Dice Math | Running the Game
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- Опубликовано: 11 сен 2024
- Episode 48
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I know this video us four years old but I want you to know that this content is still incredibly helpful for new DMs everywhere. Thank you for these videos.
Yes!
"my powers are limited" sounds like something an omnipotent being would say tbh
“Advantage is a guarantee (and yes I know it’s not)”
*thinks of multiple times I’ve manage to roll 2 and 3 on an advantage roll*
Conversely, I witnessed a person roll two Nat 20s with Disadvantage (we were using a dice roller in chat, so I knew there was no shenanigans involved). It was glorious.
@@Draeckon one of my player was a halfling, and on roll 20, he rolled at disadvantage 2 natural 1s and as a halfling was able to reroll both of the die, he then proceeded to roll 2 natural 20s. There was about 5-10 seconds of shocked silence from the whole group. Took almost 10 minutes to get back on track afterwards lol
First Rule of D&D Math: Not every single +1 or +2 matters, but they add up insanely fast.
I actually rolled my D20s a hundred times when I bought them. Also, I have to say that Han Solo dislikes this video.
@@Dehalove unless your dice are made from cheese they'll be fine, the difference would be unfathomably tiny
Mmmm, cheese dice...
@@Dehalove I rolled them over a soft surface, much like a snooker table.
@@Dehalove how would that ruin the lifespan unless they get completely rounded which would take you like decades of rolling it's still going to be a die that's going to land one side up whether the edges are a little rounded or not as long as there's a flat surface for it to land on.
After many long years of XCOM, I have learned a very important lesson about percentages:
No matter how likely you are to hit your target, even a 100% chance to hit has a chance to miss.
Magister Ogamesh
If the game is really telling you it's a 100% chance to hit then either it's a miscommunication to the player due to rounding or it's a bug.
XCOM (especially Enemy Unknown/Enemy Within) works a little differently. The number shown to the player is only the basic hit% rounded, but there are some "hidden" modifiers that apply to that number. If my soldier hit three shots in a row for example, he will get a hidden -10% chance to hit.
So for example, your hit% after aim, cover, flanking and other bonuses is 99,6%, the player will be shown a 100% hit percentage. But now the soldier that is trying to hit his target already hit his last three shots in a row, therefore the hidden -10% bonus applies. So from 99,6%, your chances of hitting the target go down to 89,6%. Yet, the game still tells you it's 100%.
It's a misconception Firaxes fixed in XCOM2 but was part for so long in XCOM1.
Not to mention the hidden seed miss chance calculated at the start of every new file. There are times where, depending on the turn I take my shot, a 100% will show up as a 99% because it is destined to miss.
DM: I know the rules say a 20 always hits, but Jeff missed because he's a rookie. He also panicked.
A 20 may always hit but does it specify whom? lol
One of the things I'd like to point out in regards to math of combat game design, but something I'd hope wouldn't be a step too far for newer players, is a concept I've heard called "effective health." It's the relationship between what D&D calls hit points and armor class, and how they interact with each other. When a GM starts monkeying around with either, they really should understand how they synergize together, or else they might unwittingly be affecting their player's enjoyment.
There's generally two different "types" of monsters: big sacks of hp that are easy to hit, or annoyingly hard to hit miscreants that have relatively few hp. Big sacks of hp ideally give players a feeling of progression: if I keep attacking, eventually it's going to go down. Conversely, the harder to hit ones give that moment of exultation of finally swatting that annoying fly that refused to leave you alone because the player just has to hit the jackpot once.
These emotional reactions are key to understanding player psychology, but both monsters have similar effective health because on average, they will both take the same amount of actions to defeat despite having vastly different hit points and armor class.
It's when you start monkeying with these stats that it effects the player experience. Take that big bag of hp with an AC of 10, and you think to yourself "10 just isn't enough, let's make it 15 to add a challenge." As a GM, you have now effectively doubled the effective health of that big bag of hp against an unmodified roll, because half the rolls that would have hit before now miss and do no damage. This would have made what might have felt like a slow, but do-able, progression styled fight, into an annoying slog where even if a player hits, they might be asking if they are making any sort of meaningful impact.
That's not to say don't ever do that, but as a GM, if you go start monkeying with stats be prepared for outcomes that you didn't foresee. That said, making that big sack of hp harder to hit, while at the same time shamelessly stealing things like "bloodied" from 4th can make for a wonderful boss encounter. (Plug: go see Matt's video on stealing from 4th) This is because with numerous stages for the party to engage with, they are now rewarded for taking an active role similar to hitting that jackpot from before, while at the same time they aren't just killing the monster outright.
@solomani It depends on the players' hit chance, and it changes based on where their damage comes from. If they have guaranteed damage effects or spells that deal damage with saving throws, then armor class isn't providing effective damage reduction in those cases. However, we can derive a formula to give us an idea of ehp by assuming that all the damage will be dealt by attack rolls with the same bonus to hit, and ignoring critical hits. Let's have A = our monster's AC, B be our players' attack bonus, and h be our monster's stated hp.
Our monster's ehp is just it's hp divided by the odds of the player hitting; if it has 100 hp and they hit 50% of the time, they need to aim 200 damage (100/0.5) of attacks at it before it dies (on average). If they hit 25% of the time, they now need to point 400 damage of attacks at it (100/0.25). If they hit every attack, they only need to attack with 100 points of damage (100/1).
So for our formula, we just need to know the odds of an attack hitting. Well, how many numbers are there that hit? As Matt showed us in the video, it's 20 minus the smallest number we need to roll in order to hit, plus one. And the number we need to hit, is just the AC minus the attack bonus. So the total number of results on the die (each representing a 5% chance to hit) is 20-(A-B)+1=21+B-A. So our odds of hitting are 0.05(21+B-A).
That makes ehp=h/0.05(21+B-A). We can simplify a bit and get 20h/(21+B-A). Let's check that answer. As h goes up, the ehp goes up proportionally. Good. As the AC goes up, the denominator shrinks, increasing the ehp. Good. As the attack bonus goes up, the denominator increases, lowering the ehp. Good.
Tldr: The monster's effective hit points = (hit points * 20)/(21 + players' attack bonus - the monster's armor class)
Very useful comment, snapping HP into the AC conversation like putting legos together
"There was a time where this was not obvious to me." The core of all videos aimed at new players. Don't forget it y'all.
"The math is linear" nominally, but not when looking at real changes. The drop from 70% to 65% is not "five percent." It's a change of over 7%; this is to say they're now _missing_ over 7% of their attacks that *would have* hit.
Similarly, the change from 45% to 40% isn't five either. It's over 11%. It "feels" like a bigger change to the players because, in real terms, it is. Every incremental drop is disproportionately bigger than the last one.
It's easier to see why when thinking smaller; the to-hit chance reduction from a 10% to 5% is a reduction by *50%!*
Ahh, thank you. I just posted this.
