Huge props to eponymous-rose for putting this together!

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I thought it might be entertaining to go through this fantastic list by @critrolestats of all the KOs in the game and see who was responsible for the healing on each one. Obviously there are a million ways everyone’s saved everyone else’s lives by now, but this is a fun way to keep a tally.

Fun facts! For “healed”, read “been directly responsible for someone recovering from unconsciousness or worse, either via potion, spell, or medicine check”.

• With Ashley’s schedule limitations and recent events, Scanlan has now surpassed her for most heals in the party (11 versus 10). After the two healing powerhouses, Vex has actually been responsible for the third-most back-from-unconsciousness heals (5), followed by Vax (4) and Keyleth (3).
• Percy has been knocked out by far the most (10 individual events), followed by Trinket (6) and Vax (5).

Who’s healed whom?

• Vax has healed Percy three times and Keyleth once.
• Vex has healed Trinket three times and Scanlan twice.
• Pike has healed Percy four times and Grog three times.
• Grog has healed Percy and Scanlan once each.
• Scanlan has healed all the main party members except for Trinket and Pike, with Vex receiving the most heals (three).
• Percy has only brought one person back from unconsciousness: Vax.
• Keyleth has healed Trinket twice and Vax once.

And who’s been healed by whom the most?

• The half-elves are all most often healed by Scanlan.
• Trinket and Scanlan are most often healed by Vex.
• Grog and Percy are most often healed by Pike.

Anyway, here’s the table and the complete list I used under the break. I’m sure there are gaps here and there, but it was fun setting this up! You know. In an emotionally scarring sort of way.

• Episode 4: Scanlan gets chomped by a bulette.
  • Pike uses her Sprinter’s Boots and just barely succeeds an acrobatics check (with the help of Scanlan’s earlier inspiration) in order to get close enough to cast Cure Wounds on him.
• Episode 4: Percy takes a couple of hits from the Duergar general’s flaming warhammer.
  • Pike casts Cure Wounds on him after the end of the battle.
• Episode 5: Percy and Scanlan are both knocked out in the flying carpet’s crash-landing.
  • Vax feeds Percy a potion and Vex feeds Scanlan a potion.
• Episode 5: Grog takes two acidic attacks of opportunity from the evil ooze (actually named black pudding, because that’s a thing).
  • Pike hits him with a Cure Wounds once the battle’s over.
• Episode 7: Vax passes out from heat damage and is badly burned by the magma.
  • Pike and Trinket manage to drag him out, and Percy immediately gives him a healing potion.
• Episode 8: Trinket takes a melee attack from the abyssal abomination.
  • A distraught Vex gives him a healing potion at the end of the battle.
  • Sam: “This is a grizzly situation.”
• Episode 11: Grog is killed by a death ray from K’Varn.
  • Pike casts Revivify mid-battle, resulting in an abbreviated version of the resurrection ritual that succeeds on a single (advantaged) Wisdom check (16).
• Episode 17: Grog is knocked out by Kern the Hammer at the end of their fight in the Crucible.
  • The clerics of Kord running the fight heal him.
• Episode 17: Trinket gets caught in a fireball that Tiberius aimed at the hydra.
  • Keyleth casts Cure Wounds on Trinket.
• Episode 19: Scanlan takes a bite attack from Rimefang… and two claw attacks after he’s already down.
  • Grog rushes in, feeds him a healing potion, and flings him across the ice, away from the battle.
• Episode 19: Percy is slammed into the ice by Rimefang’s tail attack and takes another hit on the cusp of Lyra’s fireball spell.
  • Grog just barely manages to get to him with a healing potion at the end of the battle.
• Episode 19: Lyra is knocked out by Rimefang’s ice breath.
  • Scanlan feeds her a potion at the end of the battle.
• Episode 21: A possessed Keyleth is knocked out by Tiberius’s Obelisk of Stone
  • Tiberius gets her back on her feet with a healing potion.
• Episode 25: Vax is downed by Delilah Briarwood’s Blight spell and takes another hit when Seeker Asum tries to get his unconscious body away from Sylas Briarwood.
  • Scanlan manages to get within earshot and casts Healing Word on Vax.
• Episode 28: Trinket is knocked out by the behir’s lightning attack.
  • Keyleth casts Cure Wounds on him.
• Episode 29: Percy is knocked out twice in a row by the banshee.
  • Scanlan casts Healing Words on him.
  • Vax beats him to it the second time and feeds Percy a potion.
• Episode 33: Vax is stabbed by a Helmed Horror, and stabbed again while unconscious.
  • Keyleth heals him, followed immediately by a frantic Vex.
• Episode 33: A possessed Keyleth is taken down by Scanlan’s Spirit Guardians.
  • Vax stabilizes her with a medicine check and Scanlan wakes her up with a Song of Rest.
• Episode 33: A possessed Percy is knocked out by Grog and takes another hit from the ghost’s withering touch.
  • Scanlan casts Healing Word on him.
• Episode 34: After being reduced to 1 HP by Delilah Briarwood’s Finger of Death spell, Vex is knocked unconscious by the fall after her flying spell is canceled.
  • After several failed attempts by Vax and Pike to revive her in the antimagic room, Vex rolls enough successful death saving throws to stabilize.
• Episode 39: Vax is slashed by Grog’s sword during his rescue after being swallowed by the Purple Worm.
  • Pike heals him using Heal.
• Episode 40: Trinket is felled by Vorugal’s ice breath.
  • Pike uses Cure Wounds on him.
• Episode 44: Vex is killed by a trap on the Deathwalker’s Ward armor.
  • Kashaw successfully casts Revivify on her, with contributions to the ritual from Vax, Zahra, and Percy.
• Episode 49: Vex is knocked out by a claw attack from the sphinx.
  • Scanlan heals her once he manages to return to the room.
• Episode 50: Grog is killed by Craven Edge.
  • Pike successfully casts Revivify on him, with contributions to the ritual from Vex, Vax, and Scanlan.
• Episode 52: Grog is knocked out by fall damage after his final blow on Kevdak.
  • Scanlan starts up a chant in the crowd by way of a Healing Word.
• Episode 55: Percy and Trinket are knocked out by Umbrasyl’s acid breath.
  • Pike casts Heal on Percy.
  • Vex casts Cure Wounds on Trinket.
• Episode 58: Vax is stabbed by Hotis, and then stabbed again once he’s unconscious.
  • Scanlan casts Healing Word on him after jumping off a 70-foot tower with Mythcarver to prevent Hotis from making his finishing blow.
• Episode 63: Vex is shot by Saundor, using Fenthras.
  • Scanlan casts Healing Word on her.
• Episode 66: Vex is downed by the cobalt golem’s acid breath.
  • Scanlan brings her back again with Healing Word.

