When a character hits a target with a Vex weapon, they have Advantage on their next attack roll against that creature until the end of their next turn.
Surprisingly, it can be quite hard to work out how likely you are to hit with the Vex mastery as the advantage is dependant on how likely it was that your last attack hit
P = Your percentage chance of hitting (P for probability) AC = The Armor Class you're trying to beat M = Your total to-hit Modifier (including proficiency and ability bonuses)
Example:
M= 2+3
AC = 13
Baseline: 65% chance to hit
P=((21−(AC−M))/20)×100
65%=((21-(13-5))/20)x100
Or with Advantage (rolling twice): 87.75% chance to hit
P=(1-(((AC-M-1)^2)/400))x100
87.75%=(1-(((13-5-1)^2)/400))x100
1st Attack (lets assume at advantage, every other attack following is only at advantage if the attack before it ‘hit’… otherwise it is at the baseline.)
87.75% chance to hit
19% chance to crit (I did this maths for a champion fighter, so crits with 19 or 20 on the dice, rolling twice)
Reminder, if this attack hits, the next has advantage…
2nd Attack
Last attack missed:
12.25% chance to have a 65% chance to hit = 7.963%
12.25% chance to have a 10% chance to crit (19 or 20 on the die) = 1.225%
Last attack hit:
87.75% chance to have a 87.75% chance to hit = 77.001%
87.75% chance to have a 19% chance to crit (19 or 20 on the dice, rolling twice) = 16.6725%
So to work out chance to hit for the second attack, just add then together:
Total chance to hit = 84.9635
Total chance to crit = 17.8975
Something I have observed on my spreadsheet applying this formula, is that the percentages creep towards each other if you attack enough times with Vex. Even after a few attacks lacking advantage (65% chance), the likelihood to hit starts to increase to the low 80s. Which makes sense, but also means it is the only other weapon mastery that directly rather than situationally adds damage in single target fights (Graze is the other).
I don't know if you still follow this thread, but the chance to hit with a single vex weapon with baseline chance of 65% to hit is 84.14% (260/309).
It is both easy and not to calculate:
Let p0 be the baseline chance to hit: p0 = 1-max( (19/20)*(AC-M-1)/19 , 1/20 ) = 1-max((AC-M-1)/20,1/20) = 1-max(AC-M-1,1)/20: How do i get the formula: nat 1 is always a miss, so the minimum miss chance is 1 out of 20. Also nat 20 is always a hit so in 19 out of 20 cases you might miss if you roll below (AC-M-1). In those 19/20 cases only (AC-M-1) out of 19 numbers will miss. If you now swap "out of" with "/" you get all the fractions of the formula (I did it for 19/20 once in the text).
The good thing: we don't actually need that formula anymore (just to calculate the base chance), so any (approximated or not) chance to hit without advantage is valid:
If p is the chance any attack hits, the chance for any attack to hit calculates as follows: If an attack hit previously (chance of p) the attack has advantage, if not (chance of 1-p) it doesn't, so: p = p*(1-(1-p0)^2) + (1-p)*(1-(1-p0)) = p*(1-(1-p0)^2) + (1-p)*p0 = p-p*(1-p0)^2 + p0-p*p0
it follows that: p = p-p*(1-p0)^2 + p0-p*p0 and therefor: p-p+p*(1-p0)^2+p*p0 = p0 further: p*((1-p0)^2+p0)=p0 which leads to: p=p0/((1-p0)^2+p0)
I don't know if you still follow this thread, but the chance to hit with a single vex weapon with baseline chance of 65% to hit is 84.14% (260/309).
It depends on engagement duration. That's correct over an infinite number of attacks, but typically you aren't making more than half a dozen attacks against a given target. In general your chance of hitting is 0.8775*(chance prior attack hit) + 0.65*(1 - chance prior attack hit), or 0.65 + 0.2275 * (chance prior attack hit), which over 1-6 is
Well, no. It isn't over an infinite number of attacks. It's the chance of an attack hitting without knowing the past.
You either:
1a: know the past (aka whether the last attack hit or missed). Then the chance is either 65% or 87.75% depending on what you know to be true. 1b: know the chance of the last attack hitting (aka which number of attack it was). Then your table represents the chance of hitting.
2: don't know the past. Then the chance that that attack hits is 84.14%. Because 0.65+0.2275*0.8414 = 0.8414.
Well, no. It isn't over an infinite number of attacks. It's the chance of an attack hitting without knowing the past.
If you don't know the past, you not only don't know whether the attacker hit on their prior attack... you don't know whether a prior attack even existed. The numbers you gave assume that a prior attack existed.
I built a spreadsheet that calculated it but essentially the more attacks you make the higher chance to gain advantage and therefore continue to hit.
Not true, the chance to hit stabilizes at around the 5-6 attacks range at 84% vs 88% for guaranteed advantage.