The example gets a lot clearer if you take the numbers to the extremes. 10% to 5% means twice as many misses. That's far more than a poultry 7% gain.
So thanks again for spelling out how the math really isn't linear and that's why it doesn't feel like it is.
Per 20 rolls against that specific target, sure. Y'all are correct that there's a difference between increasing to a percentage and increasing by a percentage, but the way you're interpreting/presenting it as it applies to this situation is incorrect.
Not quite twice as many misses, half as many hits
An unintended consequence of changing the flanking bonus to +2 is that now it's a flat modifier, which can stack with other modifiers, as well as sources of advantage.
It would only work that way if you rule it that way. I still wouldn't allow multiple sources of advantage to stack. That it's now a +2 doesn't matter to me, it's still advantage.
@@Draeckon You can't stack advantage. By using +2 instead of advantage it can stack. He didn't mean it would stack with multiple flankers.
As far as I cant tell you cant get multiple flank bonuses. Even if someone could make an argument for two +2 flank bonuses on one attack it would still be only +4. Using Advantage for Flanking is about +5 AND twice the chance of a natural 20 which is much more potent than +4 and only one die roll chance at a natural 20.
Matt,
If you want to mess with your players' psychology, sit behind your DM screen petting your cat.
This works even better if you don't even own a cat.
I think the psychological effect of the roll result is the most important part of this video. The math is "fun", but at the end of the day, it's about whether players have a good time at the table.
Due my dyslexia, i found your channel. With my dyscalculia, this helps thing be less like spaghetti.
I play two one shoots ages ago, now i am a DM. I think its working.
I love Matt’s love for his kitty
You can calculate the average result on any die by adding the highest and lowest numbers and dividing by 2.
ex. d12. 1 + 12 = 13, 13/2 = 6.5
for a more universal formula, you can calculate the average of multiple dice in the same roll by taking the max roll (number of dice times number of sides), add the number of dice rolled and divide the total by 2.
Example: A 3rd level fireball deals 8d6 damage. (8 * 6 + 8) / 2 = 28 and that's the formula you can use. If you see 8d6 as XdY, where x is number of dice and y is numer of sides on the dice, then the formula become (X * Y + X) / 2.
This formula is also usable for a single dice like your 1d12. (1 * 12 + 1) / 2 = 6.5. With one dice it's merely simplified because multiplying the number of dice (1) makes no difference.
The wording you used is good to remember. After all, the lowest number you can get also often equals the number of dice you're rolling. (Max roll + Min roll) / 2. Thinking of it that way might also make it easier for you when calculating the average on damage rolls where you can reroll 1s and 2s because suddenly, the minimum you can roll is higher than the number of dice you're rolling.
If you have multiple types of dice, you calculate the average of each type of die separately, add them up and divide the total by 2. Example: A paladin with a greatsword (2d6) adds a 1st level smite (2d8). Average of 2d6 is 7. Average of 2d8 is 9. average of 9 and 8 is 8.5
This is especially useful when rolling multiple dice. Like PPH explained with 8d6 the minimum roll is 8, the maximum is 48, and the average is (48 + 8) / 2 = 28. (I think 25 was a typo).
Wylliam Judd
It is worth noting however that the distribution of results is very different between single and multiple dice situations, 1D20 has a totally flat probability curve but 5D4 presents a far more shapely figure.
Yes that's very true, and yet using the minimum and maximum still (kind of amazingly if you ask me) holds true!
Want to know the odds of some really weird roll and don't feel like calculating it, and also be able to compare it with graphs and everything? I've always been using www.anydice.com for that, really recommended. It also shows that doing an advantage roll more comes down to about +3, not +5 by inputting "output [highest 1 of 2d20]" and putting "output 1d20" in the next line to compare. Try it out!
Short video = 25 minutes, gotta love him :P I love catching the videos fresh out of the upload
The patented "Colville short".
He even laughed a little as he said "short video"
@@sauceinmyface9302
n.y
54c ⁰⁰
In 25 minutes, Matt Colville and D&D taught me more about probability and statistics than an actual college course on probability and statistic did in an entire semester.
5% of getting a nat 20 unless you're percy
T M you're*
my bad :P
or if you're Will Friedle :P
I still remember that one fight at Entropis..."let's spend a grit, critical, regain grit, action surge, use grit, kill, regain grit..."
Unless my percy what?
Going from 65% to 60% is a 8% reduction ((65 - 60) / 65 = ~.077) whereas going from 45% to 40% is an 11% reduction in the chance to hit.(EDIT: explanation at the bottom) So it's not just a psychological effect, it is still mathematical. Though, for new DMs, this probably isn't the type of math they should be worrying about. I would recommend that both players and DMs who want to take D&D more seriously should learn basic statistics. Not only will certain things make more sense, it should help save time in game so that people aren't constantly explaining things to each other.
Great video Matt, as always :)
EDIT: I'm bad at writing comments that make sense at 1AM. As an example, going from a 100% chance to hit to 95% chance to hit means that your players will be hitting 5% less then they would have, versus from a 10% chance to 5% means your players are going to be hitting 50% less then they would have before the reduction. I should have said that 65% to 60% is an ~8% reduction in the NUMBER OF HITS rather than the chance. Yeah, 65% to 60% is a 5% reduction in chance, because the world has to make sense.
YoinkinatorX Hey there! Great that you are loving Matt as I do. Since I have no time, I will answer to this post later on. Your math, sadly, is flawed since you say that you should know about statistics, I hope you can find the mistake on your own until I can answer. Have a good day, mate!
60% is always 5% less than 65% because of the %. Percent means out of a hundred so they both have a 100 as the denominator. 60 is 8% less than 65 but 60% isn't 8% less than 65%
There is a difference between a *percentage* increase and a *percentage point* increase. Going from a 5% chance to hit to a 10% chance is a 5 percentage point increase, but it is also a 100 percent increase because you are now twice as likely to hit as you were before. Your odds have increased by a 100% but they have not increased to a 100%. So your odds have doubled, even if statistically speaking they are still poor.
Percentages indicates ratios, while percentage points indicate the arithmetic difference in two percentages.
If I have a monster who needs ~5 hits to kill, the main question is, how many attacks does he get before he dies?
So percentage IS the important thing. Moving a 40% chance to hit down to a 30% chance to hit is HUGE, because it means my bad guy gets to live 40/30=1.33x as long, and get 1.33x as many attacks. That's what's relevant.
Exactly, you got the point. Matt's explanation was a little misleading when he just used the word percentage. I know that your comment was supposedly written to show that I'm wrong, I only wanted to state that you can't simply use one view on the situation.
The chances to roll a 14 or higher out of twenty is 7/20. The chance to roll a 13 out of 20 is 8/20, an additional 1/20 which can be seen as 5% (percent points). Considering that you do a Laplace experiment, it is ok to say your chances increase/decrease by 5% or 1/20. Nevertheless, you are right too since the other way to look at it, is the previous chance in comparison to the new chance, hence the difference between percentage and percent points.
