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    Regarding Hit Chance, Critical Rolls

    In your Pirate101 career, you might have heard something about hit chance or hit chance / critical priority...


    As for me, I've heard various things, including...
    ー Hit chance = 75 + Accuracy - Dodge
    ー Hit chance is bounded between 5% and 95%
    ー Criticals apply before hit chance
    ー Hit chance applies before criticals

    Before looking into anything, though, the only knowledge I had of these things (the first point in the list above) came from an outdated, official Pirate101 guide.
    Other things were things I heard or assumed to be the case.

    During my investigation, I looked at critical roll / hit chance priority and minimum hit chance.
    This article states the conclusions I arrived to.


    Minimum Hit Chance
    Before I initially investigated critical roll / hit chance priority in June 2021, I assumed the minimum hit chance to be 5%.
    However, during the initial testing, I noticed something interesting: that the minimum hit chance in my sample most likely isn't 5%.



    (Regardless of whether Criticals were included, the proportion of hits was not 5%.)

    This was consistent between all of the data sets I collected at the time.

    I remember thinking it might have something to do with the bonus Critical Chance I had, but I was not sure if my testing at the time was adequate enough.

    Several months later, I remembered this and decided to test it a few times.
    I assumed that the minimum hit chance wasn't 5%, so I ran some tests against the hypothesis that the minimum hit chance was 5% (noted as the 5% Hypothesis, for easy reference).


    1st Test (Ninja Pigs)
    First, the enemies in the Hamamitsu Kitchen instance, consisting of Level 49 - 50 Swashbuckler and Musketeer enemies.
    I assumed their highest Accuracy was 108 (the highest possible Accuracy for the Level 50 Musketeer enemy in that instance, and Musketeers exceed other classes in Accuracy), while the Pirate I tested it on had 198 Dodge.*

    The resulting hit chance would be….
    Hit chance = 75 + Accuracy - Dodge
     
      = 75 + 108 - 198
        = -15
    ...which would cap off at 5% if the 5% Hypothesis was true.
    *Elusive 2's Dodge boost results in the same hit chance, regardless of whether the 5% Hypothesis is true.

    Additionally, I had a +2% Critical Chance bonus on all of them, so they had no bonus Critical Chance on me.

    Of the 342 attacks recorded:
    ー Criticals: 14 (~4.094% of total)
    ー Hits: 123 (~35.965% of total)
    ー Misses: 205 (~59.942% of total)

    If we assumed Criticals rolled before hit chance, the corresponding hit chance would be 37.5% (123 / 327).
    The corresponding z-score would be z = -12.15807002, resulting in a p-value of about 2.598 × 10
    ³.
    This means that assuming the minimum hit chance is 5%, the probability of landing 37.5% of hits in a sample of 327 is about 2.598 × 10³.
    (Okay, you get it, it's practically zero. lol)

    If we assumed Criticals rolled after hit chance, the hit chance changes to about 40.058% (137 / 327).
    The corresponding z-score would be z = -13.23107167, resulting in a p-value of about 2.903 × 10
    .
    This means that assuming the minimum hit chance is 5%, the probability of landing 40.058% of hits in a sample of 342 is about 2.903 × 10.
    (That's even closer to zero, geez...)

    Regardless of critical roll / hit chance priority, the 5% Hypothesis was rejected, leading me towards the thought that the minimum hit chance was not 5%.
    I thought after that that it might be near 35%, but wasn't sure at the time.
    I decided to carry out a few other tests to see if this conclusion was consistent.


    2nd Test (Pirate Sparring)
    The next test consisted of my Level 15 Witchdoctor attacking my Level 69 Swashbuckler.
    Their stats were:
    ー Witchdoctor: 25 Accuracy, 27 Agility
    ー Swashbuckler: 198 Dodge, 98 Agility
    Thus, there was no bonus Critical Chance, and the hit chance would be 5% if the 5% Hypothesis is true.

    Of the 300 attacks recorded:
    ー Criticals: 2 (~0.667%)
    ー Hits: 52 (~17.333%)
    ー Misses: 246 (82.000%)

    If excluding Criticals, the hit chance becomes about 17.450% (52 / 298).
    This results in a z-score of about -5.663 and a p-value of about 7.457 × 10
    ⁹.
    This means that assuming the minimum hit chance is 5%, the probability of landing 17.450% of hits in a sample of 298 is 7.457 × 10.

    If including Criticals, the hit chance becomes 18.000%.
    This results in a z-score of about -7.937 and a p-value of about 1.332 × 10¹.
    This means that assuming the minimum hit chance is 5%, the probability of landing 18.000% of hits in a sample of 300 is 1.332 × 10
    ¹.

    Either way, I reached the same conclusion as I did with the first test.


