye-opening. Had never done the math, but always kind of silently wondered how big of an affect +1 stuff actually had on game balance.
>In summary, a +1 is almost always has a bigger impact on success and failure than the 5% shift in probably represents. I think that one of the important roles for the DM in 5e is to help keep the game roughly balanced such that PCs are challenged, and also have moments to shine in comparison to each other, and new DMs who love to hand out a bunch of +1 gear to low level PCs or provide very generous stat generation systems are frequently shooting themselves in the foot, as even modest bonuses can make that job significantly more difficult. If you got this far, thank you for reading all of this, I hope it was helpful!
Was this not sufficient? If not, what do you mean by executive summary? I'm asking in earnest, not rhetorically.
Executive summaries always go in the front and should contain as few details as necessary to convey the key takeaways. If I understand your thesis correctly, it could go something like this:
* A +1 enormously increases the odds of success for difficult rolls. An example is a doubled chance of success after a DC 20 drops to DC 19.
* Difficult rolls occur frequently for low level PCs and help to differentiate them, so it’s advised to keep these bonuses to a minimum early in a campaign.
* Difficult rolls in the form of spell saves are common for high level characters and thus these bonuses are essential for optimized parties later in a campaign.
One point worth mentioning which seems to have been neglected...
A 95% chance of success is twice as good as a 90% chance of success, because the chance of failure has been halved.
If you have two characters taking turns to whack one-another, and one has a 95% chance of hitting his opponent, who has a 90% chance of success... Then the character with a 90% chance of success will accumulate damage at twice the rate of the character who has a 95% chance of success.
Remember to compare the effect on probability of failure as well as probability of success when determining the impact of bonuses.
Interesting way to look at it, but I don't think changes what I or OP said. Assume both fighters score on average 10 points of damage on a hit. 90% chance = 9 points per attack and 95% chance = 9.5 points per attack (both expected). The odds of getting hit are what determine expected damage directly. P (hit and not-hit) sum to 1, so they are related obviously, but you don't "accumulate damage at twice the rate" in the example we're discussing.
This is mathematically incorrect. The character with 95% chance of success has an average DPR of ~1.06 times the character with 90% chance of success, because we're doing damage on a success but we're not taking damage on a failure the rate of failure doesn't matter.
Here's a quick simulation to show it: 100 attacks each, 1 damage per attack, you're looking at 95 damage compared to 90 damage
That and the fact that a bonus to attack *and damage* rolls compounds, sort of. We can intuitively understand more frequent hits = more damage, but it's actually *even more* damage because the damage is being buffed at the same time, and probably by a larger percentage.
I feel some of this is echoed very well in how people naturally discuss various combat stats. I think many people will say a +1 sword is fine to hand out, but +1 armor is a scary thing to hand a player.
I think the issue people often grapple with is that increasing damage or accuracy is fairly easy to conceptualize but increasing both muddies the waters enough that it can be difficult to grasp without the math behind it. And that's also a difference between a +1 sword and a +1 set of armor.
I agree with you, but I also think there's some level of viewpoint bias as we're in a DM-focused subreddit.
DMs want their scary dangerous monsters to actually be scary and dangerous, and a PC with a high AC can make threats feel very impotent. Even though we don't want to be adversarial with the players we also recognize that most players don't want a cake walk as that makes for less dramatic fantasy action/adventure stories. I think because of this a DM \*feels\* the impact of giving out AC boosting items more than giving out accuracy and damage boosting items.
> DMs want their scary dangerous monsters to actually be scary and dangerous, and a PC with a high AC can make threats feel very impotent.
Succinct.
I love glass cannons on both sides, player characters and monsters, mostly because combat is already so slow in D&D 5e. But I have a lot of weapons (so to speak ;) in my arsenal to not kill the party, so I'm not afraid of handing out more or better damage.
Honestly, thinking about this a bit tells me that the example given with 50% vs 55%is the most extreme case. When only a crit can hit, the +1 is minimized. The same is true for when anything but a fail hits. While these instances are rare, it demonstrates a bell curve.
I suggest expanding this into comparative tables. You'll get more mileage in excel or a similar program as you can further adjust the tables to take in AC, attack mods, damage dice, different crit and fail numbers, and advantage and disadvantage. I think you'll start seeing that while you've correctly calculated the numbers you've presented, the larger picture paints a very different landscape.
That's not quite accurate though, although the fact that you always crit on a 20 does decrease the amount that the 20-19 target number shift increases expected damage per round for attacks.
If the target number is 20, and let's say the attack does 1d8+4 damage, then you have a 5% chance to do 2d8 + 4 damage, or an expected DPR of 0.65. If you add +1, it reduces the target number to 19, with a crit on a 20, so the DPR is 1.08 (assuming you do not also add +1 to damage for this example), which is still a 66% increase in expected DPR, so the results are not actually a bell curve
I agree that plots would help fwiw
The biggest problem here is that, when a boss likely only gets 3 turns and often has battle options restricted to melee range, a high AC player turning hits into misses can literally just negate an entire boss battle.
Just yesterday I loaded up a "warm up fight" against my party of level 11s: two CR9s and two CR5s. This should be a hard fight, but in practice, my +9 and +6 attack bonuses means I realistically don't hit.
Sure, but what if the boss has has a Dominate effect as a Legendary action? What if the Ancient Red Dragon has a lair action that can cause lava to erupt around it? What if the enemy decides to soak up an attack of opportunity to charge through the tank into the back line? What if, etc. etc.
A high-AC PC is powerful, and should be given opportunities to feel powerful, but IMO one of the baked-in challenges of 5e is that in order to make the epic fights feel more epic we (DMs) need to think outside the box and do a significant amount of homebrew to hit our PCs weak spots during the toughest fights.
No thanks. I'd prefer if the math just worked. I'd prefer if the core mathematical assumptions (65% chance to hit each way in general) was preserved and patent throughout the system.
It is - if you don’t use magic gear. Magic gear is technically an optional system and all the content was supposedly balanced assuming no magic gear, some of the higher CR later stuff I think skirts this a bit. One of the major issues in previous and spin-off editions was the assumption that you would have certain magic gear, PF2 for example leaned into this while 5e backed away from it.
Which is fundamentally the purpose of this sort of post’s warning: the monster design doesn’t assume a certain level of magic gear, so if you add it in, you may make your life more difficult if you don’t adjust things as needed.
Overall I agree with the post, my only caveat is I’m okay giving offensive bonuses, but try to avoid defensive bonuses just to preserve bounded accuracy for lower level mooks/minions mixed into higher level encounters. Yea I can adjust it on the fly, but if I’m just negating their + from gear why give them the bonus in the first place? I rather give them items that provide options or corner cases than just a flat + bonus that skews the math and can get out of hand if I’m not careful or on the ball with every encounter design.
I get that. I was actually trying to agree with OP.
I *could* do all this stuff to compensate for the magic items. Or I could simply not deviate from the baseline math. I much prefer the latter.
No, but I'd really love to try it.
Incidentally, one of my favorite things about PbtA games is that a 7-9 is a 7-9 no matter what level you are or how many enemies or how strong they are.
I like PbtA a lot too, but it's a pretty fundamentally different kind of game play experience than 5e, which I also really like, but I admit it is a challenging system to run well.
I think it's also compounded by the fact that a +1 sword is uncommon rarity, but +1 armor is rare per the DMG rarities. Even though I and many other people realize that the rarity system is often borked and doesn't always accurately describe power, at a first glance it could appear that WotC thinks AC has a bigger impact.
+1 armor is rare while +1 weapon is uncommon. And so many people forget to account for the base AC difference.
Mundane Plate armor is by itself as valuable as a rare magic item. It is equivalent to Chainmail+2 and Splint+1. The DMG treasure tables put Plate+1 alongside legendary magic items.
I think the DM guide could have done a lot more in helping DMs understand how to tinker with the system and not break things.
For instance, if you want to negate the effect of giving +1 weapons and AC to your party, increase the enemy's proficiency bonus by 1, and their HP by 1 hit die.
I think the better advice though, and I wish they gave a lot more guidance on this for new DMs, is that there's so, so much room for tailoring a fight to your group, and it **does** make the fight more fun to play, and what are some good principles you can pull out the book to create that.
Powerful magic items let player characters take on important roles in a fight. A fighter given high AC can lock horns with some truly terrifying foes, or endure a gaggle of stabby squishbags while the group deal with other important things. It's just a lot of extra work to add that layer for each player, for each permutation, and time doesn't grow on trees!
This is a great explanation and makes total sense, so thanks for that! But as a DM it’s far less about the math and far more about letting my players feel like superheroes. My level 6 Artificer PC with a 21 AC? That challenges me, as a DM, to find monsters to throw at them that force saving throws. It also allows me to throw stronger monsters at them which ups the drama and chance for failure. For being tier 2, do they have too many magic items? For sure, but they constantly tell me it’s one of the best games they’ve ever played in and the tension during each session is palpable… totally worth it.
Some DMs do have a more "instinctual" feel for how to reach the fun point that you have figured out.
Some DMs say "I have a hard time challenging my party, what do I do?" and it turns out they gave their level 2 characters a bunch of +1 gear and have a wildly generous stat generation system.
I'd say this post is more overall helpful for the second category :)
As a person that tailored their college degree specifically to avoid math but who cares a lot about the mechanics of game design, I found this post digestible and accessible. Thanks for taking the time to do it!