If you are looking at a situation where you have a simple fail/win condition (here: rolling a specific number) it makes more sense to use percentage points. If you rolled with advantage and get a 1 and a 2, neither of those are going to hit even if the 2 if 100% should mean the you "accumulated" the maximum amount of something which you did not.
Just regard it as an urn experiment. 13 yellow balls and 7 green balls. 14 yellow balls, 6 green balls. Just describe it with fractions for a better understanding and a closer mathematical description of the dice object.
It's been a long time since I did this in school. We don't do statistics as mechanical engineers in Germany since that is covered in High School. So, bare with me if I made a mistake here.
I live my life 5% increments at a time.
Underrated comment. I guess the intersection of D&D fans and 'Fast and the Furious' fans is low.
"This video is for new players who know nothing about math"
*has been playing D&D for a couple years*
*is literally pursuing a degree in Mathematics*
*watches video*
I probably qualified for a math degree and I still watched the video ;)
Super helpful for me that he points out that a +1 change is going to be the difference between a hit and a miss maybe once per night.
If it's for the whole party, then a +1 is maybe once per fight.
Could I do that myself? Yes. But I didn't.
A true lifelong learner right there ;)
Been Playing for a few years
has CS Degree
Still rolls dice to see which ones "feel good"
heh, yep. im doing programming and watching this video. although i have only been playing for about a year and a half. it actually brought up a heap of stuff i never thought about.
although he was wrong about the advantage +5... the average roll for d20 with advantage is 13.825
Maaaaaaath...Kitty!...Maaaaaaath
I'm so happy to see that cat.
I feel like he would be perfect James Bond villain with the cat
i think all of matt's videos are "short" at 25-30 min. love it
Matt, thank you for this video series! There is a ton of great advice, and your presentation is exceptional.
Just wanted to point out that your "advantage equals +5" is a slight overestimation. The average straight-20 roll is 10.5 (which you mentioned, I believe). The average advantage roll is 13.825 (probably could calculate this with math, but I just used a spreadsheet formula to add columns). I think that the reason for this disparity is that if the second roll is equal, then it does not contribute to the result.
This equates to an advantage of +3.325, or a +16.625% chance to hit.
1+1+2+1? No, it was 1+2+2+1, which means the gun is empty! BANG!
"...That means if I roll a die a hundred times about 5 times I'll roll a natural 20."
Unless you're Percy
Seth Williams Or Wil Wheaton
Had to reread it five times because of that misplaced comma.
Mr Knarf oops
haha, Wheaton rolls natural 1s though,
i actually want to know if he has a weighted die for the purpose of rolling horribly
Matt, this video was super useful. I'd never thought of D&D in 5%'s and how "broken" advantage can become.
Thank you
I've taken two college level statistic class and I still learned new thing.
The math showing what Matt was communicating.
The higher your AC, the greater the difference each additional +1 AC makes.
Die %Success %differential
1 95%
2 95% 0%
3 90% 5.3%
4 85% 5.6%
5 80% 5.9%
6 75% 6.3%
7 70% 6.7%
8 65% 7.1%
9 60% 7.7%
10 55% 8.3%
11 50% 9.1%
12 45% 10%
13 40% 11%
14 35% 12%
15 30% 14%
16 25% 17%
17 20% 20%
18 15% 25%
19 10% 33%
20 5% 50%
Die: represents the die result needed to hit a particular AC.
%Success: is the probability of rolling that result or higher on a d20.
%differential: is the change in probability of hitting an AC needing that result vs. the AC being 1 lower. It also represents the change in average damage taken (per attack, per round, per minute, ...). At low AC's an additional +1 will average about 6% less damage taken, about 10% at middling AC, and can cut your damage taken in half at the highest AC levels (this is ignoring bonus damage from crits. which can be highly variable and difficult to represent, the table is still relatively close even if you were to guesstimate typical bonus damage).
I gave my ghouls a breath weapon. It is a fifteen foot cone of noxious gas that they spray from their mouths that in essence has the same effect as their claw attacks and deals necrotic damage. For lower to mid level parties I use relatively few of these creatures and give them either the breath weapon or the claws. However to keep ghouls scary at higher levels and give some more variety, fighting ghouls with both abilities, I have found, works pretty well to create a dramatic and surprising encounter.
I see Legend of Drizzt in the background, I look at my shelf, I see Legend of Drizzt in my background. *feels good*
This video implicitly explained to me why D&D feels easier to balance than many other tabletop RPG systems. The statistics of single die rolls and modifiers are pretty simple. As soon as you roll more than one die, the behavior will be harder to grasp intuitively, and if there are exploding dice, you need algebra to find averages.
I am pretty good at guessing where ACs should be. 16 to 17 will be bosses, 13 to 14 is toughy goons, and 11 to 12 for minions. Every time their proficiency goes up or ability score increase, I bump these numbers by 1 or 2. Worked out so far.
You can more easily get the average of a die. Instead of adding all the numbers, just add the lowest and the highest then divide by two. So a d20 would be
1 + 20=21
21 / 2 = 10.5
Your average for a d20 is 10.5
Everyone please note this only works for dice and not usual sets of numbers
MusketPenguin that is why I specified for a die.
Our dm took this to heart. We have ran from so many enemies
Gotta love Matthew Colville, man does a "short" video clocking in 25:58, and speaks fast enough to get over an hour worth of information.
Excellent video but i just want to note:
Advantage does not always give +5 bonus, furthermore +5 is the highest bonus and it's not so likely.
Advantage bonus is +5 *ONLY* if you need 11 after bonuses.
quick math:
11 - 25% bonus = +5 exactly
10, 12 - 24.75% = almost +5 but lower
13,9 - 24% = almost +5 but lower
14, 8 - 22.75% = close to +5 but lower
15, 7 - 21% = almost +4 but higher
16, 6 - 18.75 = close to +4 but lower
17, 5 - 0.16 = almost +3 but higher
18, 4 - 12.75 close to +3 but lower
19, 3 - 0.09 close to +2 but lower
20, 2 - 0.0475 practically +1
conclusion:
If after bonuses you need 14-8 to hit than it is or very close to +5, else it's lower.
Yes, more Colville!
I clicked so fast even the thumbnail wasn't loaded!
What I love most about Matt Colville compared to other DMing channels is that he uses his videos as a method to tell an informative story, rather than a checklist. Thanks for putting all the work you do into your videos.
Being a math person first this was pretty awesome, and also accurate, probability is great. Was amazing to learn how math can be used for fun.
I have always been big on math, statistics and probability, so I find this kind of stuff fascinating. I have so many spreadsheets I've written dedicated to probabilities of things like roll xdx take highest/lowest, effects of re-rolls, effects of advantage/disadvantage, probability distributions, expected values, effects of "exploding dice" (roll a value and gain another die to roll) and other various dice mechanics. I love this stuff.
