Analysis of crit rate

Discussion in 'General Archive' started by _Baragain_, Aug 18, 2016.

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  1. _Baragain_

    _Baragain_ Living Forum Legend

    Earlier this evening I got in a discussion with a friend regarding crit rate. They were convinced that 50% is not 50% and that it is closer to 20% and talked about times where they got 20-30 non crits in a row despite having 60%+ crit rate. I wasn't buying it, so I wanted to dig a little deeper. Using the video I made for the Solo Khalys thread, I watched it frame by frame to record the damage, what attack it was, and if the attack crit. I then performed two mathematical analyses.

    The first was the running average. This is the average taken after ever attack to see how it starts to approach the expected value (which in this case is 60.37%).

    The second was local average. This value averaged the 10 attacks before a given attacks with the current attack and the 9 attacks after. This lets you see when tbe running average is improving during a period of time and when the running average is dropping.

    The graph is seen here:

    Here is some of what can be learned from this graph:

    1. "Streaks of luck": Just about any time we talk about random in this game, we talk about how the PRNG is broken and results in streaks of good luck and streaks of bad luck, As you can see, I started off with an early streak of bad luck that kept me below the 60.38% expected value for all but a short while, and things did not improve until just past the half way point where there was a streak of good luck. Actually, that streak of good luck is more surprising than the bad luck. For a period of 22 attacks (87-108, inclusive) the local average was 80%! That is an insane streak right there because it means that in a given set of 20 data points (87-106, 88-107, or 89-108), 4 out of every 5 hits was a crit as opposed to 3 out of every 5.

    2. Time and the law of averages: Over any short period of time, you could have fluctuations like we saw above where the "luck" goes better or worse, but over time, these fluctuations start to work themselves out. If my fight had been longer, say 10 min instead of 3:30 min, then maybe it would have started to line up even better with the expected crit rate.

    3. Human perception is flawed: Not calling my friend a lair (I'm sure that it was simply an exaggeration), but the odds of getting 30 attacks in a row without a crit when you have a 60% crit rate is incredibly small... 1.15x10^-12 small. To put it in easier to comprehend numbers. That if you did 30 attacks in a row and recorded each of them, there is only a one in 867 billion chance of this occurring. The PRNG may not be perfect, but it isn't that bad either. Human beings generally have a bad sense of numbers and tracking these sorts of things. The longest unbroken chain of crits I saw was two instances of 6 in a row (4.67% chance of occurring for any given set of 6 attacks), and the longest chain of non-crits I had was one instance of 4 in a row (2.56% chance in any set of 4 attacks). Neither of these sets is outside the realm of believability since there are 123 and 125 sets respectively.

    All in all, while BP's PRNG may have it's flaws, it seems to work right if you pick a large enough sample size. It is no different than flipping a coin over time. I would not be shocked if a coin flip plot looked similar to this graph, only centered around the 50% mark.
  2. Play.4.Fun

    Play.4.Fun Someday Author

    I played with my char that have 9,38% or crit rate and another with 22,48% and another with 41,28% .... and must say difference between last two are marginal to me. Maybe my "human perception" is flawed but it seems that difference between 30% or 40% is so marginal. In other word you need difference larger than 10% to have realy benefin in game.

    If you are willing repeat this math when you lower crit rate of your char to 50/40/30% that would be realy interesting.

    (Sorry for spelling mistake.... just drinking morninig coffe).
  3. _Baragain_

    _Baragain_ Living Forum Legend

    Sure, but if I do it again, I'm going to be lazy and use my basic attack against an easier boss for two reasons. First, counting the hits will be easier. Second, I'll have a much larger data pool... maybe 300+ data points as opposed to 128. But first some sleep. You may be drinking your morning coffee, but I'm going to bed after being up for 24 hours straight.
    thebearreturns likes this.
  4. thebearreturns

