@mellored - looks like my results were a bit higher than i anticipated.
As promised Precision Attack Calcs. But First:
Basic methodology -
- We want to use precision attack anytime we think we've missed by 1-5. *Note: Already have confirmed 1-5 is more optimal than 1-4.
- We need to look at this over the short rest period of 8 rounds.
- Unused Superiority dice at the end of the period cannot be applied to a different maneuver Doing so would break our first assumption. It also wouldn't match reality very well where the adventuring short rest period may go longer than 8 rounds. *Note: We could design a different algorithm for using the dice here, but let's nail the basics first.
Process -
- Determine expected number of superiority dice we can use when making 27 attacks (8 rounds of 3 attacks each + 3 (1 action surge of 3 attacks). This will be done by using the binomial distribution which can be used in excel via the formula:
=binom.dist(successes, trials, probability of success, non-cumulative)
More to come on this step further down.
- We then calculate the chance a dice converts a miss to a hit (this is easy as long as advantage is not involved). Since our dice are d10's:
miss by 1 = 100%
miss by 2 = 90%
miss by 3 = 80%
miss by 4 = 70%
miss by 5 = 60%
- Average out the above percentages, equally weighted since they all equally come up when rolling 1d20. Simply Calculation so results are here = 80%
- Multiply by the damage we deal when a miss is converted to a hit = 2d6 +1 (fighting style)+ 5 (mod) + 4 (GWM) = 17
Binomial Distribution Process -
Step 1:
In excel make a column of every possible number for misses by 1-5. This will just be a column of 0,1,2, ... ,27
Step 2:
Assuming you start 0 in A2 then in B2 you would use
=Binom.Dist(
A2,
27 for number of attacks in short rest period,
0.25 probability of d20 rolling a miss by 1-5, ,
False for exactly this number of success. True would be for cumulative.
Copy Paste this formula on down.
Step 3:
Make a column of weights in Column C 0,1,2,3,4,5,5,5,5,.....5
*
Note: Ends at 5 because you only have 5 superiority dice in a short rest period.
Step 4:
D2 = B2*C2
D3 = B3*C3
Etc.
Step 5:
Sum up column D.
This is the expected number of dice you will use on average for precision attack in a 8 round and 1 action surge short rest period when using them anytime you miss by 1-5
Results -
Binomial Distribution Process results = 4.75
Chance of converting a miss of 1-5 to a hit = 80%
Damage = 17
= 4.75 * 80% * 17 * 2 since only doing the first rest period and we have 1 other.
= 129.2 Damage. Divide by 16 Rounds
=+8.1 DPR from precision attack for the level 11 GWM Fighter.