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    Turn the Tide 5 Does Not Give Flat +25% Crit Chance

    Hello.

    It has been brought to my attention that some people think that Turn the Tide 5 grants +25% Critical Chance, in addition to the Weapon Power, Accuracy, Dodge, and Strength bonus that the previous four ranks grant.

    One of my friends ― @ultimatewizardx, in fact ― suggested that Turn the Tide 5 does not grant a flat +25% Critical Chance.
    He mains Buccaneer in PvE, has been playing for a while, and has tested Turn the Tide 5 before arriving to this conclusion, so I trust his statement.
    However, I decided recently to get some conclusive evidence to support the opposing statement ― that Turn the Tide 5 grants a flat +25% Critical Chance below 50% HP.
    Therefore, I decided to conduct an experiment to see whether Turn the Tide 5 did actually work as stated.
    Details on the experiment and its results are listed below.

    Experiment Setup

    To demonstrate the supposed effect of Turn the Tide 5 on bonus Critical, I set up an experiment to measure the proportion of criticals my Buccaneer Pirate landed on an enemy.
    Details of the experiment's setup are listed below:
    ― Attacks are recorded in a spreadsheet with the note of whether the attack was a critical hit, or the attack was not a critical hit.
    ― A set of trials will be conducted to obtain a proportion for the data, and approximation by a Normal distribution will be used to calculate a probability value that determines whether the following hypothesis should be rejected:
      Hypothesis: Turn the Tide 5 grants a flat +25% Critical Chance under satisfactory conditions (<50% HP).
    ― Information about the battle setup:
    ※ Critical Chance Setup
      Critical, excluding TtT5:
        Base ― 5% → 0.05
        Critical Mastery Bonus ― +0% → +0.00
        Stat Bonus Crit ― +3% → +0.03
      Hypothesis:
        TtT5 will grant a flat +25% Critical Chance.
         Expected Critical Chance ― 5% + 0% + 3% + 25% = 33% → 0.33
      Rejection of hypothesis:
        TtT5 does not grant a flat +25% Critical Chance.
         Expected Critical Chance ― 5% + 0% + 3% + 0% = 8% → 0.08

    ※ Character / Enemy Information
      Relevant Character Stats:
        Strength: 85 (before Turn the Tide 5)
          No Strength buffs [or debuffs] were used on the Pirate during testing.
      Relevant Enemy Information:
        Enemy: Diskylos
          No Strength [buffs or] debuffs were used on Diskylos during testing

    ※ Accepted Attacks
        Any attack the Pirate uses that does not have an inherent property of increased Critical is counted as long as Turn the Tide 5 is active when the attack happens.
        This includes, but is not limited to:
        ― basic attacks
        ― Buccaneer charges
        ― Relentless 2 / Blade Storm 3

    Results + Conclusion

    A total of 345 attacks were recorded (over a period of approximately 2 hours and 50 minutes).
    Of the 345 attacks dealt, only 26 of those attacks were Critical hits, yielding a proportion of ~0.07536 (~7.536% Critical Chance).
    Using the hypothesis stated above, I obtained a z-score of -10.05860716.
    The corresponding p-value is 4.2090 ✕ 10-24.
    This means that if the hypothesis is true, then the probability of obtaining a Critical hit proportion of 0.07536 over 345 attacks (26 Critical hits over 345 attacks) would be approximately 4.2090 ✕ 10-24.
    This is highly unlikely, so I reject the hypothesis.
    I conclude that it is likely that Turn the Tide 5 does not give a flat +25% Critical Chance when below 50% HP.

    Oh, and just to emphasize the p-value....
    That value is actually ~0.00000000000000000000000420904288106316....
    [That's 23 zeros after the decimal point, before the first nonzero digit....]

    My Thoughts

    With these results, I conclude that either Turn the Tide 5 grants +25% of your base Critical Chance when below 50% HP (+1.25% Critical Chance, which is basically negligible), or Turn the Tide 5 does not grant Critical Chance at all.
    Either way, it appears to be the case that Turn the Tide 5 is not worth going for if you can obtain Turn the Tide 4.

    Unfortunately, I do not have the time to analyze whether Turn the Tide 5 grants +25% of your base Critical Chance when below 50% HP.
    Such an experiment would require a stricter set of test conditions and at least 1,500 trials.... (approximately 13 hours of testing)


    Thank you for reading this post. (It might as well be a short report, considering how I've structured it....)
    If you have any questions about this, feel free to ask, and I'll try my best to answer as quickly as possible.