Well, the chance does continue to improve, it's just that the improvement is pretty much irrelevant (no-one cares that the 6th attack has an 84.1307% chance to hit and the 7th has an 84.1397% chance to hit).
So much math to what purpose? Advantage gives a ( roughly) +4/20% to hit. Assuming your using a vex weapon for all attacks then your initial chance of hitting is 65% and remains so until you actually hit. On the next attack your chance becomes 84-85%. If you only have one attack a round it will remain at 84-85% until you miss since vex extends to the end of the next round. Once you miss the cycle restarts. Having 2 ( or more) attacks a round ( or mixing vex and Nick weapons) opens up many possible lines of alternating odds. However, since each attack is an independant roll the history of rolls doesn’t have any actual impact on the results except for the vex bonus on the one next attack. Hit or miss that vex bonus is gone after the next attack so it’s either 84-85% or 65% .
The big problem with vex is: "okay, I hit the monster and get advantage on my next attack... but I don't have more attacks this turn so that bonus delays until next turn. Next turn comes around... and the monster is already dead so my vex did nothing".
The best use case in tier 1 tends to be that you're using two weapons (say, shortsword with vex, scimitar with nick), and you use the vex weapon first, meaning it never gets the bonus for vex... but the second weapon gets the bonus if the first weapon hits. This dramatically cuts down on "the monster's already dead" problems, though they can still happen.
I built a spreadsheet that calculated it but essentially the more attacks you make the higher chance to gain advantage and therefore continue to hit.
Not true, the chance to hit stabilizes at around the 5-6 attacks range at 84% vs 88% for guaranteed advantage.
Well, the chance does continue to improve, it's just that the improvement is pretty much irrelevant (no-one cares that the 6th attack has an 84.1307% chance to hit and the 7th has an 84.1397% chance to hit).
I guess it depends what argument one is trying to make, the chance to hit will never be more than 85% even if one rolled infinite attacks. The distribution approaches a limit (the exact value of that limit I've forgotten) so technically keeps increasing towards that limit, but OTOH it will never exceed that limit.
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Weapon Mastery Properties: Vex
When a character hits a target with a Vex weapon, they have Advantage on their next attack roll against that creature until the end of their next turn.
Surprisingly, it can be quite hard to work out how likely you are to hit with the Vex mastery as the advantage is dependant on how likely it was that your last attack hit
P = Your percentage chance of hitting (P for probability)
AC = The Armor Class you're trying to beat
M = Your total to-hit Modifier (including proficiency and ability bonuses)
Example:
M= 2+3
AC = 13
Baseline: 65% chance to hit
P=((21−(AC−M))/20)×100
65%=((21-(13-5))/20)x100
Or with Advantage (rolling twice): 87.75% chance to hit
P=(1-(((AC-M-1)^2)/400))x100
87.75%=(1-(((13-5-1)^2)/400))x100
1st Attack (lets assume at advantage, every other attack following is only at advantage if the attack before it ‘hit’… otherwise it is at the baseline.)
87.75% chance to hit
19% chance to crit (I did this maths for a champion fighter, so crits with 19 or 20 on the dice, rolling twice)
Reminder, if this attack hits, the next has advantage…
2nd Attack
Last attack missed:
12.25% chance to have a 65% chance to hit = 7.963%
12.25% chance to have a 10% chance to crit (19 or 20 on the die) = 1.225%
Last attack hit:
87.75% chance to have a 87.75% chance to hit = 77.001%
87.75% chance to have a 19% chance to crit (19 or 20 on the dice, rolling twice) = 16.6725%
So to work out chance to hit for the second attack, just add then together:
Total chance to hit = 84.9635
Total chance to crit = 17.8975
Something I have observed on my spreadsheet applying this formula, is that the percentages creep towards each other if you attack enough times with Vex. Even after a few attacks lacking advantage (65% chance), the likelihood to hit starts to increase to the low 80s. Which makes sense, but also means it is the only other weapon mastery that directly rather than situationally adds damage in single target fights (Graze is the other).
I made a spread sheet to automate the calculations for the new weapon masteries. Here are the "to hit" chances for Vex attacks:
if 1st attack is at Advantage:
1 = 0.8775
2 = 0.847
3 = 0.843
4 = 0.842
5 = 0.8415
If 1st attack doesn't have Advantage:
1 = 0.65
2 = 0.798
3 = 0.831
4 = 0.839
5 = 0.841
For those curious for a Topple weapon it is:
If 1st attack does have advnatage:
1 = 0.8775
2 = 0.7498
3 =0.7976
4 = 0.8295
5 = 0.8494
if 1st attack doesn't have advantage:
1 = 0.65
2 =0.724
3 =0.780
4 = 0.818
5 = 0.842
For Topple what stats did you measure this with and against?