And then, of course, there’s the disaster that is Episode 68:

• The mage’s chain lightning spell takes down Keyleth, Scanlan, and Trinket. Before any of them can be healed, Ripley shoots Percy, knocking him out, then shoots him twice more before anyone can get to him. One of Ripley’s gunners fires next at her urging, killing him.
  • Percy is revived by Pike’s necklace.
  • Vex heals Scanlan by casting “Cure fucking Wounds with my shit-ass healing”.
  • Scanlan brings Keyleth back with a Healing Word. 
  • Trinket returns to Raven’s Slumber and is healed by Vex after the end of the battle.
• Ripley shoots Percy, knocking him out again.
  • Vax brings him back with Lay on Hands.
• Keyleth is stabbed by Kynan.
  • Scanlan uses a Healing Word (”I look at Keyleth and I fuckin’ heal her.”)
• Percy is knocked out by Orthax and killed by Ripley.
  • Pike casts Resurrection the following day, and the ritual succeeds with help from Vex and Keyleth.

(read as “[row] healed [column] X times”)

Denizens of the Moonbrush Additional Stats

Here are some additional goofy little stats facts about the cumulative probabilities: I went ahead and repeated this sequence of events (rolling 157 d20s) 10,000 times, and in all those cases, a Natural 20 count of 14 only happened 138 times. This means that the likelihood of rolling 14 Nat 20s with a perfectly balanced die is at best only 1.4%. In contrast, rolling 8 Nat 20s under those circumstances is about ten times more likely, occurring 14.4% of the time. Pretty unusual! 

Rolling 10 Nat 1s out of 157 is a little less impressive, but still unlikely: the likelihood of such an event is 9.9%.

Thanks to @eponymous-rose for the additional statistics and explanation!

Vox Machina as Encounters

A few months back, @visuallooker asked us, “What’s Vox Machina’s [Challenge Rating]?” While we hadn’t found the chance to compute it ourselves, Joshua Miller (@jmillerone) has created encounter cards for each member, as well as calculated the challenge rating for fighting the entire party (at current level, approximately CR 26). Huge applause to him for putting these together; check out the links to the PDFs below, and the pages themselves after the break!