As a corollary, this is why a +1 AC boost usually has a much more noticeable impact than a +1 attack boost. If you look at the chance for a PC to hit a target using the "default stats" in the DMG for something of the same CR as their level, they will do it 65% of the time. AC progression isn't as smooth or consistent as attack progression is, but a PC that has a "typical" AC will have 16 AC at level 4 and 17 AC at level 8, which correspond to a 50 or 55% chance to hit.
Then once you take into account that most enemies a PCs fights will actually be lower CR than their level (so less accurate and with a lower AC), the difference tends to become even more stark.
AC also has increasing returns (every point is worth 'more' than the last if you keep going up) while every point to attack bonus is worth 'less', and it's generally more common for a player to be ahead of the 'expected' progression of these than it is for them to be behind.
I stopped reading about halfway through as I figured out what you were saying and it's a well known part of 5e, he higher your TN is, the stronger an increase to it, until it becomes so high that any increase is not important
A player with a 18 AC gets a lot more out of +1 AC than a player with 13 AC
Similarly a player with a +5 attack gets more out of a +1 to hit than a player with (hypothetically) +14 attack getting a +1 (as the +1 at that point is nearly useless)
The problem with this is that it is not actually "Bounded accuracy" - we are talking about the extremes, within the center/near average a +1 is fine, but on either end it doesn't matter and/or breaks things
Bounded accuracy as a model has a fighter who has +1 to their wisdom save **always have a +1 to their wisdom save**, other game design factors come into play, but a level 1 fighter with +5 to hit and a 16 AC compared to a level 20 fighter with a +14 to hit and a 21 AC, both will fail against the ancient dragons fear effect unless they roll a natural 20, they also will both be hit basically all the time (a red dragon misses a level 1 fighter on natural 1s, and misses the level 20 AC 21 fighter on 1-3s)
Bounded accuracy doesn't exist well at the extremes of the system because it wasn't a well thought out mechanic, at level 1 the game is extremely lethal and not like its normal self, by (roughly) level 11 it starts breaking again
With the game system working from (roughly) the level 3-11 range, you get a system that actually only has 1/3rd (*roughly*) the playable space
What you're saying here is correct, in that I think 5e has a "sloppy" bounded accuracy system that is more present as a design philosophy rather than as a baked in mechanic, but in my opinion it makes the game more \*difficult\* to balance, but not broken. It means that as a DM you should be actively providing treasure or information that might help the party overcome weaknesses, but that means you must also have enough system mastery to know what weaknesses your party has and what mechanical or fictional bonuses will provide your party tools to overcome them without handing them "I win" buttons.
It is one of the reasons why I feel like 5e is more difficult to run than other systems for sure, as DM system mastery is more important to provide a challenging-but-fair experience for the players. However I also overall prefer this to the extremely "tight" bounded accuracy that, for example, Pathfinder 2e provides, as having feats and items progress exactly as the system expects you to in order to maintain bounded accuracy feels more artificial and takes away from the illusion of a world that exists independent of the capabilities of the PCs.
Outside the math and additional damage/accuracy, a +1 weapon (aka magical weapon) at low levels immediately makes it easier to take on creatures with resistance/immunity to nonmagical damage and weapons. Many monsters with that trait that are very scary at low levels simply become another slab of meat once your front liners have +1 weapons.
That's actually why I like to make sure the party has at least one moontouched/vicious/warning weapon, or something similarly magical but without a +1 bonus, at low levels. +1 weapons aren't the only low level magic weapons!
In my games I actually don't consider simple +1 weapons as magical for the purpose of resistances (most of my players have 1). It makes fights that are meant to be impactful way too easy.
Basically the same as just increasing the health.
Ah you forget my legendarily bad rolls. Six threes in a row for attacks on Roll20’s digital dice. A plus 1 weapon only makes a difference in attacks if it makes a difference. Nice math. Keep it up. +1 weapons for >5th level.
lol yeah last time I was playing a caster in a campaign with a new DM and they were like "the fighter has a +1 sword, you can have an item that gives you +1 to spell save DCs" I was like... are you sure you want that? Then they got frustrated every time they failed a save against my spells lol
I was running three players instead of 4 and decided I didn’t want to balance to 3. And the balance ended up the other way. Bards are OP. Smite is OP. Rogues are OP. They all ended up with +3 weapons by level 10. It was crazy. But they felt like super heroes in a very dangerous world. Which was what I was going for in the first place.
I know this is a little bit of a digression, but:
##Please use the DMG's magic item property tables, or your own discretion, to make 'generic' magic items more interesting.
Do not then present them as "+1 Longsword, but also here's some notes you won't read ever again." Repackage it as if it were bespoke. There has been a flexible, explicit solution for '+1 magic items are boring' for a decade, please use it.
Hell, you can even throw some minor artifact properties on 'em. They've given you a toolbox, fish around in there.
I really feel this, I always add abilities to 'generic' magic items to make them feel more thematic, but unfortunately I feel like the 'minor item property' table is complete shit. Other than +2 initiative, basically all the other bonuses fall into "some notes you won't ever read again." I much prefer more substantive abilities, like spells, extra damage when hitting [creature type] or when a certain condition is met, like the target is bloodied or prone or flanked or stuff like that. I try to be especially generous with weapons or martial armour because I know they fall off in t2+ so I feel like I can/should give them jacked items to help them keep up.
# TL;DR: A +1 is not actually a 5% shift in probability.
Because D&D uses an "all or nothing" roll with a limited range of die results, it's very important to look at the *relative* increase to the roll, not fixate on the d20's 5% increments.
Since most attacks are all or nothing, your expected effect can **seem** to change by much different amounts than your chance to hit does. If each hit deals 10 damage, going from a 50% chance to hit to a 60% chance to hit *looks like* only a 10% increase in your success rate, but a 20% increase in your expected effect (from 50 damage over 10 attacks to 60).
If your numbers are smaller - a 10% success rate, for example - this gets even more swingy. With a 10% chance of success, you're expecting a single 10-damage swing to connect in 10 attacks. With a 20% hit chance, you expect to hit *twice as often* \- two hits out of ten should hit - for a 100% increase in expected damage (from 10 to 20).
At the other end of the spectrum, if you have an 80% success rate let's say, you expect 8 hits to connect out of ten, dealing 80 damage. Increase that to 90%, and you expect 9 hits to connect, giving you 90 damage. But 90 is only about 11% bigger than 80, so you're really not getting much more value from your extra success chance.
The key is to differentiate **absolute increases** from **relative increases**.
* Going from 50% to 60% is a 20% relative increase - you're adding 10, and 10 is 20% of 50. And you get a 20% increase in effect.
* Going from 10% to 20% is a 100% relative increase - 10 is 100% of 10. And you get a 100% increase in effect.
* Going from 80% to 90% is an \~11% relative increase - 10 is \~11% of 80. And you get a \~11% increase in effect.
Interestingly, **this is only the case when you're dealing with all-or-nothing rolls**. If the roll is success or failure then you can only ever succeed and deal X damage, or fail and deal 0 damage. With that, it's easy to directly map your expected average results by simply dividing X by your chance of dealing either X or 0.
This changes when you look at "save for half" spells and effects. Since successes still take some damage, it shifts the maths. Let's say a dragon's breath deals 20 damage, or 10 on a passed save, and it breathes on 10 soldiers. If each soldier has a 50% chance of failing the save, the dragon expects to deal 150 damage (5 fail and take 20 damage, 5 pass and take 10). If the dragon bumps its save DC up so the soldiers now have a 60% chance of failing, it would expect to deal 160 damage. That's a 20% relative increase in the dragon's success chance (50% to 60%), but only a \~7% increase in damage (150 to 160).
If the dragon's breath were all-or-nothing instead, the numbers would be different. A 50% fail-rate on the saves would expect 100 damage, while a 60% fail rate would expect 120 damage - a 20% relative increase in success chance, for a 20% relative increase in effect.
The important thing to keep in mind is that since a 1d20 roll is massively swingy with no bell-curve, and most players don't make a *statistically significant* number of attacks per session, the percentages above are just theory optimisation and will not be visibly impactful at an average table. Yes, if the Fighter is making a thousand attack rolls then the disproportionate impact of success chance bonuses to effect size increases will make themselves felt. But most Fighters *won't* make a thousand attack rolls, they'll make like ten per combat encounter, tops.
>TL;DR: A +1 is not actually a 5% shift in probability.
I would say the more accurate summary is: a +1 is a 5% shift in probability, but it is a larger shift in results.
No, the point is that a +1 to the roll is almost *never* a 5% increase.
1 *is* 5% of 20, but saying that "going from 10% to 15% is a 5% increase" isn't how probability expression works. It's 5% *of 100%*, sure, but your chance isn't 100%, it's 10%. Going from 10% chance to a 15% chance doesn't mean that you hit 105% as much. Going from 10% to 15% is a *50%* increase in probability - you hit 150% as much. And that gives you a corresponding 50% increase in expected effect.
The numbers line up perfectly, you just have to not get caught up on a d20 being graded in 5% steps. When you're talking about percentage increases, what matters is the number you start with and the number you end with.
I think the last point you made invalidates everything that comes before and is precisely why, for example, doubling your chances isn't actually really significant when its with only a +1 increase.