I was nodding my head madly at Matt's comments about using the flanking rule - biggest mistake I think I allowed in my current game. Next time I start a new campaign I'm not including it (as much as some of my players won't be happy).
Joel McKinnon Agreed. As a Pathfinder player I assumed flanking= +2 to hit. When he said that flanking gave advantage, I was like whoooooa wait up that's... That's not fair. +2 to hit is a good bonus, though.
I briefly tried the facing rule in a one shot at the weekend, it's really no better, although obviously, only one person can gain an advantage this way, rather than all flaking attackers, so it's probably better in that sense.
The issue I had with facing is how silly it feels in combat when people are constantly circling around each other, and depending on the turn order it felt really arbitrary for who benefited and who suffered for it (as you can literally take turns on who's behind the target for their turn if you move to the side again after you attack, and there is no penalty for dancing around the target, as long as you don't leave the area they threaten).
Like you, I'll probably go back to no flanking, or use Matt's 1d4 system.
Flanking is just a popular house rule in 5e, there's no written basis for it in 5e material. Modify it how you want. I personally like using it to punish players that rush in and get surrounded, and to reward players that focus targets.
I use a homebrew flanking rule in our D&D sessions: a d4 "flanking die," which I have the players role and add to the attack roll if they are in a tactical flanking position. It is less likely to hit than Advantage (as Matt mentioned, a statistical +5), and operates similarly to a Bard's Inspiration die given to a PC. But it allows the players a tactical way to gain that extra d4 when they work together.
Perhaps limit it to rogues only so they can get more sneak attacks?
I did the math on the advantage, and it is actually *at best* a +5. Sometimes, it is less than a +1. The more you are in the "swing zone" -- that is, you need around an 11 to hit, which is basically a coin flip -- the more effect advantage has. However, if you only need to not get a 1 or you need to get a 20, then the effect is only a 4.75% point change. Need to not get a 1 goes from a 95% chance to a 99.75% chance, and needing a 20 goes from a 5% chance to a 9.75% chance. Advantage is actually a roughly +3 effect, assuming all possibilities are likely to come up equally. As you said at the beginning of the video, however, players are most likely going to need about a 7 to hit. With advantage, the chances of getting a 7 go from 70% chance to a 91% chance -- roughly a +4 increase.
I actually really like this, because it means that people with reliable skill and people with no skill can only get so much value out of advantage. Someone who is really good doesn't need it, and someone who is really bad wouldn't know how to capitalize on it. But people who have a decent amount of understanding of something, but not the practiced expertise of someone who is really good, can really benefit from that advantage and know how to exploit it.
AC 13 Super Ghoul.
Beware, the Ghoul with a ONE Higher AC!
Working in the casinos gives you a good sense of odds as well. I had an argument with the an engineer about odds in a game. We were playing Avalon, and she could not believe that this one player was always the good guy, especially after 5 games. She said "mathematically he should have been the bad guy once by now!" I tried explaining to her how the odds reset every single game, but she wouldn't have it. It's like Roulette, I could spin the same number 5 times in a row, or I could not spin it all day long. The odds always reset.
It should be noted that humans are biased to remember failures with twice as much gravity as successes.
So, if it's a 60% chance to fail and 40% to succeed, your players will experience it as 12 to 4 rather than 6 to 4. Or 3 to 1 rather than 3 to 2.
50/50; 2 failures to 1 success rather than 2 to 2.
40/60; feels like 8 failures to 6, rather than 4 failures to 6.
35/65; feels like 14 failures to 13, rather than 7 to 13.
30/70; feels like 6 failures to 7, rather than 3 to 6.
25/75; feels like 10 failures to 15 successes, rather than 5 failures to 15.
As you can see above, 70% success _feels_ like ~50/50. Actual 50/50 _feels_ like ~66/33.
This is why Gygax recommended that a 75% success feels like you are proficient. By these calculations, that feels like 60% success. 70% and 65% feel like more or less 50%. Dip below that and it starts feeling like you're losing more than winning.
Keep into account that an armored zombie that is hard to hit, but also barely hits the players will feel different from an unarmored ghoul that hits players often. The latter feels like a priority threat, the former feels like a fairly predictable obstacle.
This can change if the unarmored zombie consistently tries to activate a trap. Now, it feels like it's succeeding a lot more than it's failing, because it only failures for as often as it is hit, as opposed to hitting.
This is a good way of changing the perception of the same enemy's threat without even changing the numbers.
"This is why Gygax recommended that a 75% success feels like you are proficient." - Can you please tell me where he said that?
Thanks!
I don't remember precisely anymore. I wish I had stored it. I was paraphrasing anyhow, but I remember that either 75% or 70% success rate felt the best. I've been using that benchmark ever since.
In the version of D&D that me and my brother run (which is entirely homebrew rules so there are some other key differences which affect this) we have flanking grant the following bonus: the target getting attacked has all non-armour based armour class reduced to 1. This has worked pretty well for us so far because it means that a flank basically removes the ability to dodge and avoid damage from the PC, but if they're heavily armoured they will still have that bonus.
In the last election when they said Hillary had a 75% chance of winning my response was "I've rolled far too many 4-sided dice to count on that."
For my own D&D inspired game, I use +1 to AC rolls for each engaged ally* adjacent to the target. Because I use hexagon maps for overworld, and square maps for towns and dungeons, this stacks up to either +25% or +15%, but requires much more coordination or sheer numbers to accomplish.
* "Ally" is used loosely in this context. Anyone is considered an ally for the AC bonus as long as they are against the target, even if they are also against the attacker. It is thus possible for the same character to grant AC bonus to *both* sides, so long as all three factions are actively fighting one another. After all, a sword coming at you does not become less distracting just because the other attacker does not like the person that swung the sword.
As an aside: I recommend considering a combination of hexagon and square maps in any applicable D&D-style game. Hexagon maps offer a more "open" feel to combat, allowing more opportunities to maneuver and flee if necessary. Square maps, on the other hand, work wonders for setting up towns and dungeons with more natural-feeling roads and corridors, and makes creating choke-points, traps and designated escape routes easier. If you add in a system like my +1 to AC for each surrounding ally, you also make the way PCs (and mobs) behave in combat vary simply based on terrain. Expect more body-blocking in square maps and more tactical retreats in hexagon maps!
Hey Matt, I don't remember if you've said this before, but next time you mention that you're only going send the us one email in regards to the Stronghold stuff, you should also mention that you aren't going to sell the email to advertisers and whathaveyou. As always, well wishes and thank you for all of your work!
one point, Matt, You say that a +1 weapon provides the same bonus (+5%) whether the monster has an AC of 12 or 16, and that is certainly true, from a certain perspective; However, from the perspective of the player, a 5% bonus to the chance of hitting AC 12 corresponds to a 5/70 = ~7% increase in the expected amount of hits, while the same bonus against AC 16 corresponds to a 5/50= 10% increase in the expected amount of hits (rises to ~14 % at AC 19, 20 % at AC 21 and 100 % at AC 25). So the harder a monster is to hit, the more a +1 bonus increases the amount of hits a player will get in
Five minutes since it was posted, always perfectly timed.
