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The law of averages

Discussion in 'Off-Topic' started by BlueRuby, Mar 28, 2019.

  1. BlueRuby

    BlueRuby Well-Known Member

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    Within alliance chat, we’ve been discussing how averages work, in this case, around the loot wagon chances of receiving a shard.

    My fellow warlord seems quite clued up, enjoys a 50% drop rate, and emphasises the chances are the same for all, calculated for each individual warlord, therefore we should all receive the same.

    I hope I’m clued up in my own way, seem set at a 30% drop rate and suggest that, though the potential drop rate is the same for all, that doesn’t need to translate practically for each individual warlord, the averages to be calculated over the community as a whole.

    On paper, the drop rate chance will be the same.
    Practically, some seem to showered in them, whilst others have to search.

    What do others think?
    Why might this be?

    Oh, and I have heard suggestions about a bias towards remembering our disappointments over our successes. For info, we’re both logging our drop rates for hard data.
     
  2. Hackuuna

    Hackuuna Well-Known Member

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    I don't really have much data to back up my theory but from my own personal experiences I've noticed that LW reward rates seem to change depending on where your regiment's shard total is at. For example, I've noticed that the last 10 shards going from 4* to 5* are incredibly low odds (It was less than 10% drop rate of shards over 100 LW) but from 30-130 I enjoyed a 50% drop rate (about 200 LW)

    I've also noticed increased odds of getting items when I have inferior gear equipped. It's definitely possible my perceptions aren't the reality but thought I'd throw that in there. Perhaps odds change depending on a mixture of your total shards for that particular regiment, what gear is equipped, and maybe other factors.
     
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  3. Dezytrius

    Dezytrius Active Member

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    I'm of the "belief" that you only get multi shard drops if you dont do LW as often per day. That if you are doing so many a day, it will simply never drop multi shards, and logically it follows to my "belief" more LW completions a day will equal less shard drops.

    Another way of stating my unsubstantiated belief is that the LW has a cap on max shard drops per day and conversely a minimum/higher chance shard drop if you do LW less often.
     
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  4. Jin

    Jin Well-Known Member

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    I've been rotating LW between 3 regiments, SM, IR & FK, in Jin2 account. For the last 6 LW, all were shards and even got a 3 shards for SM. Lucky streak!!??
     
    Last edited: Mar 31, 2019
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  5. BlueRuby

    BlueRuby Well-Known Member

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    Thanks guys,

    I only do an everage of 3 LW a day and still have low (er than other player) shard drop rates: 30% my standard. I’m also in the 3* - 4* bracket.

    I am interested in other factors: currently wondering about Owain’s theory about CVs affecting drop rate: other alliance members playing around with this and noticing an increase. I will too.

    And, as Primer suggests, it may just be random, which prompted my asking the above here in the off-topic section. There is already a shard-drop rate-thread in general, so I won’t seek to include it here. Mostly, I was wondering if any clever peeps had an idea about how ‘average’ works?

    (Don’t get too caught up in the loot wagon part here, but) I’ve been counting for 167 Loot wagons now and 30% shards is a standard figure for me: was 33 at 100 loot wagons.
    Others report an easy 50% rate and, though over a smaller sample, others reporting something much higher.

    Why do people receive different ‘averages’? One approach is that it should work the same for all.
    And maybe it does, given a sample size of 1000+ each, say.
    And, maybe, it doesn’t: that, maybe, the average is for the community overall; that some will receive higher, while others receive lower - it’s the community average that works, not necessarily the individual average.

    Wondering if there’s something in this...or if the inside of my head needs a spring clean?
     
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  6. BlueRuby

    BlueRuby Well-Known Member

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    Goes looking for the feather duster to pass between the ears...
     
  7. Primer

    Primer Well-Known Member

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    I will say this (and whether others do or not I cannot say).

    There have been very few times I have made the effort to record every battle necessary to determine an “average”. I have taken the approach if I do 6 to 7 LW each day and then average out what I receive over 20 or 30 days. Not scientifically accurate by any stretch of the imagination.

    But I also think the Devs make behind the scenes changes they don’t announce. Two examples.

    When I first became all 5s I started using PES to fight all my LW battles. Upgrade Ceremony of Sun is worth the most gold and I need a Prophets Armor.

    The first three weeks, I averaged 2.5 shards per day. I did not record exact number of fights, but there was nothing unusual afftecting my game play so I am comfortable it was normal. That was Feb 28 that I started.

    I now have 115 PES shards. A bit over 5 weeks. 23 per week or 3+ per day. Even more when you take into account the 2.5 average before. I think shard drop rate went up about 3 weeks ago, but have absolutely no evidence other than my total going up more than expected.