    thebearreturns Exceptional Talent

    Yea, many times i'm playing and like: oh man! 4 consecutive hits and no crit!, Or 2 iron brows and no crit!... but then realizar the rest of the time i'm getting yellow numbers!... i mean with that... i get used to yellow numbers SO MUCH that, when they doesn't appear i feel it A LOT.... so i feel more perception when they are not THAN when they are... and THIS makes the feeling of getting worse yellow numbers than the crit rate i have... it's just subjective ... but this is my point, doesn't mean to be the same for every one ;)
    It's also kinda like looking for fissure portales of matery frags... bara told they appear like 1/4 maps... and i even run 14 maps entries without!!... but later i did like 3 consecutive succesfully entries, my rate is 1/8 but i was thinking it was even worse , also may be depends on the day.
    Btw what does it means PRNG? Is it something like "Programmed RandomaZinG"?
    Last edited: Aug 18, 2016
  5. _Baragain_

    _Baragain_ Living Forum Legend

    PRNG Means "PseudoRandom Number Generator." Computers are very bad at making random numbers and can't do true randomness. Instead, there are algorithms that can generate numbers that appear random, but it follows a formula. Good PRNGs look rather random in "small" sample sizes (small being like 10,000 data points or less), but bad PRNGs can get stuck and start producing recognizable patterns over short periods of time.


    Here it is. I did the analysis with Heredur I with 60.37%, 40.73%, and 25.69% crit rates and the results pretty much followed what I expected.

    This round started off with a streak of good luck and the rest of the fight was spent slowly moving the average towards the 25% mark. The final average was 28.79% over the 131 attacks. With the exception of one period of really bad luck, this fight was really crit heavy for the rate.

    This one went back and forth at the start, but it quickly settled into an average crit rate that closely approximated the expected crit rate. In fact, the final average was 41.88%, but you can see that it regularly fluctuated over and under the average.

    This one surprised me. It started out really bad with a 40%-50% rate for most of the beginning due to some really bad luck. I was wondering if I was going to have to explain that even a sample of 117 is "small" and odd things happen in small batches. Then, at about the half way point, the crits noticeably improved and you can see that for the more than the last half of the run, the local average stayed over 60%. Because of the incredible streak for the second half, it ended at 59.32%. However, if we just consider from that point where the luck turned, the average was 67.64% while the average leading up to that point had been 50.0%. It just goes to show the same thing I talked about in the opening post that the PRNG seems to get stuck in ruts sometimes, but these ruts usually work themselves out over time.
    thebearreturns likes this.
  6. Dragonnns

    Dragonnns Forum Veteran

    Interesting... (I know, silly word but really.. it is!)

    Thanks for taking the time to spell it out. It is almost as if DSO rewards you if you stick it out.
  7. _Baragain_

    _Baragain_ Living Forum Legend

    Or the PRNG gods start to penalize you if you start out with too good of luck (looking at you, Mr "25%" case :p).

    On another note, when I gathered this data, I also tracked which attack I used and the damage done. I'm thinking that for my next math project, I'll normalize the data by dividing the data by my crit damage and the %damage of the skill and the 50% reduction that monsters have and build a bell curve (or at least I expect it will be e bell curve) of what damage I'm doing in my range of damage. I mean, we all know that if your damage is 4000-6000, most of your hits will likely be in the 4500-5500 range while the 4250-4500 and 5500-5750 ranges are more rare, and rarer still should be the 4000-4250 and 5750-6000 ranges. Expect that sometime in the next couple of days.
    Troneck86 likes this.
  8. thuglifederp

    thuglifederp Active Author

    Is Baragain human ?? o_O
    Last edited: Aug 23, 2016
    thebearreturns likes this.
  9. silverseas

    silverseas Forum Commissioner

    I have a different crit-related question. It be somewhat subjective. :p What quantity of change in crit rate would actually be humanly perceptible [in your opinion]?