    [I will likely be sending an email to KI Support in a day or two regarding TtT5 not granting +25% Critical Chance below 50% HP, linking this thread and the spreadsheet (with the raw test data) as supporting evidence.]
    Last edited by Cody Nightblade; 10-09-2020 at 12:24 AM. Reason: corrected something to proper English, added some other information as needed



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  3. #2
    RealDux's Avatar
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    My Pirate101 Character is a Musketeer

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    Re: Turn the Tide 5 Does Not Give Flat +25% Crit Chance

    Very provocative investigation! I've always assumed it was a straight 25% like the rest.

    It could somehow scale with the natural bonus, which might've resulted in the very low numbers having tested on another buccaneer?

    You did some excellent number-crunching and I can't wait to see the results on more classes. Perhaps those other pieces of information can lead to a more clear conclusion.

    "Blessed are those whose ways are blameless, who walk according to the law of the Lord." Psalm 119:1



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    Re: Turn the Tide 5 Does Not Give Flat +25% Crit Chance

    Quote Originally Posted by RealDux View Post
    Very provocative investigation! I've always assumed it was a straight 25% like the rest.

    It could somehow scale with the natural bonus, which might've resulted in the very low numbers having tested on another buccaneer?

    You did some excellent number-crunching and I can't wait to see the results on more classes. Perhaps those other pieces of information can lead to a more clear conclusion.
    Might I ask what you mean by "natural bonus"...?
    If you mean the stat-based Critical Chance boost, I'd think you might be implying that the game would take 25% of that Critical Chance boost.
    I highly doubt the game would go to such extent, but I would need to test that to be sure. (est. 650 trials)
    However, if you mean the base Critical Chance (which has been estimated to be 5%), then that would be one of the theories I mentioned in the OP, which would require testing with 1,500 trials to reject or fail to reject said statement.



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    ToonTown565's Avatar
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    Re: Turn the Tide 5 Does Not Give Flat +25% Crit Chance

    yeah tide 5 is bugged- had tide 5 on my buck for a long time and there's no way it's giving an extra 25% (which idk might be good, an extra 25 crit chance for tide would probably be broken)
    Indeed!
    Verily, I say...
    Ergo!



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  8. #5
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    Re: Turn the Tide 5 Does Not Give Flat +25% Crit Chance

    besides Diskylos have you considered or tried another boss? Just curious because maybe the factor of the enemy's crit chance can be thrown into the equation, too. Ya never know. That, and maybe grab test subject vs test subject data.... unless that's existed, and I wasn't completely aware.
    Last edited by Crushcut; 10-17-2020 at 02:41 PM.



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    Re: Turn the Tide 5 Does Not Give Flat +25% Crit Chance

    Quote Originally Posted by Crushcut View Post
    besides Diskylos have you considered or tried another boss? Just curious because maybe the factor of the enemy's crit chance can be thrown into the equation, too. Ya never know. That, and maybe grab test subject vs test subject data.... unless that's existed, and I wasn't completely aware.
    Interesting.....

    Honestly, when oding these tests, I assumed that the chance the enemy had to critical did not affect my chance to critical on them.
    My idea for Critical Chance was that the total Critical Chance was equal to your base Critical Chance (assumed to be 5%, as 1 Crit Rating is 5% Crit Chance), plus Talents (Critical Mastery, Turn the Tide 5) and buffs / debuffs.
    This model does not take into account the enemy's chance to critical.
    The reason why this would be hard to test is that I would need someone with the same Strength stat as Diskylos (plus, say, Critical Mastery and extra Critical Chance through stat bonus of eithe1r Agility or Will, whichever is chosen for attacking).
    At least to my knowledge, no one has any data on Diskylos's stats. Also, getting the appropriate stats for such a test likely requires another max Pirate.

    If I could, I would have gotten test data for Pirate v. Pirate, as that would be the experiment setup with the most information ― you know your base Critical Chance, bonus Critical Chance, etc.

    Honestly, this sounds like it would be a potential factor for either TtT5 or Critical Chance in general....
    I would love to say that neither are true, but we cannot say for sure unless we see the game's source code (which is not going to be given for obvious reasons), although more testing might be able to shed some more light on this.


    Unfortunately, I am getting pretty busy with real-life stuff, so I might not be able to carry out more trials for a while @[email protected] apologies.
    Good news though, it seems Kingsisle has responded to my email and has all the necessary information for the bug report (meaning that all of the needed work on my end is done).



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