Super important in the bug bear discussion: while every +1 to hit or AC influences the rolls by +-5%, this 5% is, as Matt has pointed out, additive. A battle against someone with AC 10 and the attacker has no bonuses, chance to hit is 55% (10 or higher hits, 20-19 = 11, 11*5% = 55%).
The important part is seeing how this plays out in relative terms. Meaning, how much increase/decrease in hit chance have you had relative to before? Example: You start with having 25% hit chance against the enemy. That would be an AC 16 enemy against someone with no bonuses (16/17/18/19/20 all hit, meaning 5*5% chance = 25%).
If you now instead have a bonus of +5 to hit, your hit chance goes from 25% to 50%. But this means, you doubled your actual chance to hit, so you will see a 100% aDPR increase. These relative changes are important, if you change the numbers, a small absolute increase can be a giant relative increase.
If you balance a monster (in an extreme case) to only have a 5% chance of being hit, changing the bonuses by 1 will basically make it much more weaker then expected, since the players will hit is twice as often. That's why ACs and Bonuses to hit basically scale linearly, because the hit chance should always be somewhere around 60-75% to not be frustrating.
Where I realized this most was in Path of Exiles critical strike system. Most skill actually have a lot of DnD inspiration, so most skills have a base crit chance of 5%. Some have 6% and a very few have 7%.
Now, most of the bonuses you get are multiplicative, meaning if you get a stat "+100% Critical Strike chance" means, you go from 5% to 10%. That is why a base crit increase of +1% if often more valuable than a "+100% increase Critical Strike chance", depending on how much you already have. If you already have +1000% crit strike chance, you are at 55% Crit chance. Another +100% will get you to 60%, but if you increase your base crit chance by +1%, instead you land at 66% crit chance.
To the point of advantage, this is where the maths get a bit trickier than simply adding numbers. Most DMs already know, that a d12 and 2d6 is different. The more dies you have, the more spiked the distribution gets around the average of those rolls. There is a reason, why the Bandit is on a 7 in Settlers of Catan. It's the most likely number to come up, linearly decreasing to both sides. 1 die as an absolute flat distribution, 100d2 have a very stark bell shape.
For any one interested in a more exploration, I suggest anydice.com
There you can plug in a number of scenarios and you get a comprehesive distribution curve.
That's how I found out, that my SorLock had, with Hexblades curse 19-crit and Elven Accuracy a 27% chance to crit on each attack - not HIT, but crit.
Best way to understand the chance to lose in high percentages. Play XCOM. A 70% is not a sure thing. A 70% in XCOM, seems like a 50%. You begin to doubt 99% chances.. You can't even trust 100% chances (It rounds up), even that 0.4% to miss counts.
I’m a player, maybe soon DM, and there’s one thing I wish at least one of my DMs had done to tweak the psychology of misses: Assume character competence. “The ranger’s arrow is deflected off the bandit’s armour,” or “the bandit sees you drawing your bow at the last second and dodges your shot,” not “the arrow lands somewhere in the next postal code.”
At least then the frustration of the miss is tempered into “damn, these guys are tough” as opposed to “damn, I suck at this.”
*sigh You know your fanbase so well. Around the three minute mark I was about to stop watching since there didn't seem to be anything new here, but since you call me out on that, I'll watch the rest of the video.
Although I usually like Matt Colville things, I believe this is one heck of a case of spherical goblins in a vacuum.
There is nothing wrong in have monsters with high AC, as long as it is intuitive enough to the players to know that, and have options to deal with it.
For example, having a turtle formation of lizardfolk has a lot of mileage in a fight: first line of defensive position and half cover (AC 17 plus disadvantage), back lines with three quarters and full cover, and pikes. Players see now the turtle formation, the high AC and nearly impossible AOE effects as a tactical puzzle more than a straightforward dice throwing. Fighters, in this scenario, will be more likely to use Athletics to disrupt the formation via shoves or attempt disarms, and rogues and monks will try to use their mobility and nimbleness to circumvent the formation. This leads to risky positioning and hard battle thinking. Sometimes, event to retreat, regroup, and other types of actions. When they do think a way to defeat such challenge, they will feel rewarded.
What players do not like isn't don't hit. What they don't like is feeling like they have no options, and their actions have no meaning. A battle that can only be won by slowly sapping HP is a slog, to either a wizard or a fighter. High AC is like every challenge met by the players: an obstacle to overcome.
While the whole video was helpful, sincerely helpful because the math bits have always given me the brain worms, the real thing I took away was the, "I roll to hit, I miss, and my entire turn was 30 seconds. That's incredibly frustrating!"
My current party is 9 people, so combat is a chore that I try to streamline by delegating tasks. I think in my case, I'll have to make sure the AC is in the 55% and above range and just inflate the hit points if need be.
Also, kitttyyyyyy. 💙
Flanking + advantage in the case of flanking granting +2, only actually boosts the chance to hit by 7% compared to normal advantage, however a disadvantaged player gains the most by flanking, cause that +2 raises there chance to hit by 13%
Hell. I was just about to do homework
dont worry this video has math in it its fine.
🤔
SUPER-crucial information! Ran a campaign for three years and did not know this information! For us mathematically-challenged people, this video is a lifesaver.
I recently began prepping a Halloween-themed game for the impending holiday and have been constructing a balanced yet challenging series of fights in our first ever 5e game (we are 4e players) and have been lurking the Reddit boards and the like to better understand the math itself as the greatest ally, and enemy, you'll ever have is the die in your hand.
I calculated all the probabilities through division, but the fact that you can literally deal in 5s the whole time is even better. Keep up the great work, Matt, and know no matter what the views may say, for many of us you're our first stop on RUclips as often as a player hits with Advantage.
"It's gonna be a short video."
I am not a math person so I have to say, Matt you REALLY opened my eyes. As a GM I never considered the math, I've always just "winged it". Now I understand how to adjust how challenging (or not challenging) a monster can be.
How many times has Matt said "This is gonna be a short video"?
25 minutes later...
Jesus Christ..."new Dungeon Masters who know nothing about math"...this video was genuinely designed for me, and what's even stranger is that I'll run my first game ever this weekend. Really needed this video, Matt. Thanks.
Reverse maths.
Jacob Malone you mean subtraction?
It is CR meme
shtam
Here’s the gem: +1AC means one additional miss per encounter. Brilliant!
I’m an engineer with multiple decades experience playing DND. I’ve spent a silly number of hours calculating complex probabilities of multiple rolls of multiple dice. Somehow I missed this simple distillation of THAC0. Super useful. Thank you.
Hey Mr.Matt. I love your content, but when do you sleep?? It seems like your always active on social media, and the like.