    3rd Test (Troggies)
    To conclude my minimum hit chance testing, I designed a test to see how often the Flooded Shrine's enemies would land a hit on me.
    The enemies were Troggies (all three types), Level 1 - 2, and I was testing as a Level 69 Swashbuckler with 198 Dodge, so they should theoretically have a 5% chance to land a hit on me.
    (If you Charm and use Espirit de Corps on the same turn, you'll see that they gain a boost of at most 1 - 2 Accuracy. The Level 2 Troggy Hunter actually seems to lose Accuracy from Espirit de Corps...)
    Also, my lowest stat was Will (which, I had 39 Will), which I still had bonus Critical Chance with (+11% vs the Level 2 Troggy Shaman enemy).
    Therefore, I assumed that they had no bonus Critical chance on me.


    Of the 307 attacks recorded:
    ー Criticals: 4 (~1.303%)
    ー Hits: 50 (~16.287%)
    ー Misses: 253 (~82.410%)

    If excluding Criticals, hit chance is 16.502% (50 / 303).
    This results in a z-score of about -5.394 and a p-value of about 3.453 × 10
    .
    This means that assuming the minimum hit chance is 5%, the probability of landing 16.502% of hits in a sample of 303 is 3.453 × 10.

    If including Criticals, hit chance is 17.590% (54 / 307).
    This results in a z-score of about -5.794 and a p-value of about 3.441 × 10
    .
    This means that assuming the minimum hit chance is 5%, the probability of landing 17.590% of hits in a sample of 307 is 3.453 × 10.

    Either way, I was led to the same conclusion as in the previous tests ー that the minimum hit chance was not 5%.


    Critical Roll / Hit Chance Priority
    To test which occurs first, I conducted a brief experiment, where my Level 15 Witchdoctor attacked a Level 49 Sky Snake companion, collecting two sets of 305 attacks each.
    One set would have +1% Critical Chance (close enough to +0%), while the other would have +23% Critical Chance.
    At 25 Accuracy and 100 Dodge, hit chance was minimal (whatever it actually was).

    In theory, if Critical rolled before hit chance, then in the data for +23% Critical Chance, we'd see about 28% of the sample data landing Critical hits.


    Landing Attacks: 1% vs 23% Critical Chance


    +1% Critical Chance +23% Critical Chance
    Criticals 9 (2.9508%) 32 (10.4918%)
    Hits 119 (39.0164%) 85 (27.8689%)
    Misses 177 (58.0328%) 188 (61.6393%)


    Of the 305 attacks recorded in the +23% CC data, 32 were Criticals (10.4918%).

    In doing a hypothesis test, the z-score would be about 9.9778, resulting in a p-value of about 9.532 × 10
    ².
    This means that assuming critical rolls take priority over hit chance, the probability of landing 10.4918% of hits as Criticals in a sample of 305 with 28% Critical Chance is 9.523 × 10
    ².

    I reject the hypothesis that Criticals apply before hit chance, concluding that hit chance applies before Criticals.

    This further supports Ratbeard's official statement regarding Critical chance / hit chance priority.
    (...which I found after doing my testing...go figure, lol.)


    Minimum Critical Chance
    The September 2016 patch notes state that 1 Critical Rating = 5% Critical Chance.
    By then, it was intuitive to me that base Critical chance is 5%.

    Thankfully, I did not have to test this, as Ratbeard did officially state that base Critical Chance is 5%.


    Speculation / Guesses
    I briefly looked up posts to find more information on minimum hit chance.
    Unfortunately, though, I could only find two posts.

    One post I found states that the minimum chance of hiting is 5% to 10%.
    However, my data does not support that statement.

    The other post I found stated that it's about 20%.
    This isn't far off from what I thought at first, as it agrees with what my second and third tests would imply.
    Admittedly, though, this doesn't account for my first set of test data, or in my data sets while testing Critical roll / hit chance priority, all of which had total hit chances of approximately 40%, even though hit chance was at its minimum for all testing setups.


    Also, my data has since disproven my initial thought that the minimum hit chance was 5%.
    For now, all I can say is that I don't know what it is, and that it's likely bounded between about 15% and 40%.
    (Good grief, if that comparison function is somehow involved in thisー)


    Summary
    The minimum hit chance is not 5%. It's likely closer to about 15% - 40%, but the actual value is unknown.
      The reason for this is currently unknown, but it definitely warrants further investigation.
    Criticals apply after hit chance.
    Minimum Critical Chance is 5%.

    The only question left is what the minimum hit chance is, exactly. (also consider that it's different for different attacks ― e.g. Blade Storm 3 uses primary stat comparison instead of Accuracy and Dodge, Ratbeard's statement on this can be found here)
    However, analyzing it properly would take many hours of data collection that I am not currently able to spend, not to mention that I have no idea on what the potential factors could be. (I don't feel like speculating, either, and I haven't encountered any leads.)

    Until then, perhaps it'd be nice to get an official statement from the developers regarding minimum hit chance.
    Honestly, it would be highly appreciated, but it isn't something someone like me can just go and ask.
    (Maybe someone else could ask for me..?)


    Thank you for reading this short article.
    If there are any questions, please feel free to leave a reply, and I'll try to answer to the best of my ability.
    Until then, stay safe, and happy Piratin'!


    This post contains 1 auto-link(s) to our wiki for your reference.



  2. The Following User Says Thank You to Cody Nightblade For This Useful Post:

    RealDux (08-03-2022)




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