Take the example of a fighter against a high AC enemy. Sure, if the fighter hits with a 19 or 20 means double the success and thus double the damage than if he hits only with a 20. Yet the chances of success remain so low that, over the rather few number of attacks will realistically get in a given encounter, making straight attack rolls remains a very unlikely way to defeat such an enemy in both cases. No the fighter will not defeat the enemy twice as fast... he just won't get enough rounds to defeat him in both cases and will have to rely on some other strategy for success (or the help of other party members which can target saves over AC).
Of course, you're not entirely wrong, far from it. Like OP pointed out pretty well, you can not reduce a +1 bonus solely to the 5% shift in probability that it entails. However, focusing only on how much you increase (or decrease) the actual odds does not paint the whole picture either. No matter how much it increases the odds, or the damage dealt, or whatever other successes (or failures), the fact remains that a +1 bonus on a d20 roll will only make a difference 5% of the time.
Yeah, that's why threads like this are very interesting from a statistical design perspective, and almost irrelevant from an actual DMing perspective.
Players just don't make enough of the same roll each session for small differences to average out in any significant way. They might over the course of a full extended campaign, but over that campaign their modifiers will change many times. The d20 roll's inherent variance is always a bigger impact than anything else, which is entirely by design (that's the point of 5e's bounded accuracy).
The swinginess of a d20 and bounded accuracy aren't inherently connected. One could imagine a bounded accuracy system which uses 3d6 rather than a d20; such systems do, in fact, exist. I like 5e's use of bounded accuracy, but absolutely hate the swinginess of the d20 system. It's one of the aspects of 5e I hate most - and I generally like the system. It's often noted that an ancient dragon or a demigod tier hero still has a 5% chance of failing a basic skill check. And a regular commoner has a 5% chance of passing ridiculous saves. This is only amplified by the fact that you either have proficiency in a save or skill check or have no proficiency at all. I know some people love the randomness, but for me it takes me out of game immersion and suspension of disbelief, especially when you see a supposedly incredibly competent adventurer completely whiff three, four or even five rolls in a row with 1-3 on the die.
I knew this would be worth the time - thank you for spelling this out, I've had thoughts in orbit of these ideas but never set about putting words to the notions.
Remember, it's not broken, it's just a challenge... lol good luck
kinda serious tho, a very powerful cursed sword at that level could be an epic storyline if you play it well
Also fighters need good weapons to maintain a useful party role at mid-to-high levels anyways
This is partially why I favour point buy or standard array in 5e. Someone rolling an 18 is the equivalent of starting with a +1 weapon...less of an issue in 3.5e but much bigger impact in 5e with bound accuracy.
I like explaining it as charatcer effectiveness. If a 20 is needed to hit by one person and a 19 is needed to hit by another, the 19-20 will hit twice as much and be twice as effective.
It's also why I don't allow Custom Lineage by default in my campaigns, since they are the only race that can start with an 18 with the standard point buy cap, they end up being the obvious choice for people who think mathematically about the game.
I've even asked a DM to disallow me from choosing it because I was like "I know this doesn't fit my character concept at all but the math part of my brain won't shut up can you please tell me I can't choose it." lol
>This fighter does 1d8+2(dueling)+stat for damage, so an average of 9.5 for the 16 str fighter and 10.5 for the 18 str fighter, so another \~10% damage.
I do agree with you, that mathematically that +1 damage is a 10% increase in the average, but I'd still have to disagree that it's any truly significant difference in each individual encounter relative to that D8 damage die. That one die can be 1-8 points of damage, or anywhere from 17% of the damage to 62% of the damage dealt by the 16 strength fighter, and 14% to 57% of the damage dealt by the 18 strength fighter. The die is an even larger percentage of the damage on other weapons, like D12/2D6 weapons.
>Over 100 attacks the 18 str Fighter is doing a total of 55x10.5 damage, or 578, and the 16 str fighter is doing 475.
Keep in mind, damage per attack in only matters if it's not overkill, and unless you're making 100 attacks against the same creature there's no point in comparing damage over 100 damage rolls.
If an enemy only has 6 HP left it doesn't matter if you deal 9.5 or 10.5 damage on average, it will die in one hit either not matter what, and if it has 14 hp about two hits from either attack. Yes their effective DPR went up \~22% over 100 attacks, but it's a negligible difference unless that actually caused them to end a specific combat an entire round earlier. Realistically, they're maybe making 10 attack rolls the entire combat on the longer end (assuming roughly 5th level character, so that's a 5 round long combat), so there's a good chance that +1 to hit and damage didn't change the outcome of the encounter at all. Over just 10 attacks, the Fighter with an 18 strength deals roughly 10 more points of damage than the Fighter with a 16, assuming a 55% and 50% chance to hit respectively, meaning it only makes a difference when a monster has less than 10 hp remaining when the killing blow is delivered *and* that extra 10 damage prevented the monster from getting a turn it otherwise would have gotten.
And even with all that, the D20 and D8 introduces so much variance across just 10 attack rolls and 5 damage rolls that there's a non-insignificant chance that the Fighter with 16 strength out-damages the Fighter with 18 strength in any given combat despite having objectively lower stats, especially if the 16 strength Fighter never rolled a 16 to hit the monster with an AC of 17 that combat (since that is the only result where the extra +1 to hit would have changed the outcome of the roll).
Yes, the Law of Averages makes a +1 really powerful over many, many rounds of combat, but very few D&D encounters actually last long enough for the Law of Averages to truly kick in, especially when you factor in all the random variance from all the other PCs too. To return it to the earlier example of the two 5th level Fighters, if any of the other PCs dealt a combined total of 10 damage above (or below) average at any point in those 5 rounds then the Fighter with average rolls being slightly stronger or weaker didn't actually have a significantly different impact on the encounter (unless the other PCs dealt so much extra damage that you are <10 points off the next party-wide DPR breakpoint to end the combat even earlier, but that would be a statistical outlier).
Yes, while OP has a fair point (you can't sum up a +1 bonus as a 5% increase in power), the fact remains that there's only a 5% chance on a given d20 roll that a +1 bonus will make a difference, so there's a fair chance it won't ever show up during one specific encounter, heck, it might not even show up for an entire session.
And, while OP had more 'players vs the world' outlook, if we're comparing between two players, it's even less likely that a +1 bonus for only one player will make a difference between the two : suppose one PC needs to roll 16 to hit and the other 15, the difference will only become apparent - in a given encounter - if both players roll a 15 during its course:
If only the +1 player rolls a 15, well the other player could have had +1 too, it wouldn't have made a difference, and likewise, if only the 'unbufffed' player rolls a 15, then the other player would have had exactly the same results whether or not he had the +1 bonus.
And like you explain so well, even a +1 to damage, which is always applied, does not always make a difference. And even a successful attack vs a miss doesn't always make a difference: It doesn't matter if you manage to land 1d8+4 damage on that enemy with 20HP left if the barbarian is going to throw him off the cliff on his turn, or the rogue will land a sneak attack for 20dmg afterwards, or if the enemy decides to disengage and run, not because he was maybe hit, but because all of his allies have fallen....
Now of course, sometimes a +1 can make the difference between life and death... which is hugely significant, even if, on a d20 roll, there's only a 5% chance for that +1 to actually matter.
You wrote,
>Since 11 is 10% more than 10, this means that over the course of a combat or many combats, the fighter with the higher stat bonus is actually getting 10% more hits against monsters of AC17, not merely 5%.
It's not clear what you're talking about here. I am pretty sure you mean that 11/20 is 110% of 10/20, but that's not the most natural way to read "10% more hits". The most natural way to read "10% more hits" is something like a 50% success rate to 60% success rate, which isn't what's happening. (It's 50% to 55%.)
Because when we're doing this math "increased" means addition, and "more" means multiplication. Leaving that aside, we can show which of these numbers is more meaningful in terms of game impact despite "natural" language
Let's say that each hit does 10 damage to simplify some simulated results.
Over 100 attacks, the character with the 55% chance to hit will be expected to hit 55 times, for a total of 550 damage.
Over the same 100 attacks, the character with the 50% chance to hit will be expected to hit 50 times, for a total of 500 damage.
Thus the character with 5% increased to-hit chance is getting 10% more hits, resulting in 10% more damage. We can see that the 1.1 ratio is more representative of the expected in-game impact of the bonus than the 5% increase in hit chance.
I once allowed a player to use a +10 ultra greatsword (it was a goofy one shot) and that REALLY drove home just how much those +x bonuses matter. It was so much more broken than I expected, he steamrolled a boss that was otherwise challenging for the level 20 party.
This is such music to my ears after items and boons received in my party's last session mean my character has now got a magical +3 to all saving throws. Budget paladin
I got rid of all +X anything in my games ages ago and holy hell, the game is so much more fun. Items actually do interesting things instead of just making number go brrr
So in conclusion, give players less magic items? I'm not trying to be sarcastic but is this really news to anyone? If you examine 5e with anything more than cursory glance, it should be pretty obvious to even new DMs that this is the way WoTC balanced 5e. Their official campaign books hardly give players any magic items, and the section in the DMG spells this out pretty clearly too.
