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
65% hit chance, 65% average hit rate.
80% hit chance, 72% average hit rate.
83% hit chance, 76% average hit rate.
84% hit chance, 79% average hit rate.
84% hit chance, 80% average hit rate.
84% hit chance, 81% average hit rate.
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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