• Vex’ahlia- http://homebrewery.naturalcrit.com/share/H1IqDfMN
• Vax’ildan - http://homebrewery.naturalcrit.com/share/Hy-4s-HXE
• Percy - http://homebrewery.naturalcrit.com/share/HkvfZ9zV
• Scanlan - http://homebrewery.naturalcrit.com/share/ByfD1Fm4
• Keyleth - http://homebrewery.naturalcrit.com/share/BytiwMXE
• Pike - http://homebrewery.naturalcrit.com/share/SJanT0EV
• Grog - http://homebrewery.naturalcrit.com/share/SkINxyEV

Dominant Hands

Considering Tyriok’s sudden reliance on his ambidexterity, we found it fitting to examine just what each player’s dominant hand is. While we can’t say for sure that each PC shares the same dominant hand as their player (e.g., Liam appears to be right handed but Vax is ambidextrous thanks to Dual Wielding), thanks to some observation, we can at least be confident which hand each cast member favors. Thanks to MomStats for her support, curiosity, and findings!

Right-Handed Players

• Matthew Mercer
• Ashley Johnson
• Liam O'Brien
• Marisha Ray
• Sam Riegel
• Taliesin Jaffe
• Travis Willingham
• Orion Acaba
  
• Dan Casey
• Ify Nwadiwe
• Mary Elizabeth McGlynn
• Felicia Day
• Will Friedle
  
• Kit Buss
  
• Jason Charles Miller
• Chris Hardwick
  

Left-Handed Players

• Laura Bailey
• Wil Wheaton
• Zac Eubank

Quadridextrous

• Sid the Sloth
  

Save Against the Beholder Odds

IsYitzack returns, with the odds on how often the party could have saved against the beholder’s eye ray attacks!

Matt was surprised to see how well the party was rolling against his beholder on Thursday. I was wondering how surprised he should be. And the answer is very. I’ll be using DCs of 16 for all eye ray attacks (including the eyeball that came out of the column to shoot at Scanlan). The tendrils coming from the wall only required a DC 15 Dex Save to avoid. (They didn’t last long enough to require acrobatics or athletics checks to escape their grasp.) Finally, I’ll be using the Saving Throw values calculated by CritRoleStats in their character sheets.

They made 14 of 19 saving throws. That happens 15,763,665,194,354,589,813 in 2^16*10^16 events (Mathematica does arbitrary integer and fraction arithmetic so long as the RAM holds out). That is approximately 2.41% of the possible ways will come out this good. I would expect 9.82 successes (out of 19) instead. There is a 3.35% chance of doing this well or better (see Figure 1). I wouldn’t be too terribly concerned about doing this well, but it is much better than I would have expected. The most likely outcome: 10 successes at 19.3% chance of happening.

Figure 1: The plot of the likeliness of making n saves. The X axis is the number of saves (out of 19), while the Y axis is the percent chance of that many saves happening. Vox Machina in The Sunken Tomb fall very far to the right, at 14 on the X axis.

For my initial calculations, I started my computer Sunday night to begin printing out every possible combination of fails and saves of the 19 ray attacks, using the brute force method. Turns out that after reducing the probabilities from out 20 and 400 to the simplest fractions, there are still 2^16*10^16= 65,536 * 10^16 possibilities. I stopped my computer Monday morning and it was nowhere near finishing. I took inspiration from what I had done whilecalculating the odds of Vex’s resurrection ritual (Ed: coming soon!) and worked on a network of nodes to arrive at a final result in much less time.

Most of the chances of success are fairly straight-forward. Critical failures and successes would have been failures or success without being aided in any of these cases. Grog has Danger Sense which he can always use to gain advantage on Dex saves. Travis stated that “I’m not raging yet” as he rolled the dice; while he theoretically should still have it when he isn’t raging, since he didn’t claim it, I won’t claim it for him in this calculation.

Figure 2: A graph of the probability of rolling a specific number on a d20.

Figure 3: A graph of the odds of beating a DC of n. Keep in mind that DC 2 is technically the lowest possible, as 1 always fails.

Thanks again to IsYitzack for this, and the resurrection odds!

D20 Roll Analysis (With Graphs!)

@dragonmustang01 has been a long time contributor to the All Rolls project, as well as many others. Well, after we finally published, she decided to add up how many rolls have actually been made by each character, as well as graph how many they rolled each episode. Thanks, Lauren, and enjoy her handiwork and commentary!

We have an excellent table of all rolls, but I find that graphs are sooo much easier to read and find patterns in than a huge list of numbers, so here we are (as of Episode 44):

Episodes 1-11:

Episodes 13-22:

Episodes 23-33:

Episodes 34-44:

A couple of things I noticed:

• Combat-heavy episodes, like The Temple Showdown (Episode 11) and Reunions (Episode 33) obviously have more rolls than other episodes like Shopping and Shipping (Episode 14) and the Winter’s Crest Festival (Episode 36).
   