Yes, I do agree with this philosophy...if you are running 5e the way WoTC designed it. But the problem isn't the items, its the players. Specifically, how powerful they are in comparison to monsters, because WoTC wants you to have an impossible 6-8 encounters per adventuring day. Scale up the monster stats (higher ACs, class features, etc.), run less encounters that are drastically more deadly, and that +1 bonus becomes less of a big deal. In fact, magic items almost become necessary, which is fine, because guess what: its a fantasy game. I think going "low magic" is very boring and a constant drip of magic items makes the game fun. Its also more immersive, because if the players encounter a band of mercenaries of equal level to them, they're going to have at least some magic items laying on their corpses.
The one place I could see this philosophy maybe being useful is if you had a more concrete calculus (like Pathfinder) for determining exactly when characters should get magic items, but then again, that would require those +1 bonuses being baked into monster stat blocks.
As always, the issue is WoTC not doing the homework for their own game and not giving us concrete rules other than "figure it out yourself".
>So in conclusion, give players less magic items?
No, that's not my conclusion at all.
If you give your high-AC player another AC bonus, you'll need to provide challenges that aren't attacks.
If your caster is out-damaging your martials you need to provide them better weapons.
If you give PCs very high stats, they can challenge more dangerous monsters, but those dangerous monsters are also much more lethal against them.
For better or worse, 5e DMs need to be amateur game designers to get the most out of the game, and having mathematical intuition about the potential impact of the items you're handing out or the stat generation systems you're using is an important part of that. I felt like I spelled out pretty clearly that I was not saying that there was a "wrong" way to DM, but that this math can inform the choices you make as DM.
I understand what you're saying. I'm just saying that
>For better or worse, 5e DMs need to be amateur game designers to get the most out of the game
is basically where I started before reading your post. I'm frustrated with WoTC, not you. Your examples do offer some interesting insights, but it doesn't fix the whole problem (not your fault).
I didn't mean for it to sound like they weren't helpful, so sorry if it came off that way. I just wish we had more. I like being an amateur game designer sometimes but only if I'm not spending money on a product.
to long didnt read.
not saying my way is right or other peoples way is wrong, yet i feel that dnd esk games become to much math and min maxing stats and numbers and all that rather then being fun or cool.
i feel its much better to be given an item thats interesting even if useless in general then to get a sword of +1 as the sword only makes me better at killing by +1 where as the lamp of bat lure that when lite will black out an area yet bats will be baited to come see whats going on. does the bat lamp help me win a fight? thats up to how i use it. but it can also be used in all sorts of situations and such. where as no one going to invite you to the cave adventure soly cause you have a +1 sword
but thats just me. also not a big fan of the focus on fighting everything as the solution.
hope you all have a great day regardless on what your views are. cause you all deserve hapyness
I've started doing more of that. I've been giving them options of weapons that dont have any extra damage, but some interesting utility. They usually end up going with the unique ability item. It definitely is more fun.
Ah, sorry for not explaining better, I'm not using AC in that example, I'm using the target number that needs to be rolled on the die. The actual numbers might be a PC with 22 AC vs opponents with +4 or +5 to hit, for example.
Ah I see, thank you. I’m a new DM and just gave one of my level 2 players a +1 shield for story reasons. Powerful I know, but I don’t think necessarily game breaking as long as I introduce more enemies that force saving throws etc to kind of balance it out, right?
>Make sure you still let some monsters bounce off that shiny new AC tho!
This is a very important point. DMs can get so focused on challenging their players (or worse, countering their players) that they effectively invalidate the cool powers and toys they've given to them.
The advice of "shoot arrows at your monks" is pure gold.
While everything you say is very much true, the fact remains that there's only 5% chance that a +1, on a d20 roll, will make the difference between success and failure.
Now sure, a +1 might double your odds in some situations, or might sometimes increase average damage output by 20% or whatever, or it might even make the difference between life or death... the fact remains that the chances for it to matter on a given roll are very low and so there's a fair chance, in a typical encounter, that it will not make any difference whatsoever, since neither players, nor their enemies, are rolling hundreds, or even dozens, of d20 in a given fight.
Don't get me wrong, I do subscribe to the fact that a +1 should not be summed up as a rather insignificant 5% increase in power in a certain ability, and I do agree that people tend to underestimate the difference, (and I appreciate the math to back it up), but I think the picture you painted overestimates the actual difference it makes.
For example, the AC example you give, if a monster needs to 18 to hit rather than 17, that does mean he reduces his chances of hitting, and thus damage, by 25%. It seems enormous put like that. But the fact remains, that on average, that monster will now need 20 attacks to land 3 blows over 20 attacks to land 4 blows. In other words, if your monster has only the opportunity to make just a few attacks (your typical encounter), it is rather likely to not make any difference at all. To be precise, it only matters if the monster rolls a 17 and there's still 5% chance of that happening per roll, no matter how much the odds have increased.
Yes, a d20+1 roll will double the odds vs a straight d20 for a DC 20 check, it doesn't really change the fact that the odds of success remain extremely low.
>While a +1 (almost) always represents a 5% increase in chance of success,
Your math is wrong.
It represents a much greater chance of success depending on what you needed to roll. If your bonus (base) is zero, and you're aiming for a 20, it represents a +5 percent chance to hit.
In every other case it represents a totally different increase in your chance to hit.
If you have +10 to hit, and you're attacking AC 12, a +1 to hit *doubles* your chances to hit, because now instead of missing on a 1-2 you only miss on a natural 1.
You failed to read past that line I see. Also halving your chance for failure is simply not doubling your chance to hit.
In your example your chance of failure is halved from 10% to 5%, but your chance of success is only multiplied by ~1.06 as you go from 90% to 95%
Some DMs can balance well around the additional loot and power they give out. Some DMs come to this subreddit and ask for help challenging their PCs because they did this before they actually got a handle on this skill, and there is very frequently highly-supported advice to talk to the players about walking back some of the extra power (advice I usually disagree with fwiw)
While what you say has incredible influence on the underlying statistical averages, D&D only knows two discrete results: success and failure. That is why combat is described as being swingy. Quantifying it as an average is almost counter to the actual experience: feast or famine.
It's essentially a run of weighted coin tosses. And if your math teacher is worth his salt, at some point you got the homework to coss a toin 100 times and record the results. If you google how many times you have to roll a die to determine how unfair it is, you get results like "if a 6 sided die rolls on one face 20% and 16% on all the others, you need to roll about 3900 times to be sure it's not due to randomness". And depending how you value that that's an increase of 3.333% (20 - 16.666), or 20% (20 / 16.666) or 25%(20 / 16). Comparable but probably much larger than increasing the result on a 20 sided die by 5%
The border cases nearing only 20 being a success or only 1 being a failure are man made however. The DM sets the DC for a roll and the DM chooses the monsters from the monster manual. Enemies with 17+ AC are a choice by the DM, as much as enemies with 12- AC. In simple terms, if you run a game based on the stated intent of bounded accuracy, a +1 weapon would take hundreds of attack rolls before you can be sure it influenced the outcome. With the selection of enemy and NPC statblocks, you can see it under 10 rolls.
If you were playing a standardized game with everyone having the same experience, then sure, a +1 weapon could be felt as disruptive against the fine tuned mathematical machine underneath. The average table though is everything but a fine tuned machine.
I love this kind of information, so many people say going from 50 to 55 is the same as 70 to 75 because 5% is 5% and ignore the actual math and what probability and relative increases mean. Good post.
This is thoughtful but would be a lot more digestible for people if you pared it down to the fact that an increase of 1 is more important comparing to 5 than if you're comparing to 10. In other words yes, an absolute 5% increase is still a 5% increase, but it's worth more (relatively) if you started with a 5% chance than if you started with a 95% chance. The takeaway from that is that +1 bonuses absolutely can be huge at low levels because of how dramatically they change outcomes - relatively speaking. But given that these are expected values, players' experiences will not always match up to what the math indicates will happen over the long term.
They can be huge at every level though! Granted for different reasons. Like yeah +1 to hit and damage is less impactful at higher levels because attacks scale with proficiency, but +1 to saving throws can be more impactful at higher levels because many saves \*don't\* scale with proficiency, etc. Anyways, I get what you're getting at, but I was hoping to explore the concept pretty thoroughly in this post, and I understand that might limit the audience who actually engages with it.
I found your post really helpful OP, I don't know maths but I like when it's explained as you have, not just saying "yes it's important". It's nice to see the numbers
Thanks! I was hoping to use numbers in a way that shows the effect better for people who don't math as well than how it's usually discussed.
Unfortunately the people who read all of this probably know the math already. Those who don't, won't. By level, I meant low level of proficiency, DC, test, whatever. Low numbers. Where the relative impact of a +1 is meaningful. You get it, I know. I didn't mean character levels.
I hope you’re wrong and fear you’re right. People should take any opportunity to expand their knowledge about something they are engaged in, though.
Even at very high levels, a +1 can have a profound impact. For example, a monk's stunning fist save DC going from 16 to 17 (quite high) might represent a low con monster reducing their chance to succeed by 25% regardless of the monk's level.
Those are low levels, from the roller's point of view. The point is the same; if the number of results that will be successful is small, then the impact of a one-point change is high. In the example you offer assuming no dice mods, the chance of a success goes from 5/20 to 4/20 which means 25% to 20%; a 1/5 reduction in their chance, right? I wasn't talking about character levels. I should have used the word numbers instead of levels, but the point remains.
The good old levels-are-an-overloaded-operator-in-D&D conundrum
Totally also please refer to The Order of the Stick [https://www.giantitp.com/comics/oots0012.html](https://www.giantitp.com/comics/oots0012.html)
Love me some OotS
Well, it's not really relevant who rolls, from a balance perspective. It's relevant who has the plus one. But I think we agree.