That One Guy he prescribes to the matt mercer school of thought on working. Say yes to everything you can, worry about sleep later
Oh okay. Thanks
Your comment about waiting 20 minutes for your turn in a party of 6, rolling 1 die, missing, and then having to wait again after spending 30 whole seconds strikes home hella hard man. That sums up my current group all too well. 6 players, I pre roll for my character, a fighter, so even if I hit, I just can say whether or not I hit and how much damage I do, then it's back to not paying attention while our terrible wizard player looks up her spells on her turn, making everyone wait, because she can't be bothered to pay attention. Year long campaign at this point, each session a slog.
Fun fact: odds of rolling a 20 with advantage is slightly less than 10 percent
Odds of NOT rolling a 20 = .95
Odds of a NOT rolling a 20 twice in a row = (.95 * .95) = .9025
Odds of rolling at least one 20 in two die rolls = (1 - .9025) = .0975 = 9.75 percent
Odds of rolling a 1 with advantage = (.05 * .05) = .0025 = (1/400)
Some dice just suck
Eli Feliciano this is a two year old comment so I have no idea why I’m responding other than a need to correct your math, but the odds of rolling at least one natural 20 with advantage is exactly 10%. What you did was the math representing the odds of rolling exactly one natural 20 with advantage and the missing .25% is the chance of rolling both as natural 20’s.
On the range of 50% to hit vs 40%to hit.
This is a more intuitive way to see it: if the monster is 50%to hit, that means that on average you need to make 2 attacks in order to score a hit.
If the monster is 40% to hit it is more like you must make 2.5 attacks in order to hit once.
So you basically made the number of attacks required to hit enough times to bring the monster down, 25% higher.
If you're Wil Wheaton the AC doesn't matter unless the AC is 1
JohnnyBoy even then you auto miss on wil Wheaton dice. Nat 1s auto miss. Even a negative ac wil will still miss
Such a good point right before 11:00! It could be better for player "feelings" to have many, easy to hit monsters, vs. few, hard to hit, monsters. The math might work out the same, but for theme/feel (heroic vs. gritty), it makes sense to have things that the heroes can destroy (but still have a challenge overcoming) instead of something that they could defeat "if only they could hit it." The math might be the same, but it could make all the difference to the feel of the encounter.
Great video as allways, but I do have a single comment. The difference between going from ac 7 to 8 is not the same as going from 17 to 18. The more AC you have, the better 1 more becomes. if a super high AC taget requires a roll of 19 to hit, and you raise the AC by 1. the number of hits required to kill the target have now doubled from that +1 ac. So it isn't just player psychology.
Quick math to do to work out accuracy. 21-AC+Hit Bonus and multiply that by 5 and you get your %. It's the same thing for a DC saving throw 21-DC+Saving Throw. If you want either in a fraction divide by 20 instead of multiply by 5.
posted 7 minutes ago, 25 minutes video, 26 likes, I like to see that I'm not the only one liking before watching
We don't need to know what Matt has to say. We just need to know that Matt is going to say it to us.
You can also start with the hit chance that you want. 3 simple steps:
Step 1. Pick a hit chance. Say, 65%.
Step 2. Divide that by 5, you get 13. That means the PCs should hit on an 8 or higher (8 to 20 = 13 die faces).
Step 3. Add the PC's to-hit bonus. Say, +7. So 8 + 7 = 15. That's the AC you want.
Armor class is NOT linear. Imagine you only hit on a 20(5%). Then you get a +1 sword, now you can hit on a 19 or 20(10%)! You just doubled your chance to hit!
Conversely, if you hit on anything more than a 2(85%), then find a +1 sword, changing than to everything more than a 3(90%) is not as significant.
gerbster14 That's not what linearity means. Every +1 is a 5% chance to hit. That's linear. And always equally significant. Going from 5% to 10% is, yes, technically doubling your odds, but that doesn't mean you are gaining more of an added chance to hit than going from missing on a 2 to only missing on a 1. Either way, you have increased your chance to hit by 5%.
Thus, linear.
A non-linear growth would be in games where you roll multiple dice with a TN per die, like Shadowrun or White Wolf's story teller system. In these systems, more dice move you toward a more stable bell curve, but each die doesn't give you the same increase in your chance of success. Going from 1 to 2 dice is significant, but going from 20 to 22 dice mostly matters in stabilizing your rolls and eliminating disadvantageous outliers rather than actually improving your rolls.
I.E. Adding a die has diminishing returns, and, therefore, isn't linear. Adding +1 in a D20 system is neither diminishing nor increasing returns, and therefore is (outside of fringe cases where you already hit on everything but a 1 or miss on everything but a 20, where +1 gives no advantage, but 5ed has mostly eliminated those edge cases by design)
Sure, I guess linearly significant is a better way to say it. A 5% increase does not always have the same significance or value. For example, if you could choose would you rather increase your attack by 1, chance to hit from 5% to 10% (doubling your DPS) or increase your armor class from 4 to 5?
That is not really true if you look at it as "how long will this monster live". Lets say to begin with you only hit on a 20. This monster has tons of armor and is very tough to hit. The monster lives 50 rounds in that scenario. Get a +1 sword. Now you hit on a 19-20. Suddenly the monster only lives 25 rounds. That is a MASSIVE DIFFERENCE. That +1 bonus just reduced the monsters expected life by 25 rounds.
Whereas if you hit on a 3 or higher the monster will live (lets say) 3 rounds. Get a +1 sword so that now you hit on a 2 or higher. The monster still lives 3 rounds. The difference is minor.
Both of those scenarios are talking about just a +1 bonus, but the difference in how they influence the outcome of a fight is huge. Of course it is at the most noticeable ends of the spectrum where the example is obvious, but the premise still holds up when talking about differences in the more middling numbers like 25%-30% vs 75%-80%.
Advantage is actually (on average) +3.25. The average roll is actually 13.825, but since the average roll for 1d20 is 10.5, 13.825 - 10.5 = 3.25... And DOUBLE ADVANTAGE (rolling 3d20 and taking the highest) would be +4.9875. But I can kinda see why +-5 is used instead of +-3... if you would normally need to roll anywhere near the average on the 1d20 (like between 5 - 15), then +5 is closer to the real statistical improvement -- because of the way the probabilities are skewed across target number ranges. For example if you need to roll a 20 to hit, then advantage is EXACTLY equivalent to a +1 bonus (and double advantage is the same as +2). So, the advantage mechanic is great at making easy and moderately difficult rolls a LOT easier. I do like flanking when using grid combat because combat will be so slow anyways when using a grid, adding one more rule to it won't affect the speed much.
I still don't quite know how advantage equates to a +5 bonus, to be quite honest.
Can someone in the comments explain that like I'm 5?
John van Capel I think that's wrong actually. I don't know how knowledgeable Matt is about math (I certainly ain't no expert on the matter), but it looks like he got it won't for some reason. I'm part of a game Dev study group in my University and some guys from a DnD study team there have assessed the medium impact of advantage as being a completely different % to what Matt says. And those guys are actual mathematicians.