• Vax rolls a lot. He usually has a higher number of rolls per episode than anyone else, and his total number of rolls is about 200 more than the next highest, Grog (Vax has 893, where Grog has 687). Suddenly his large number of natural 20s makes sense. He has a tendency to dominate combat-heavy episodes in particular, probably thanks to his boots of haste granting him three attacks per round, even before Percy got his third attack. Grog also has three attacks, but doesn’t tend to make as many skill checks as Vax outside of combat, granting the rogue the edge there.
   
• Spellcasters, in general, roll less than the melee and ranged fighters. Many of their attacks do not require attack rolls, and they get fewer attacks per round. These combined more than make up for the increased arcana and nature checks that these characters perform.
   
• Trinket tends to roll less than of all the PCs. Here I invoke critrolestats rule number 6 to forestall the inevitable Trinket usefulness discussion. Let it be known, however, that Matt and Laura often forget to roll for him for things like stealth, especially in early episodes, and he doesn’t usually get to roll for things like initiative (the exception here is in episode 27, where he was separated from Vex and went into combat with Percy against the invisible stalkers). (#TeamLeaveNoBearBehind)
   
• Grog’s got two big peaks coinciding with his two fights against Kern (of course). I strongly suspect that this is where he gets the jump on Vex in total number of rolls, since Vex is a little more consistent through all episodes and he still just barely beats her out.
   
• Percy started rolling a lot more in the Whitestone arc (Episodes 26-35), even beating out Vax for highest episode total a couple of times. This is also where he significantly increased his natural 20 count (he had 7 in episode 33 alone).
   
• Speaking of natural 20s, now that we have a count of all rolls, we can calculate the frequency at which everyone crits. Vax is actually the closest to the expected frequency of 5% at 5.04%. Percy is the highest, thanks to the golden snitch, at 7.05% (excluding Lillith, who only rolled twice and got one natural 20, and Garthok, who is at 12.5% thanks to only rolling 8 times and getting a single crit). Trinket and Pike are also both fairly high. Despite Grog’s brief run of luck with Craven Edge and intelligence crits, he’s still behind the regular members of Vox Machina at only 3.49%. Thorbir brings up the rear at 2%, because of course he does.
   
• Scanlan appears to be the luckiest PC when it comes to avoiding natural 1s, at 1.59%. Trinket, however, seems to fumble the most often of the regular members of Vox Machina, but still is lower than the expected frequency of 5% at 4.88% (though the margin of error here is fairly high; Trinket has significantly fewer rolls than the regular PCs). Zahra and Thorbir (of course) are the only other PCs with a higher fumble rate, at 5.77% and 20%, though there are caveats to Thorbir’s count, as has been discussed previously, and Zahra also has a relatively low number of rolls. Keyleth fumbles the most of the humanoid regular members of Vox Machina, at 4.41%.

The odds of Wheatoning

Earlier this month, we put together all of Wil’s rolls from the Trial of the Take and attempted to calculate how much he “broke math.” Now, actual statistician IsYitzack has sent in his analysis of the data (along with the numbers retrieved from Mathematica): 

If you’d like to see what else IsYitzack has calculated for us, check out the stats on Saving Throws and the odds of the second Kern fight!

Vox Machina of Emon (To the Tune of "Fresh Prince of Bel Air Theme Song")

We asked; we received.

Now, this is a story all about how
Our lives got flipped-turned upside down
And I’d like to take a minute
Just sit and hang on
I’ll tell you how we came to sit on the council of Emon

In Southwest Taldorei the party was raised
Out in the Swamp was where we spent most of our days
Chillin’ out maxin’ relaxin’ all cool
And all gangin’ up and killin’ an undead fool
When a Wizardly guy who was up to no good
Started making trouble in the neighborhood
We got in one little fight and Grog lost his mind
So we broke into a mage tower an arch wizard to find

We begged and pleaded for him to find a way
To remove the silly lich and make the ass pay
We had to get two items in order to succeed.
The hearts of a Nightmare and a Nymph we would need.

Nymph heart, yo this is bad
How can we get it ‘th'out making it die?
Grog just stepped forward said “I have an idea!”
Hmmmmm this turns out alright.

But wait We hear problems in Westruun
We come across a dragon and slay it so much fun!
I don’t think so
Who brought the egg to the fair?
I hope they’re prepared for us to get there!

Well, we get settled and when we came out
There was a dude with gold eyes takin’ all the children out
We got into a fight and took him out
He didn’t fight fair.
We found the royal family bound demonicly.

Allura did speak and listen we did hear
We fought the demon with justice we ended its fear
We saved rulers, two daughters, and their one son
We’re given a keep and seats on council Emon

We accept and say it’s just great
And we partied with the citizens, it was such fun.
We looked at our kingdom
There in the setting sun
To sit on the council of empire Emon!