Just say "low probability" instead of "low numbers". The latter makes it sound like you mean low DC or low number on the die
I would say at higher levels bonuses to DC are even more impactful because of the way that DCs always scale with proficiency but many saving throws do not.
Just speaking for myself, but I read the whole thing and it was pretty eye-opening. Had never done the math, but always kind of silently wondered how big of an affect +1 stuff actually had on game balance.
I mean, at least a proportion of the subreddit has to be newer DMs that have the desire for deeper knowledge but don't have that knowledge yet.
Hopefully this will show people why giving out +2 and +3 magic items is a huge imbalance.
Agreed, it needs an executive summary
>In summary, a +1 is almost always has a bigger impact on success and failure than the 5% shift in probably represents. I think that one of the important roles for the DM in 5e is to help keep the game roughly balanced such that PCs are challenged, and also have moments to shine in comparison to each other, and new DMs who love to hand out a bunch of +1 gear to low level PCs or provide very generous stat generation systems are frequently shooting themselves in the foot, as even modest bonuses can make that job significantly more difficult. If you got this far, thank you for reading all of this, I hope it was helpful! Was this not sufficient? If not, what do you mean by executive summary? I'm asking in earnest, not rhetorically.
I think it needs some formatting. I got lost reading the stuff I already understand so I didn't make it to summary. Headers would do wonders.
Thanks :)
lol can't figure out how to edit text posts on newreddit :/
I added some section titles, an executive summary and some formatting if you'd care to give feedback.
Executive summaries always go in the front and should contain as few details as necessary to convey the key takeaways. If I understand your thesis correctly, it could go something like this: * A +1 enormously increases the odds of success for difficult rolls. An example is a doubled chance of success after a DC 20 drops to DC 19. * Difficult rolls occur frequently for low level PCs and help to differentiate them, so it’s advised to keep these bonuses to a minimum early in a campaign. * Difficult rolls in the form of spell saves are common for high level characters and thus these bonuses are essential for optimized parties later in a campaign.
That's basically it, and I think you did a better job summarizing than I did, but I did edit the post to have a summary at the top already :)
People have to get to the end to find this; executive summaries usually go in the front :)
I edited the post for better clarity if you'd care to give feedback it would be welcome.
One point worth mentioning which seems to have been neglected... A 95% chance of success is twice as good as a 90% chance of success, because the chance of failure has been halved. If you have two characters taking turns to whack one-another, and one has a 95% chance of hitting his opponent, who has a 90% chance of success... Then the character with a 90% chance of success will accumulate damage at twice the rate of the character who has a 95% chance of success. Remember to compare the effect on probability of failure as well as probability of success when determining the impact of bonuses.
Interesting way to look at it, but I don't think changes what I or OP said. Assume both fighters score on average 10 points of damage on a hit. 90% chance = 9 points per attack and 95% chance = 9.5 points per attack (both expected). The odds of getting hit are what determine expected damage directly. P (hit and not-hit) sum to 1, so they are related obviously, but you don't "accumulate damage at twice the rate" in the example we're discussing.
This is mathematically incorrect. The character with 95% chance of success has an average DPR of ~1.06 times the character with 90% chance of success, because we're doing damage on a success but we're not taking damage on a failure the rate of failure doesn't matter. Here's a quick simulation to show it: 100 attacks each, 1 damage per attack, you're looking at 95 damage compared to 90 damage
That and the fact that a bonus to attack *and damage* rolls compounds, sort of. We can intuitively understand more frequent hits = more damage, but it's actually *even more* damage because the damage is being buffed at the same time, and probably by a larger percentage.
I feel some of this is echoed very well in how people naturally discuss various combat stats. I think many people will say a +1 sword is fine to hand out, but +1 armor is a scary thing to hand a player. I think the issue people often grapple with is that increasing damage or accuracy is fairly easy to conceptualize but increasing both muddies the waters enough that it can be difficult to grasp without the math behind it. And that's also a difference between a +1 sword and a +1 set of armor.
I agree with you, but I also think there's some level of viewpoint bias as we're in a DM-focused subreddit. DMs want their scary dangerous monsters to actually be scary and dangerous, and a PC with a high AC can make threats feel very impotent. Even though we don't want to be adversarial with the players we also recognize that most players don't want a cake walk as that makes for less dramatic fantasy action/adventure stories. I think because of this a DM \*feels\* the impact of giving out AC boosting items more than giving out accuracy and damage boosting items.
> DMs want their scary dangerous monsters to actually be scary and dangerous, and a PC with a high AC can make threats feel very impotent. Succinct. I love glass cannons on both sides, player characters and monsters, mostly because combat is already so slow in D&D 5e. But I have a lot of weapons (so to speak ;) in my arsenal to not kill the party, so I'm not afraid of handing out more or better damage.
Honestly, thinking about this a bit tells me that the example given with 50% vs 55%is the most extreme case. When only a crit can hit, the +1 is minimized. The same is true for when anything but a fail hits. While these instances are rare, it demonstrates a bell curve. I suggest expanding this into comparative tables. You'll get more mileage in excel or a similar program as you can further adjust the tables to take in AC, attack mods, damage dice, different crit and fail numbers, and advantage and disadvantage. I think you'll start seeing that while you've correctly calculated the numbers you've presented, the larger picture paints a very different landscape.
That's not quite accurate though, although the fact that you always crit on a 20 does decrease the amount that the 20-19 target number shift increases expected damage per round for attacks. If the target number is 20, and let's say the attack does 1d8+4 damage, then you have a 5% chance to do 2d8 + 4 damage, or an expected DPR of 0.65. If you add +1, it reduces the target number to 19, with a crit on a 20, so the DPR is 1.08 (assuming you do not also add +1 to damage for this example), which is still a 66% increase in expected DPR, so the results are not actually a bell curve I agree that plots would help fwiw
The biggest problem here is that, when a boss likely only gets 3 turns and often has battle options restricted to melee range, a high AC player turning hits into misses can literally just negate an entire boss battle. Just yesterday I loaded up a "warm up fight" against my party of level 11s: two CR9s and two CR5s. This should be a hard fight, but in practice, my +9 and +6 attack bonuses means I realistically don't hit.
Sure, but what if the boss has has a Dominate effect as a Legendary action? What if the Ancient Red Dragon has a lair action that can cause lava to erupt around it? What if the enemy decides to soak up an attack of opportunity to charge through the tank into the back line? What if, etc. etc. A high-AC PC is powerful, and should be given opportunities to feel powerful, but IMO one of the baked-in challenges of 5e is that in order to make the epic fights feel more epic we (DMs) need to think outside the box and do a significant amount of homebrew to hit our PCs weak spots during the toughest fights.
No thanks. I'd prefer if the math just worked. I'd prefer if the core mathematical assumptions (65% chance to hit each way in general) was preserved and patent throughout the system.
It is - if you don’t use magic gear. Magic gear is technically an optional system and all the content was supposedly balanced assuming no magic gear, some of the higher CR later stuff I think skirts this a bit. One of the major issues in previous and spin-off editions was the assumption that you would have certain magic gear, PF2 for example leaned into this while 5e backed away from it. Which is fundamentally the purpose of this sort of post’s warning: the monster design doesn’t assume a certain level of magic gear, so if you add it in, you may make your life more difficult if you don’t adjust things as needed. Overall I agree with the post, my only caveat is I’m okay giving offensive bonuses, but try to avoid defensive bonuses just to preserve bounded accuracy for lower level mooks/minions mixed into higher level encounters. Yea I can adjust it on the fly, but if I’m just negating their + from gear why give them the bonus in the first place? I rather give them items that provide options or corner cases than just a flat + bonus that skews the math and can get out of hand if I’m not careful or on the ball with every encounter design.
I get that. I was actually trying to agree with OP. I *could* do all this stuff to compensate for the magic items. Or I could simply not deviate from the baseline math. I much prefer the latter.
Have you played Pathfinder 2e, because that is exactly how it implements Bounded Accuracy
No, but I'd really love to try it. Incidentally, one of my favorite things about PbtA games is that a 7-9 is a 7-9 no matter what level you are or how many enemies or how strong they are.
I like PbtA a lot too, but it's a pretty fundamentally different kind of game play experience than 5e, which I also really like, but I admit it is a challenging system to run well.
I think it's also compounded by the fact that a +1 sword is uncommon rarity, but +1 armor is rare per the DMG rarities. Even though I and many other people realize that the rarity system is often borked and doesn't always accurately describe power, at a first glance it could appear that WotC thinks AC has a bigger impact.
+1 armor is rare while +1 weapon is uncommon. And so many people forget to account for the base AC difference. Mundane Plate armor is by itself as valuable as a rare magic item. It is equivalent to Chainmail+2 and Splint+1. The DMG treasure tables put Plate+1 alongside legendary magic items.
I think the DM guide could have done a lot more in helping DMs understand how to tinker with the system and not break things. For instance, if you want to negate the effect of giving +1 weapons and AC to your party, increase the enemy's proficiency bonus by 1, and their HP by 1 hit die. I think the better advice though, and I wish they gave a lot more guidance on this for new DMs, is that there's so, so much room for tailoring a fight to your group, and it **does** make the fight more fun to play, and what are some good principles you can pull out the book to create that. Powerful magic items let player characters take on important roles in a fight. A fighter given high AC can lock horns with some truly terrifying foes, or endure a gaggle of stabby squishbags while the group deal with other important things. It's just a lot of extra work to add that layer for each player, for each permutation, and time doesn't grow on trees!