What I believe he might have gotten wrong is that he thought that the medium impact would be equal to the impact at the medium chance when you roll a d20, instead of the sum of all chances divided by the sum of the number of posible outcomes. If you need to roll a 10 or 11, advantage DOES equal ROUGHLY a +5. But if you need to roll a 2 or above, advantage equals about a +1 (a tiny bit less than that actually, it equals exactly a +4.75%). Your chance of success would be of 99.75%. If you need to roll a 20, it also equals roughly a +1, and your chances go from 5% to 9.75%.
The graph for those chances of you calculate all of them is a bell curve with its peak around 25%.
So what really happens is that 25% is not the average bonus advantage gives, it's the maximum bonus advantage gives. The average bonus should be closer to half of that, probably something between 13 and 14%.
25% is not the average bonus, but the bonus at the average.
I'll risk it's because the standard bonus in the video is 5.
You get literally another roll, so you double your odds, basic probability speaking.
It doesn't actually equate to +5. On average it is more like +3.5. But in order to keep this simple, consider that you normally have a +5 bonus to hit and that you want to get 15 or higher, meaning that you want to roll 10 or higher on your d20. Normally the probability is (20-10+1)/20=11/20=55%. Now consider doing this with advantage, you roll two d20s and you look if any of those two has a 10 or higher. The probability is now (11*20+9*11)/(20*20)=80%. When you split the difference in chunks of 5% then it is (80%-55%)/5% = 25%/5% = 5 such chunks, therefore we get that +5 bonus. Hope this helps! :)
As can be seen here in this link to the github page of those dudes I mentioned, the medium of a dice with advantage is 13.825.
github.com/uspgamedev/rpg-systems/blob/master/advantage.md
The medium of a d20 without advantage is 10.5. This means advantage gives a +3.325 medium, which is roughly a +3 (and therefore a little over +15%).
THIS /\
Thanks for explaining things much better than I did!
My custom rule is to remove dexterity from armour class when flanking witch means it’s highly effective against some but does nothing to others
Excellent video!! And one I'll absolutely be using as I create a custom Big Bad fight for my players out of a modified Stone Giant Dreamwalker.
It is worth pointing out, for the more mathematically adept, that advantage is not a static bonus. It's a moving scale that depends on the target number. I wish I could remember who posted this originally so I could give credit, but here's a good explanation.
"The thing to take away from Advantage and Disadvantage is that its worth more when you are aiming for lower numbers than when you are aiming for higher numbers. For instance if you need to roll an 11 on the d20 before modifiers to succeed, you have a 50% chance normally, but you have a 75% chance if you have advantage. That is an increase of 25% or +5. If on the other hand you need a 19 before modifiers to succeed then on a normal d20 roll you have a 10% chance, whereas with advantage you have a 19% chance. A difference of 9% rounded up that's equivalent to a +2 bonus.
Originally Posted by Jack of Spades
For the percentages, I just compared the number of cases that would produce a specific roll with the total of 400 possible rolls.
For the average improvement, I added up the 'bonus' from each possible case (rolling a 19 and a 20 would yield a 'bonus' of 20, for example) and then averaged them. I'm not entirely sure why my number comes out so much lower than Seppo87's here:
But I'm always willing to bet against my own math.
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My earlier post details the math behind it. The bonus is entirely reliant on what number you need to roll on the d20 and varies from +2 to +6. Furthermore the closer you are to 10 or 11 the more of a bonus you get and the further away the less of a bonus. Which when you add it up turns it into a very interesting mathematical curve, which makes it problematic when swapping it out for something that is static.
It appears www.anydice.com is down at the moment so this should be helpful www.wolframalpha.com/input/?i=N*%2820-N%29%2F20
Quote Originally Posted by Sartharina
Again - it depends on the target AC.
Yes, my point exactly. There is no easy or obvious way for the player to know when its a good idea to give up advantage for sneak attack damage or just to keep advantage. This is because of the parabolic curve that advantage generates. It changes based on the target d20 roll that is needed."
Managed to complete my very first D&D session on Saturday night with 3 friends, we absolutely loved it and had to immediately continue on Sunday! it was hard at first and i had no idea how much improv i would need to do, but i was confident about it and its all down to your channel. Thank you for all the effort you put into this.
I personally like flank advantage because being attacked from outside your line of sight would really be that effective. It stresses the importance of forming a unit, covering each others backs (by filling a would-be flank position with an ally), and using obstacles tactically.
Awesome video.
I've also just found the most amazing pasttime: pausing your videos at random spots and looking at the faces you make. It's amazing.
Floofy kitty is adorable. Kitties make math more interesting. Well played.
Love the quality content of your videos. Really appreciate the time and effort you put into them. Just wanted to point out, with respect to flanking, I really like the optional rule of advantage attacks as using this is how a group of characters who are normally unable to routinely hit a high armour class; can now more easily hit a high armour class. I keep reading, and hearing, comments that say Advantage is equivalent to +5 to hit. I find that to be very miss leading, which the following should help explain:
Roll of 20 (39 in 400) or 9.75% (almost doubles the chance to hit AC 20 without any modifiers) about +1
Roll of 19 (37 in 400) thus 19% to roll 19 or 20 (almost doubles the chance to hit AC 19 without any modifiers) about +2
Roll of 18 (35 in 400) thus 27.75% to roll 18,19,20 (almost doubles the chance to hit AC 18 without any modifiers) about +3
Roll of 17 (33 in 400) thus 36% to roll 17,18,19,20 (not quite almost doubles the chance to hit AC 17 without modifiers) about +3
Roll of 16 (31 in 400) this 43.75% to roll 16,17,18,19,20 (less than doubles the chance to hit AC 16 without modifiers) about + 4
Roll of 15 (29 in 400) this is 51% to roll 15,16,17,18,19,20 (less than doubles the chance to hit AC 15 without modifiers) about +4
...
Roll of 10 (19 in 400) this is 79.75% to roll 10 -> 20 (well under doubling the chance to hit AC 10 without mods) about +6
Sure, when looking at the lower armour classes ( 11 - 14) it works out to about +5, however, that makes sense when two opponents collaborate when attacking one enemy, yet more importantly the tactic makes attacking a higher armour class opponent a viable plan.
The rule I use for flanking is that the second attacker can ignore shield AC (if the defendant has a shield) instead of advantage. It only reduces the enemy's AC by 2 (10% more likely to hit) for a single attacker, but more importantly it rewards tactically trying to surround armored "tank" enemies to receive a bonus instead trying to do it to a mage with no Armor. It also makes sense because one can realistically only block one assailant with a shield, and is surprisingly not hard to track and encourages players to ask which enemies have shields.
I rewatch this video a lot, it's one of the times where the old style of presenting the information as many ways as possible is actually helpful, because there's a bunch of ways of understanding it.
Here’s a helpful formula when working with Advantage. 1 - (x / 20) = chance to hit, where x = how many numbers you can roll on a d20 that will cause you to miss. If you have Advantage, the formula becomes 1 - (x / 20)^2.