    I ask this because if I upgrade one item and gain a fraction of a percent of crit, I certainly don't notice a difference. Ditto if I lose that fraction of a percent. Sometimes (Ok... lots of times in my case) I have traded items that technically have lost me dps because of a moderate dip in crit rate, but made gains elsewhere, but I can kill that much faster with that trade off.
  10. _Baragain_

    _Baragain_ Living Forum Legend

    I'm part calculator. :p:D

    I can actively "feel" the difference in about 10% crit rate, most noticeably when it comes to healing. Because I have nearly x3.0 crit damage, when I heal and don't crit, I may get 2k-6k back depending on my essence, but with a crit, I get back 6k-16k. When you "only" have 14.5k HP, that is either 1/7th of your HP, or nearly half (with greens), and when you are low and hoping for a crit to fill you up, it really hurts when you don't. In my 25% fight, I had one time where I did 8 spins in a row with my basic attack in between, and of those 8, only one crit.

    I can also perceive a difference as small as 5% when gauged against an average. For example, if I can usually do 10x three boss runs of Stonekeep in 20 min, and then I switch some gear around and only lose 5% cirt and those same 10 runs take me 21 min, then I can tell the difference by looking at the macro scale, even though I may not actively feel it. I just keep pushing for two reasons. First, the little differences will eventually add up, and second, the math doesn't lie and I think that differences of as little as 1% should start to show up when you are talking about 100-200 attacks, and differences smaller than that show up for even more data. Ask yourself this. How many times do you hit an enemy (point targets and AoE) in a given day? Just doing dailies, most hit and kill 1000 monsters and most of those monsters take 2-3 hits to kill. That is likely 2500+ hits in a day, and a difference of 0.5% crit rate is a difference of 13 crits a day. If you are talking about doing a serious farming day and you brun through an entire parallel world in one day while helping a friend, that is easily 3000-4000 enemies with approaching 10000 hits and that half a percent could account for as many as 50 crits in a day. While this isn't huge, it doesn't hurt either.

    Finally, you touched on the most important part right here:
    Sometimes a small loss in one place can mean huge gains elsewhere, and vice-versa. My target DPS to get to is 27k-28k while still being reasonably strong defensively. I could push that DPS higher using other sets or items and push that target to over 30k, but that 2k-5k DPS that I think I could get would come at the expense of making a glass cannon 2H DK which is next to worthless except while fighting monsters who don't need that sort of DPS to begin with. If my math is right, I'd have only about 55% armor, 8k HP, and no blocking stats to help a little, and that is unacceptable losses for something as small as 2k-5k DPS compared to the total DPS we are talking about... 10%-20% more DPS, but at a loss of over 50% of my effective HP. If you are chosing to lose 1%-2% crit rate, but you gain 1000 HP, then you should probably go for it. If that 1%-2% loss only gets you 200 HP, the I'd stick with the crit.

    In the end, it is all about feel, and while math may not lie, you need to have confidence in your equipment. I have confidence because of the math, but some people out there will ignore hard evidence if it conflicts with their preconceived notions. I hope my math helps, and that you find the balance that is needed between offense and defense to do whatever you want to do.
  11. silverseas

    silverseas Forum Commissioner

    Interesting. My primary skill of choice to use is Frozen Sphere, so it does something like 3-4 (I tested this months ago, but I just can't remember off the top of my head how many) small hits and then the 1 bigger explosion at the end. Since every skill cast is a multi-hit, I can notice a difference of about 2% change in crit rate since I have that many more numbers popping out at me.
    Wow, you actually said feels>math. #shocked :eek::D:eek::D:eek:
  12. _Baragain_

    _Baragain_ Living Forum Legend

    But I also said that my feeling is informed by the math. :p
    thebearreturns likes this.
  13. silverseas

    silverseas Forum Commissioner

    Go work on your damage output thingy and I might be able to use math to support my build and play style too. Otherwise I rely on flailing around to see if it works. :p
  14. trakilaki

    trakilaki Living Forum Legend

    Baragain ... I will challenge you on this one! :p
    From the start ... I won't say your math is inaccurate because it is probably correct.
    But you are using wrong methods ... and your job is not even 0.5% finished :D
    But later man ... i have a work to do at TS and Wiki :p
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