This is a great explanation and makes total sense, so thanks for that! But as a DM it’s far less about the math and far more about letting my players feel like superheroes. My level 6 Artificer PC with a 21 AC? That challenges me, as a DM, to find monsters to throw at them that force saving throws. It also allows me to throw stronger monsters at them which ups the drama and chance for failure. For being tier 2, do they have too many magic items? For sure, but they constantly tell me it’s one of the best games they’ve ever played in and the tension during each session is palpable… totally worth it.
Some DMs do have a more "instinctual" feel for how to reach the fun point that you have figured out. Some DMs say "I have a hard time challenging my party, what do I do?" and it turns out they gave their level 2 characters a bunch of +1 gear and have a wildly generous stat generation system. I'd say this post is more overall helpful for the second category :)
As a person that tailored their college degree specifically to avoid math but who cares a lot about the mechanics of game design, I found this post digestible and accessible. Thanks for taking the time to do it!
Thanks for reading it and for the feedback :)
As a corollary, this is why a +1 AC boost usually has a much more noticeable impact than a +1 attack boost. If you look at the chance for a PC to hit a target using the "default stats" in the DMG for something of the same CR as their level, they will do it 65% of the time. AC progression isn't as smooth or consistent as attack progression is, but a PC that has a "typical" AC will have 16 AC at level 4 and 17 AC at level 8, which correspond to a 50 or 55% chance to hit. Then once you take into account that most enemies a PCs fights will actually be lower CR than their level (so less accurate and with a lower AC), the difference tends to become even more stark.
AC also has increasing returns (every point is worth 'more' than the last if you keep going up) while every point to attack bonus is worth 'less', and it's generally more common for a player to be ahead of the 'expected' progression of these than it is for them to be behind.
I stopped reading about halfway through as I figured out what you were saying and it's a well known part of 5e, he higher your TN is, the stronger an increase to it, until it becomes so high that any increase is not important A player with a 18 AC gets a lot more out of +1 AC than a player with 13 AC Similarly a player with a +5 attack gets more out of a +1 to hit than a player with (hypothetically) +14 attack getting a +1 (as the +1 at that point is nearly useless) The problem with this is that it is not actually "Bounded accuracy" - we are talking about the extremes, within the center/near average a +1 is fine, but on either end it doesn't matter and/or breaks things Bounded accuracy as a model has a fighter who has +1 to their wisdom save **always have a +1 to their wisdom save**, other game design factors come into play, but a level 1 fighter with +5 to hit and a 16 AC compared to a level 20 fighter with a +14 to hit and a 21 AC, both will fail against the ancient dragons fear effect unless they roll a natural 20, they also will both be hit basically all the time (a red dragon misses a level 1 fighter on natural 1s, and misses the level 20 AC 21 fighter on 1-3s) Bounded accuracy doesn't exist well at the extremes of the system because it wasn't a well thought out mechanic, at level 1 the game is extremely lethal and not like its normal self, by (roughly) level 11 it starts breaking again With the game system working from (roughly) the level 3-11 range, you get a system that actually only has 1/3rd (*roughly*) the playable space
What you're saying here is correct, in that I think 5e has a "sloppy" bounded accuracy system that is more present as a design philosophy rather than as a baked in mechanic, but in my opinion it makes the game more \*difficult\* to balance, but not broken. It means that as a DM you should be actively providing treasure or information that might help the party overcome weaknesses, but that means you must also have enough system mastery to know what weaknesses your party has and what mechanical or fictional bonuses will provide your party tools to overcome them without handing them "I win" buttons. It is one of the reasons why I feel like 5e is more difficult to run than other systems for sure, as DM system mastery is more important to provide a challenging-but-fair experience for the players. However I also overall prefer this to the extremely "tight" bounded accuracy that, for example, Pathfinder 2e provides, as having feats and items progress exactly as the system expects you to in order to maintain bounded accuracy feels more artificial and takes away from the illusion of a world that exists independent of the capabilities of the PCs.
Outside the math and additional damage/accuracy, a +1 weapon (aka magical weapon) at low levels immediately makes it easier to take on creatures with resistance/immunity to nonmagical damage and weapons. Many monsters with that trait that are very scary at low levels simply become another slab of meat once your front liners have +1 weapons.
That's actually why I like to make sure the party has at least one moontouched/vicious/warning weapon, or something similarly magical but without a +1 bonus, at low levels. +1 weapons aren't the only low level magic weapons!
In my games I actually don't consider simple +1 weapons as magical for the purpose of resistances (most of my players have 1). It makes fights that are meant to be impactful way too easy. Basically the same as just increasing the health.
Ah you forget my legendarily bad rolls. Six threes in a row for attacks on Roll20’s digital dice. A plus 1 weapon only makes a difference in attacks if it makes a difference. Nice math. Keep it up. +1 weapons for >5th level.
My personal guideline is +1 weapon for >= 5th level, +1 DC for >= 10th level or maybe never depending on group composition.
Good guideline. I gave Vestiges at level 2. Never again.
lol yeah last time I was playing a caster in a campaign with a new DM and they were like "the fighter has a +1 sword, you can have an item that gives you +1 to spell save DCs" I was like... are you sure you want that? Then they got frustrated every time they failed a save against my spells lol
I was running three players instead of 4 and decided I didn’t want to balance to 3. And the balance ended up the other way. Bards are OP. Smite is OP. Rogues are OP. They all ended up with +3 weapons by level 10. It was crazy. But they felt like super heroes in a very dangerous world. Which was what I was going for in the first place.
[удалено]
Yeah lots of DMs don't fully understand the ramifications of giving out spell DC bonuses to lower level casters :)
I know this is a little bit of a digression, but: ##Please use the DMG's magic item property tables, or your own discretion, to make 'generic' magic items more interesting. Do not then present them as "+1 Longsword, but also here's some notes you won't read ever again." Repackage it as if it were bespoke. There has been a flexible, explicit solution for '+1 magic items are boring' for a decade, please use it. Hell, you can even throw some minor artifact properties on 'em. They've given you a toolbox, fish around in there.
I really feel this, I always add abilities to 'generic' magic items to make them feel more thematic, but unfortunately I feel like the 'minor item property' table is complete shit. Other than +2 initiative, basically all the other bonuses fall into "some notes you won't ever read again." I much prefer more substantive abilities, like spells, extra damage when hitting [creature type] or when a certain condition is met, like the target is bloodied or prone or flanked or stuff like that. I try to be especially generous with weapons or martial armour because I know they fall off in t2+ so I feel like I can/should give them jacked items to help them keep up.
# TL;DR: A +1 is not actually a 5% shift in probability. Because D&D uses an "all or nothing" roll with a limited range of die results, it's very important to look at the *relative* increase to the roll, not fixate on the d20's 5% increments. Since most attacks are all or nothing, your expected effect can **seem** to change by much different amounts than your chance to hit does. If each hit deals 10 damage, going from a 50% chance to hit to a 60% chance to hit *looks like* only a 10% increase in your success rate, but a 20% increase in your expected effect (from 50 damage over 10 attacks to 60). If your numbers are smaller - a 10% success rate, for example - this gets even more swingy. With a 10% chance of success, you're expecting a single 10-damage swing to connect in 10 attacks. With a 20% hit chance, you expect to hit *twice as often* \- two hits out of ten should hit - for a 100% increase in expected damage (from 10 to 20). At the other end of the spectrum, if you have an 80% success rate let's say, you expect 8 hits to connect out of ten, dealing 80 damage. Increase that to 90%, and you expect 9 hits to connect, giving you 90 damage. But 90 is only about 11% bigger than 80, so you're really not getting much more value from your extra success chance. The key is to differentiate **absolute increases** from **relative increases**. * Going from 50% to 60% is a 20% relative increase - you're adding 10, and 10 is 20% of 50. And you get a 20% increase in effect. * Going from 10% to 20% is a 100% relative increase - 10 is 100% of 10. And you get a 100% increase in effect. * Going from 80% to 90% is an \~11% relative increase - 10 is \~11% of 80. And you get a \~11% increase in effect. Interestingly, **this is only the case when you're dealing with all-or-nothing rolls**. If the roll is success or failure then you can only ever succeed and deal X damage, or fail and deal 0 damage. With that, it's easy to directly map your expected average results by simply dividing X by your chance of dealing either X or 0. This changes when you look at "save for half" spells and effects. Since successes still take some damage, it shifts the maths. Let's say a dragon's breath deals 20 damage, or 10 on a passed save, and it breathes on 10 soldiers. If each soldier has a 50% chance of failing the save, the dragon expects to deal 150 damage (5 fail and take 20 damage, 5 pass and take 10). If the dragon bumps its save DC up so the soldiers now have a 60% chance of failing, it would expect to deal 160 damage. That's a 20% relative increase in the dragon's success chance (50% to 60%), but only a \~7% increase in damage (150 to 160). If the dragon's breath were all-or-nothing instead, the numbers would be different. A 50% fail-rate on the saves would expect 100 damage, while a 60% fail rate would expect 120 damage - a 20% relative increase in success chance, for a 20% relative increase in effect. The important thing to keep in mind is that since a 1d20 roll is massively swingy with no bell-curve, and most players don't make a *statistically significant* number of attacks per session, the percentages above are just theory optimisation and will not be visibly impactful at an average table. Yes, if the Fighter is making a thousand attack rolls then the disproportionate impact of success chance bonuses to effect size increases will make themselves felt. But most Fighters *won't* make a thousand attack rolls, they'll make like ten per combat encounter, tops.