    Maybe this is Explains different results, maybe not. Some players are meticulous about what they record and I respect what they do. I am not one of them.
     
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  8. BlueRuby

    BlueRuby Well-Known Member

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    @Primer thanks for the reply :)

    How and what we record is certainly a factor.
    I, personally, am not being ‘scientific’ about it, seeking necessarily to isolate the causes of particular dynamics through rigorous testing and recording. As such, the results of my recording are going to be rough; are probably going to be rough for most peoples’ results.
    Still, whilst not of a standard bone fide scientists would put their name to, they do provide a picture: a broad-brush sketch, maybe, rather than fine art. Still, a picture anyone would recognise.

    It could very well be that my samples are still too small to find the average.
    You yourself, Primer, see, to be reporting a shard drop rate of something akin to 50%. This accords with others in my alliance.
    However, I’m closer to 30% over a similarly-sized sample:

    Why would this be?

    In my recording, I am noticing certain differences:
    I’ve put in another thread, my results so far:

    To get my weaker units to 3*, I’ve been taking out my ‘C’ team for loot wagon battles, rarely getting CV’s, and achieving a 30% shard drop rate (67 shards / 200 LW’s)

    Now I’ve switched to my A team to get them to 4* and always get CV, now receiving a shard drop rate of over 50% (currently 21 shards / 35 LW’s).

    A small sample, admittedly; it could be coincidental...and...just as you were wondering a while ago about the incidence of 4S battles in pvp for different people (in fact there were several threads involving many along these lines: top warlords seem to have too few; I was getting too many), I too am wondering about shard drop rates in relation to CV’s, troop quality and luck...

    Do some people benefit from more ‘luck’ than others?
     
    Last edited: Apr 8, 2019
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  9. Lundene

    Lundene Member

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    really think that it’s an understanding of the mathematical algorithm used by the programmers that influences the drops and the perception of luck. I suspect they create a loot table from existing upgrades, mythical items and shards with set boundary conditions as per the smuggler ships. We know that by leaving an upgrade needed free we can get that upgrade (I.e reduce potential outcomes for upgrade to just one). The simple routine may be 45% chance shard, 45% chance upgrade, 10% item when a CV occurs (30% hard, 60% upgrade, 10% item when V). This is simple to create programmatically and has same luck for all times you do a LW.

    though it does mean a person can be unlucky and have a run of upgrades but each time the event is independent of last event - effectively the chance of getting 3 upgrades in a row would be 9.11% odd but still possible I.e 1 in 11 people will get 3 upgrades in a row (be considered unlucky) and conversely 1 in 11 will get 3 shards in a row as each time the chance of getting a shard etc is independent of last one. Just means you are a statistical outlier on the probability function.
     
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  10. Hackuuna

    Hackuuna Well-Known Member

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    I used to think it was a simple loot table lookup but I've encountered a wall far too many times now that I'm beginning to think it's not just an outlier. I tend to focus on one regiment at a time so I mostly collect LW with the same regiment for more than a month at a time and every time I'm nearing the end of collecting with that regiment the rate of shards drop immensely.

    It could happen that I'm an outlier, it could also be some sort of throttling mechanism to prevent folks from accumulating too quickly, or it could even be a mechanism that throttles at certain thresholds. This time I'll be collecting with 2-3 different regiments and randomly rotating through them to see if I encounter the same wall.
     
  11. Primer

    Primer Well-Known Member

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    Another thing to keep in mind...

    It is very possible the Devs make changes that we are not aware of behind the scenes. This could explain why things seem different at times.

    We used to get 5v7 PVP and 203t battles. I doubt anyone has seen these in the last half dozen seasons. Never announced, just changed.

    I went three weeks averaging 2.5 shards per day for 7 to 8 LW battles. The last three weeks I have averaged 3.5 shards per day for the same.

    It also seems my Stronghold battles have gotten harder. I am not able to get as far as I used to before I start losing multiple units.

    All seemed to change about the time scrolls were introduced.

    But of course, it could all be my imagination (except for 5v7 going away - that is real).
     
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  12. Lundene

    Lundene Member

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    Agree primer that devs can make changes to fine tune the game behind the scenes. This also leads me to conclude that they are using an algorithm for each LW with % chance for shard etc. this means they can make changes without causing an unintended bug else where in the game (which can easily happen when you change code).
     
  13. Hackuuna

    Hackuuna Well-Known Member

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    I agree. I was looking forward to 5v7 and notice I haven't seen a single one since returning to play.
     