In Matt’s example, the PC has +5 to hit. The ghoul has AC 12. The player needs to roll a 7 or greater to hit the ghoul. There are six numbers on a d20 that the player can roll that will make them miss (1 through 6). 1 - (6 / 20) = 0.7, which means a 70% chance to hit.
If that same PC has Advantage, it looks like this: 1 - (6 / 20)^2 = 0.91, which means a 91% chance to hit. Advantage is pretty good!
Let’s see how much this changes when our heroes are fighting a monster with a tougher hide, or a more nimble foe. Let’s say that they’re fighting a monster with an AC of 15, such as the mighty goblin. With a +5 attack bonus, our heroes must roll a 10 or greater to hit this foul creature. That means there are nine numbers on a d20 that will make them miss. 1 - (9 / 20) = 0.55 = 55% chance to hit. A true challenge worthy of our adventurers! With Advantage, this fearsome knave will be laid low when our heroes have a 1 - (9 / 20)^2 = 0.7975 = 79.75% chance to hit. Victory seems assured!
But what is this? A great wailing rises through the fog of war as the footsteps of Doom herald our end. The Hobgoblin has come. His armor is thick, and his shield broad. Surely none can penetrate his AC 18. With their humble +5 to hit, our heroes only have a 1 - (12 / 20) = 40% chance to hit this harbinger of destruction. He will be our ruin before our heroes can smite him down.
And then, somewhere deep in the city, a rooster crowed. Shrill and clear he crowed, recking nothing of wizardry or war, welcoming only the morning that in the sky far above the shadows of death was coming with the new dawn. And as if in answer there came from far away another note. Horns, horns, horns. In dark Mindollun’s sides they dimly echoed. Great horns of the North wildly blowing. Advantage had come at last.
Arise, arise, Riders of Advantage! Fell deeds awake: fire and slaughter! Spear shall be shaken, shield shall be splintered, a sword-day, a red day, a 1 - (12 / 20)^2 = 64% chance to hit day, ere the sun rises! Ride now, ride now! Ride to the nearest game store that runs D&D!
Great video Matt. Yes, i already knew this, but, it was nice hearing how you explained it. The only thing I would add is that this is how they come up with the different formulas in the books. Like Armor Class being 10+whatever, or better yet, overcoming spell resistance being 11+level. This means that if both participants are the same level, you have a 50/50 of succeeding. It's amazing how the math just rerolls all over itself from every perspective of the game. Well done, Matt!
Ooh I love this. And because I'm terrible at math I love this twice as much ever since I noticed one of the handbooks pointing out that d20s give you 5% increments and realized I was being a dumb and stopped being a dumb.
So it's super easy. Level 1 players in 5E typically get a +2 proficiency bonus with their weapons and typically use said weapons. Armor class of 12 means 10 (50%) + 2 (10%) - the players' 2 proficiency (-10%) meaning their odds are about even. It's slightly weighted, I think, since they can't roll a zero, but that's close enough for gaming purposes.
So level 1 players hit or miss at about the same rates. Except we didn't add ability modifiers. Hoping for at least a +3 and ideally a +5 means anywhere from 65% to 75% chance to hit. Because 3*5% and 5*5%, so base 50% plus 15-20-25 chance to hit!
It's trivial to calculate this. You start with 10AC and for pretty much everything you add a couple more points which gives you easy multiples of 5 and in very rare cases subtract from 10AC to 8 or 9, and with proficiency bonus and ability modifiers it makes it really super quick to calculate. Which is important for generating difficulty checks or armor classes on the fly. If your players only have at best a +7 to hit then 18AC gives them a 45% chance to hit, since they have to roll 11-20, which is nine numbers, multiplied by five, equals 45.
It's really simple math and it really seems trivial but realizing this changed the way I DM. Toss a 20AC badass against your players with +5s and watch them cry.
You're awesome, Matt! I get a lot of value from your videos, this one is not an exception. Abstract math doesn't come intuitively to me, yet the concept of basic statistics is simple. Thanks for taking the time to explain with many examples. You do make a good teacher: I'll be thinking differently about everything, now.
PS. The Math vs. Psychology of the game mechanics was rad. Never thought about that before. I hope to push my players' buttons in the right way to up the ante!
First off, thank you for making this video. I'm typically really good at math but for some reason D&D stat blocks have never....really made sense to me. I wasn't thinking about it in the right light. However, I did want to ask about the other half of dice math, the one that has a lot more variables - hit points and damage. This goes both ways, in my mind, of "sure the monster has X many hit points but how much damage should it be dishing out?" Obviously, it involves a lot more kinds of dice, and more familiarity with the classes around your table. This may not be a thing you can talk about in a video. But I know that I, for one, would appreciate it.
I try to have the soft encounters often so players feel good about the campaign. I like to then sprinkle in the higher ac to make the battle seem at times tougher. Don't want to make it too easy or make it a blood bath for players is the happy medium. Thanks for the video Matt
Thank you so much Mat, your videos have helped me SO MUCH with getting on my feet as a DM, my players are enjoying everything I am doing!
The Rag Tag group of adventurers( Shadow Monk Halfling, DragonBorn Fighter, Moon elf Sorcerer, DragonBorn Rogue, and sometime a Half-Orc Ranger, and Wood elf Druid) are after the Pieces of Light (magical Items, Weapons, & armour) that will help in the fight against the evil cult of Vecna, who plan to taint the holy sites the PoLs reside to use there power to resurrect Vecna and make him whole again. Who in turn will turn the world into an undead wasteland!
As a new DM who's Math skill isn't my strongest tool in the tool shed I found this video very helpful. Once you broke down the Math and explained the individual components to the formula it all made perfect sense. Thanks for the videos, really enjoying the content. I am running my first D&D session as the DM next week, wish me luck!
Excellent. This stream definitely gave me, as a new DM, a much better handle on planning around CR at the per PC level. Also you sprinkle in lots of great advice along the way, such as players want to hit (so don't make it insanely difficult). Your channel is the best! Thank you for putting so much effort into it.
I actually had to pause the video to comment. When I started 5e, I couldn't get flanking out of my head, just like I kept calling for reflex and will saves. I didn't even realize flanking was a variant until I read more into it. I was wondering why my players were just steam rolling through encounters. It was because advantage flanking is such a HUGE advantage (pun intended), that every combat encounter was tunnel vision to GET that flanking advantage. This is when my life started working in 5% increments behind the screen, as you say.
After discussing with my players, I decided to find a happy medium, it's similar to your +2 idea, but for every 2 allies in flanking, everyone gets +1 to hit. In a 5 player game, depending on summons and stuff, it's usually only a +1, sometimes a +2, that they'll get, which isn't huge, but combats are much more interesting now. The single minded advantage flanking tactic is gone, and they're thinking more.
Confirmation bias from Colville videos is the best feeling.