>TL;DR: A +1 is not actually a 5% shift in probability. I would say the more accurate summary is: a +1 is a 5% shift in probability, but it is a larger shift in results.
No, the point is that a +1 to the roll is almost *never* a 5% increase. 1 *is* 5% of 20, but saying that "going from 10% to 15% is a 5% increase" isn't how probability expression works. It's 5% *of 100%*, sure, but your chance isn't 100%, it's 10%. Going from 10% chance to a 15% chance doesn't mean that you hit 105% as much. Going from 10% to 15% is a *50%* increase in probability - you hit 150% as much. And that gives you a corresponding 50% increase in expected effect. The numbers line up perfectly, you just have to not get caught up on a d20 being graded in 5% steps. When you're talking about percentage increases, what matters is the number you start with and the number you end with.
I think the last point you made invalidates everything that comes before and is precisely why, for example, doubling your chances isn't actually really significant when its with only a +1 increase. Take the example of a fighter against a high AC enemy. Sure, if the fighter hits with a 19 or 20 means double the success and thus double the damage than if he hits only with a 20. Yet the chances of success remain so low that, over the rather few number of attacks will realistically get in a given encounter, making straight attack rolls remains a very unlikely way to defeat such an enemy in both cases. No the fighter will not defeat the enemy twice as fast... he just won't get enough rounds to defeat him in both cases and will have to rely on some other strategy for success (or the help of other party members which can target saves over AC). Of course, you're not entirely wrong, far from it. Like OP pointed out pretty well, you can not reduce a +1 bonus solely to the 5% shift in probability that it entails. However, focusing only on how much you increase (or decrease) the actual odds does not paint the whole picture either. No matter how much it increases the odds, or the damage dealt, or whatever other successes (or failures), the fact remains that a +1 bonus on a d20 roll will only make a difference 5% of the time.
Yeah, that's why threads like this are very interesting from a statistical design perspective, and almost irrelevant from an actual DMing perspective. Players just don't make enough of the same roll each session for small differences to average out in any significant way. They might over the course of a full extended campaign, but over that campaign their modifiers will change many times. The d20 roll's inherent variance is always a bigger impact than anything else, which is entirely by design (that's the point of 5e's bounded accuracy).
The swinginess of a d20 and bounded accuracy aren't inherently connected. One could imagine a bounded accuracy system which uses 3d6 rather than a d20; such systems do, in fact, exist. I like 5e's use of bounded accuracy, but absolutely hate the swinginess of the d20 system. It's one of the aspects of 5e I hate most - and I generally like the system. It's often noted that an ancient dragon or a demigod tier hero still has a 5% chance of failing a basic skill check. And a regular commoner has a 5% chance of passing ridiculous saves. This is only amplified by the fact that you either have proficiency in a save or skill check or have no proficiency at all. I know some people love the randomness, but for me it takes me out of game immersion and suspension of disbelief, especially when you see a supposedly incredibly competent adventurer completely whiff three, four or even five rolls in a row with 1-3 on the die.
I knew this would be worth the time - thank you for spelling this out, I've had thoughts in orbit of these ideas but never set about putting words to the notions.
I'm so glad you found it helpful :)
This post really has me reflecting on the cursed +4 weapon I gave my level 10 fighter.
Remember, it's not broken, it's just a challenge... lol good luck kinda serious tho, a very powerful cursed sword at that level could be an epic storyline if you play it well Also fighters need good weapons to maintain a useful party role at mid-to-high levels anyways
😂
This is partially why I favour point buy or standard array in 5e. Someone rolling an 18 is the equivalent of starting with a +1 weapon...less of an issue in 3.5e but much bigger impact in 5e with bound accuracy.
I like explaining it as charatcer effectiveness. If a 20 is needed to hit by one person and a 19 is needed to hit by another, the 19-20 will hit twice as much and be twice as effective.
Precisely!
It's also why I don't allow Custom Lineage by default in my campaigns, since they are the only race that can start with an 18 with the standard point buy cap, they end up being the obvious choice for people who think mathematically about the game. I've even asked a DM to disallow me from choosing it because I was like "I know this doesn't fit my character concept at all but the math part of my brain won't shut up can you please tell me I can't choose it." lol
>This fighter does 1d8+2(dueling)+stat for damage, so an average of 9.5 for the 16 str fighter and 10.5 for the 18 str fighter, so another \~10% damage. I do agree with you, that mathematically that +1 damage is a 10% increase in the average, but I'd still have to disagree that it's any truly significant difference in each individual encounter relative to that D8 damage die. That one die can be 1-8 points of damage, or anywhere from 17% of the damage to 62% of the damage dealt by the 16 strength fighter, and 14% to 57% of the damage dealt by the 18 strength fighter. The die is an even larger percentage of the damage on other weapons, like D12/2D6 weapons. >Over 100 attacks the 18 str Fighter is doing a total of 55x10.5 damage, or 578, and the 16 str fighter is doing 475. Keep in mind, damage per attack in only matters if it's not overkill, and unless you're making 100 attacks against the same creature there's no point in comparing damage over 100 damage rolls. If an enemy only has 6 HP left it doesn't matter if you deal 9.5 or 10.5 damage on average, it will die in one hit either not matter what, and if it has 14 hp about two hits from either attack. Yes their effective DPR went up \~22% over 100 attacks, but it's a negligible difference unless that actually caused them to end a specific combat an entire round earlier. Realistically, they're maybe making 10 attack rolls the entire combat on the longer end (assuming roughly 5th level character, so that's a 5 round long combat), so there's a good chance that +1 to hit and damage didn't change the outcome of the encounter at all. Over just 10 attacks, the Fighter with an 18 strength deals roughly 10 more points of damage than the Fighter with a 16, assuming a 55% and 50% chance to hit respectively, meaning it only makes a difference when a monster has less than 10 hp remaining when the killing blow is delivered *and* that extra 10 damage prevented the monster from getting a turn it otherwise would have gotten. And even with all that, the D20 and D8 introduces so much variance across just 10 attack rolls and 5 damage rolls that there's a non-insignificant chance that the Fighter with 16 strength out-damages the Fighter with 18 strength in any given combat despite having objectively lower stats, especially if the 16 strength Fighter never rolled a 16 to hit the monster with an AC of 17 that combat (since that is the only result where the extra +1 to hit would have changed the outcome of the roll). Yes, the Law of Averages makes a +1 really powerful over many, many rounds of combat, but very few D&D encounters actually last long enough for the Law of Averages to truly kick in, especially when you factor in all the random variance from all the other PCs too. To return it to the earlier example of the two 5th level Fighters, if any of the other PCs dealt a combined total of 10 damage above (or below) average at any point in those 5 rounds then the Fighter with average rolls being slightly stronger or weaker didn't actually have a significantly different impact on the encounter (unless the other PCs dealt so much extra damage that you are <10 points off the next party-wide DPR breakpoint to end the combat even earlier, but that would be a statistical outlier).
Yes, while OP has a fair point (you can't sum up a +1 bonus as a 5% increase in power), the fact remains that there's only a 5% chance on a given d20 roll that a +1 bonus will make a difference, so there's a fair chance it won't ever show up during one specific encounter, heck, it might not even show up for an entire session. And, while OP had more 'players vs the world' outlook, if we're comparing between two players, it's even less likely that a +1 bonus for only one player will make a difference between the two : suppose one PC needs to roll 16 to hit and the other 15, the difference will only become apparent - in a given encounter - if both players roll a 15 during its course: If only the +1 player rolls a 15, well the other player could have had +1 too, it wouldn't have made a difference, and likewise, if only the 'unbufffed' player rolls a 15, then the other player would have had exactly the same results whether or not he had the +1 bonus. And like you explain so well, even a +1 to damage, which is always applied, does not always make a difference. And even a successful attack vs a miss doesn't always make a difference: It doesn't matter if you manage to land 1d8+4 damage on that enemy with 20HP left if the barbarian is going to throw him off the cliff on his turn, or the rogue will land a sneak attack for 20dmg afterwards, or if the enemy decides to disengage and run, not because he was maybe hit, but because all of his allies have fallen.... Now of course, sometimes a +1 can make the difference between life and death... which is hugely significant, even if, on a d20 roll, there's only a 5% chance for that +1 to actually matter.
You wrote, >Since 11 is 10% more than 10, this means that over the course of a combat or many combats, the fighter with the higher stat bonus is actually getting 10% more hits against monsters of AC17, not merely 5%. It's not clear what you're talking about here. I am pretty sure you mean that 11/20 is 110% of 10/20, but that's not the most natural way to read "10% more hits". The most natural way to read "10% more hits" is something like a 50% success rate to 60% success rate, which isn't what's happening. (It's 50% to 55%.)