  14. Enodrevo

    Enodrevo Active Member

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    One thing to consider is the mathematical term "variance." Over the long run two series of random events may have the same average result, but one may have greater variance- a greater swing from top to bottom.

    Think of rolling to 6-sided dice and adding the total. The average is 7. If you changed the dice and removed the 3 and 4 from each die and replaced them with 1 and 6 respectively. Now your dice numbers are 1, 1, 2, 5, 6, 6. You still get an average of 7 when you roll and add the numbers, but your going to also get a lot more rolls of 1 and 1 or 6 and 6 (totalling 2 and 12 respectively). The average is still the same but you will be prone to more "bad rolls" or "awesome rolls."

    Conversely, if you replace the 1 and 6 with 3 and 4, you still have an average of 7 but will never get a total of 2, 3, 11 or 12. The same average but much smaller variance. If you change the dice so that one is all 3 and the other all 4 you only get a roll of 7. Same average and 0 variance.

    Over enough rolls all these dice average out, but the swing from extreme to extreme means it takes more rolls to show the average.

    I think LW have a high variance.
     
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  15. Hackuuna

    Hackuuna Well-Known Member

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    What makes you think that?
     
  16. BlueRuby

    BlueRuby Well-Known Member

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    Thanks, Enodrevo, that really makes sense to me.

    Still 1 question(s): why do some reasonably reliably achieve a 50% drop rate, where I was reasonably reliably achieve 30%? (It has gotten better now I’m working with my A team and getting CV’s...though, maybe, this doesn’t really mean anything?).
    Shouldn’t we all get similar variance? How big a sample do you feel is reasonable before we can feel confident about our averages?
    ...or, maybe, I can look forward to a 70% drop rate soon to make up for it...?

    ...or am I being blind and still missing what you were saying?
     
    Last edited: Apr 23, 2019
  17. Enodrevo

    Enodrevo Active Member

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    I think it's high because lots of people go a long time with few shards and others get runs with many shards.

    No, you get it. The higher the variance the larger the sample size you need to see it average out. Over all the thousands of players, it probably averages out daily. But for a single player it may not average out until you've had 1000 LW.

    If for argument's sake the drop rate is supposed to be 50% (it may only be 30 or 40 and your friend is having an awesome run!), you may run at 30% for 100 LW, then at 55% for 400 LW. You "feel" like the 55% is back to normal but it is slightly higher. Over 500 LW you average 50% but it always seems like you had that run of bad luck that the game never "made up" for. The high variance means the bad run is more dramatic but eventually it all evens out.
     
  18. Primer

    Primer Well-Known Member

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    I still like my theory best. Not mathematically based, but proven in many psychological studies.

    We “expect” a good result (in this case assume we want shards). When we get that good result we dismiss it from our minds because, after all, that is what it “should” have been. When we get something else, we are disappointed and remember that disappointment.

    I do believe the math evens out in the long, long run. But I also believe the Devs adjust the formulas from time to time without telling us. They have admitted to doing it for what type of opponents we spawn, why not for rewards also? Some rewards updates have even been made in the Announcements section.

    I still remember ships giving shards for units that were already 5star instead of them being guaranteed to be something you still need. Sooooo glad they stopped that.
     
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  19. BlueRuby

    BlueRuby Well-Known Member

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    I like them all:

    The mathematics of the averages, the idea that there are some hidden factors, which may influence the drop rate, the idea of ‘luck’ and the idea that we notice our disappointments more. We may never really know, in the case of shard drop rates from the loot wagon: it may be 1, it may be all 4. I suspect all 4.

    And I really like that it matters less now that we have a far more ’sexy’ way of accruing shards: alliance quests. I did feel I was banging my head a bit with the above, but to be able now to actively work together towards something openly, feels better than trying to understand the hidden.

    Thanks all! I like that there are loads of clever people here :)
     
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  20. Hackuuna

    Hackuuna Well-Known Member

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    The problem with the idea of a high variance in this case is that it needs to be able to account for the absence of high shard streaks while at the same time allowing for a consistent 50% shard rate at other times. I can say for certain that I've never encountered a shard streak lasting more than 8 shards in a row but I have experienced several shardless streaks extending to 60 or more.

    I'm leaning toward a system that adjusts itself based on other factors, such as how many shards your regiment has in total, whether the regiment is one of your weaker ones, how close your regiment is to becoming 5*. It's been mentioned on this forum a few times from different players that shards seem to come a lot easier in LW while at low levels, which strongly suggests that there are other factors at play rather than a simple variance.

    Lots of possibilities and I'm sure there's a combination of everything mentioned in this thread. The devs probably get a kick out of reading our wild theories (I know I was corrected by one in the past so they do read them :)).
     
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