For Topple it was baseline 65% chance to hit and 50% chance that the enemy fails the saving throw.
I don't know if you still follow this thread, but the chance to hit with a single vex weapon with baseline chance of 65% to hit is 84.14% (260/309).
It is both easy and not to calculate:
Let p0 be the baseline chance to hit: p0 = 1-max( (19/20)*(AC-M-1)/19 , 1/20 ) = 1-max((AC-M-1)/20,1/20) = 1-max(AC-M-1,1)/20:
How do i get the formula: nat 1 is always a miss, so the minimum miss chance is 1 out of 20. Also nat 20 is always a hit so in 19 out of 20 cases you might miss if you roll below (AC-M-1). In those 19/20 cases only (AC-M-1) out of 19 numbers will miss. If you now swap "out of" with "/" you get all the fractions of the formula (I did it for 19/20 once in the text).
The good thing: we don't actually need that formula anymore (just to calculate the base chance), so any (approximated or not) chance to hit without advantage is valid:
If p is the chance any attack hits, the chance for any attack to hit calculates as follows:
If an attack hit previously (chance of p) the attack has advantage, if not (chance of 1-p) it doesn't, so:
p = p*(1-(1-p0)^2) + (1-p)*(1-(1-p0)) = p*(1-(1-p0)^2) + (1-p)*p0 = p-p*(1-p0)^2 + p0-p*p0
it follows that:
p = p-p*(1-p0)^2 + p0-p*p0
and therefor:
p-p+p*(1-p0)^2+p*p0 = p0
further:
p*((1-p0)^2+p0)=p0
which leads to:
p=p0/((1-p0)^2+p0)
if p0=65%:
p=0.65/(0.35^2+0.65)=260/309
It depends on engagement duration. That's correct over an infinite number of attacks, but typically you aren't making more than half a dozen attacks against a given target. In general your chance of hitting is 0.8775*(chance prior attack hit) + 0.65*(1 - chance prior attack hit), or 0.65 + 0.2275 * (chance prior attack hit), which over 1-6 is
Well, no. It isn't over an infinite number of attacks. It's the chance of an attack hitting without knowing the past.
You either:
1a: know the past (aka whether the last attack hit or missed).
Then the chance is either 65% or 87.75% depending on what you know to be true.
1b: know the chance of the last attack hitting (aka which number of attack it was).
Then your table represents the chance of hitting.
2: don't know the past.
Then the chance that that attack hits is 84.14%.
Because 0.65+0.2275*0.8414 = 0.8414.
@puffpoldi why would you assume you don’t know the past, that is vital data.
I built a spreadsheet that calculated it but essentially the more attacks you make the higher chance to gain advantage and therefore continue to hit.
Vex benefits from attack quantity… and Elven Accuracy
If you don't know the past, you not only don't know whether the attacker hit on their prior attack... you don't know whether a prior attack even existed. The numbers you gave assume that a prior attack existed.
Not true, the chance to hit stabilizes at around the 5-6 attacks range at 84% vs 88% for guaranteed advantage.
Well, the chance does continue to improve, it's just that the improvement is pretty much irrelevant (no-one cares that the 6th attack has an 84.1307% chance to hit and the 7th has an 84.1397% chance to hit).
So much math to what purpose? Advantage gives a ( roughly) +4/20% to hit. Assuming your using a vex weapon for all attacks then your initial chance of hitting is 65% and remains so until you actually hit. On the next attack your chance becomes 84-85%. If you only have one attack a round it will remain at 84-85% until you miss since vex extends to the end of the next round. Once you miss the cycle restarts. Having 2 ( or more) attacks a round ( or mixing vex and Nick weapons) opens up many possible lines of alternating odds. However, since each attack is an independant roll the history of rolls doesn’t have any actual impact on the results except for the vex bonus on the one next attack. Hit or miss that vex bonus is gone after the next attack so it’s either 84-85% or 65% .
Wisea$$ DM and Player since 1979.
The math has a purpose for if someone is trying to mathhammer out builds to work out what works better.
Which was what I was doing when I made this thread - I thought I’d share
The big problem with vex is: "okay, I hit the monster and get advantage on my next attack... but I don't have more attacks this turn so that bonus delays until next turn. Next turn comes around... and the monster is already dead so my vex did nothing".
The best use case in tier 1 tends to be that you're using two weapons (say, shortsword with vex, scimitar with nick), and you use the vex weapon first, meaning it never gets the bonus for vex... but the second weapon gets the bonus if the first weapon hits. This dramatically cuts down on "the monster's already dead" problems, though they can still happen.
I guess it depends what argument one is trying to make, the chance to hit will never be more than 85% even if one rolled infinite attacks. The distribution approaches a limit (the exact value of that limit I've forgotten) so technically keeps increasing towards that limit, but OTOH it will never exceed that limit.