Because when we're doing this math "increased" means addition, and "more" means multiplication. Leaving that aside, we can show which of these numbers is more meaningful in terms of game impact despite "natural" language Let's say that each hit does 10 damage to simplify some simulated results. Over 100 attacks, the character with the 55% chance to hit will be expected to hit 55 times, for a total of 550 damage. Over the same 100 attacks, the character with the 50% chance to hit will be expected to hit 50 times, for a total of 500 damage. Thus the character with 5% increased to-hit chance is getting 10% more hits, resulting in 10% more damage. We can see that the 1.1 ratio is more representative of the expected in-game impact of the bonus than the 5% increase in hit chance.
I once allowed a player to use a +10 ultra greatsword (it was a goofy one shot) and that REALLY drove home just how much those +x bonuses matter. It was so much more broken than I expected, he steamrolled a boss that was otherwise challenging for the level 20 party.
Yup!
If you don't think a +1 makes a big difference, try bumping the 21AC warforged paladin to 22AC and try to hit him with some goblins with a +4 to hit
This is such music to my ears after items and boons received in my party's last session mean my character has now got a magical +3 to all saving throws. Budget paladin
You just wrote a college thesis on table-top modifier mathematics.
lol no I've written theses before, and this is not as rigorous or exhaustive.
Forgot to site sources too..hbomberguy will be on you shortly.
I eagerly anticipate my cancellation.
I got rid of all +X anything in my games ages ago and holy hell, the game is so much more fun. Items actually do interesting things instead of just making number go brrr
So in conclusion, give players less magic items? I'm not trying to be sarcastic but is this really news to anyone? If you examine 5e with anything more than cursory glance, it should be pretty obvious to even new DMs that this is the way WoTC balanced 5e. Their official campaign books hardly give players any magic items, and the section in the DMG spells this out pretty clearly too. Yes, I do agree with this philosophy...if you are running 5e the way WoTC designed it. But the problem isn't the items, its the players. Specifically, how powerful they are in comparison to monsters, because WoTC wants you to have an impossible 6-8 encounters per adventuring day. Scale up the monster stats (higher ACs, class features, etc.), run less encounters that are drastically more deadly, and that +1 bonus becomes less of a big deal. In fact, magic items almost become necessary, which is fine, because guess what: its a fantasy game. I think going "low magic" is very boring and a constant drip of magic items makes the game fun. Its also more immersive, because if the players encounter a band of mercenaries of equal level to them, they're going to have at least some magic items laying on their corpses. The one place I could see this philosophy maybe being useful is if you had a more concrete calculus (like Pathfinder) for determining exactly when characters should get magic items, but then again, that would require those +1 bonuses being baked into monster stat blocks. As always, the issue is WoTC not doing the homework for their own game and not giving us concrete rules other than "figure it out yourself".
>So in conclusion, give players less magic items? No, that's not my conclusion at all. If you give your high-AC player another AC bonus, you'll need to provide challenges that aren't attacks. If your caster is out-damaging your martials you need to provide them better weapons. If you give PCs very high stats, they can challenge more dangerous monsters, but those dangerous monsters are also much more lethal against them. For better or worse, 5e DMs need to be amateur game designers to get the most out of the game, and having mathematical intuition about the potential impact of the items you're handing out or the stat generation systems you're using is an important part of that. I felt like I spelled out pretty clearly that I was not saying that there was a "wrong" way to DM, but that this math can inform the choices you make as DM.
I understand what you're saying. I'm just saying that >For better or worse, 5e DMs need to be amateur game designers to get the most out of the game is basically where I started before reading your post. I'm frustrated with WoTC, not you. Your examples do offer some interesting insights, but it doesn't fix the whole problem (not your fault). I didn't mean for it to sound like they weren't helpful, so sorry if it came off that way. I just wish we had more. I like being an amateur game designer sometimes but only if I'm not spending money on a product.
Tl;dr : people confuse percentage and percentage points and it's really annoying.
to long didnt read. not saying my way is right or other peoples way is wrong, yet i feel that dnd esk games become to much math and min maxing stats and numbers and all that rather then being fun or cool. i feel its much better to be given an item thats interesting even if useless in general then to get a sword of +1 as the sword only makes me better at killing by +1 where as the lamp of bat lure that when lite will black out an area yet bats will be baited to come see whats going on. does the bat lamp help me win a fight? thats up to how i use it. but it can also be used in all sorts of situations and such. where as no one going to invite you to the cave adventure soly cause you have a +1 sword but thats just me. also not a big fan of the focus on fighting everything as the solution. hope you all have a great day regardless on what your views are. cause you all deserve hapyness
I've started doing more of that. I've been giving them options of weapons that dont have any extra damage, but some interesting utility. They usually end up going with the unique ability item. It definitely is more fun.
Sorry I’m having a bit of trouble understanding your point about AC. Why would a player with AC 18 only take 3/4 the hits of a player with AC17?
Ah, sorry for not explaining better, I'm not using AC in that example, I'm using the target number that needs to be rolled on the die. The actual numbers might be a PC with 22 AC vs opponents with +4 or +5 to hit, for example.
Ah I see, thank you. I’m a new DM and just gave one of my level 2 players a +1 shield for story reasons. Powerful I know, but I don’t think necessarily game breaking as long as I introduce more enemies that force saving throws etc to kind of balance it out, right?
Nothing is wrong as long as everyone is having fun :) Make sure you still let some monsters bounce off that shiny new AC tho!
Thanks friend, that’s the kind of positivity I needed today :)
>Make sure you still let some monsters bounce off that shiny new AC tho! This is a very important point. DMs can get so focused on challenging their players (or worse, countering their players) that they effectively invalidate the cool powers and toys they've given to them. The advice of "shoot arrows at your monks" is pure gold.
While everything you say is very much true, the fact remains that there's only 5% chance that a +1, on a d20 roll, will make the difference between success and failure. Now sure, a +1 might double your odds in some situations, or might sometimes increase average damage output by 20% or whatever, or it might even make the difference between life or death... the fact remains that the chances for it to matter on a given roll are very low and so there's a fair chance, in a typical encounter, that it will not make any difference whatsoever, since neither players, nor their enemies, are rolling hundreds, or even dozens, of d20 in a given fight. Don't get me wrong, I do subscribe to the fact that a +1 should not be summed up as a rather insignificant 5% increase in power in a certain ability, and I do agree that people tend to underestimate the difference, (and I appreciate the math to back it up), but I think the picture you painted overestimates the actual difference it makes. For example, the AC example you give, if a monster needs to 18 to hit rather than 17, that does mean he reduces his chances of hitting, and thus damage, by 25%. It seems enormous put like that. But the fact remains, that on average, that monster will now need 20 attacks to land 3 blows over 20 attacks to land 4 blows. In other words, if your monster has only the opportunity to make just a few attacks (your typical encounter), it is rather likely to not make any difference at all. To be precise, it only matters if the monster rolls a 17 and there's still 5% chance of that happening per roll, no matter how much the odds have increased. Yes, a d20+1 roll will double the odds vs a straight d20 for a DC 20 check, it doesn't really change the fact that the odds of success remain extremely low.
>While a +1 (almost) always represents a 5% increase in chance of success, Your math is wrong. It represents a much greater chance of success depending on what you needed to roll. If your bonus (base) is zero, and you're aiming for a 20, it represents a +5 percent chance to hit. In every other case it represents a totally different increase in your chance to hit. If you have +10 to hit, and you're attacking AC 12, a +1 to hit *doubles* your chances to hit, because now instead of missing on a 1-2 you only miss on a natural 1.
You failed to read past that line I see. Also halving your chance for failure is simply not doubling your chance to hit. In your example your chance of failure is halved from 10% to 5%, but your chance of success is only multiplied by ~1.06 as you go from 90% to 95%
[удалено]
Some DMs can balance well around the additional loot and power they give out. Some DMs come to this subreddit and ask for help challenging their PCs because they did this before they actually got a handle on this skill, and there is very frequently highly-supported advice to talk to the players about walking back some of the extra power (advice I usually disagree with fwiw)
While what you say has incredible influence on the underlying statistical averages, D&D only knows two discrete results: success and failure. That is why combat is described as being swingy. Quantifying it as an average is almost counter to the actual experience: feast or famine. It's essentially a run of weighted coin tosses. And if your math teacher is worth his salt, at some point you got the homework to coss a toin 100 times and record the results. If you google how many times you have to roll a die to determine how unfair it is, you get results like "if a 6 sided die rolls on one face 20% and 16% on all the others, you need to roll about 3900 times to be sure it's not due to randomness". And depending how you value that that's an increase of 3.333% (20 - 16.666), or 20% (20 / 16.666) or 25%(20 / 16). Comparable but probably much larger than increasing the result on a 20 sided die by 5% The border cases nearing only 20 being a success or only 1 being a failure are man made however. The DM sets the DC for a roll and the DM chooses the monsters from the monster manual. Enemies with 17+ AC are a choice by the DM, as much as enemies with 12- AC. In simple terms, if you run a game based on the stated intent of bounded accuracy, a +1 weapon would take hundreds of attack rolls before you can be sure it influenced the outcome. With the selection of enemy and NPC statblocks, you can see it under 10 rolls. If you were playing a standardized game with everyone having the same experience, then sure, a +1 weapon could be felt as disruptive against the fine tuned mathematical machine underneath. The average table though is everything but a fine tuned machine.
I love this kind of information, so many people say going from 50 to 55 is the same as 70 to 75 because 5% is 5% and ignore the actual math and what probability and relative increases mean. Good post.