Quantitative Analysis of Event Rewards (TLDR at bottom)

Discussion in 'World 90' started by Sinful Super Unicorn, Dec 9, 2016.

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  1. Sinful Super Unicorn

    Sinful Super Unicorn Active Member

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    Hello

    My name is Nate, I'm a player on the Natticus account. I love math and statistics, and I often use them to analyze different situations and scenarios in TribalWars. The rewards from this ongoing event (Battle of the Tower) are different from the rewards of previous events, as it isn't completely obvious which reward is best, so I thought I'd share some of the math I did in determining the optimal purchases during this event with you guys; the players of W90. If I get positive feedback on this post I'll be happy to post more of these. As always, if I did any math wrong, please let me know. Anyway, let's jump right in:

    A good baseline to start with are the resource packages. They add a percentage of your warehouse capacity in resources to every one of your villages. The resource packages being offered during this event are the following:

    5% Resource Package -- 360 Glory
    10% Resource Package -- 600 Glory
    20% Resource Package -- 990 Glory
    30% Resource Package -- 1550 Glory

    By dividing the Warehouse percentage by the cost in glory, we can find the efficiency of these items in terms of Percentage of Warehouse Per Glory (in other words, how much Total Warehouse Capacity each point of Glory is worth)

    5% -- 0.01389% Total Warehouse Capacity/Glory
    10% -- 0.01667% Total Warehouse Capacity/Glory
    20% -- 0.02020% Total Warehouse Capacity/Glory
    30% -- 0.01935% Total Warehouse Capacity/Glory

    As can be seen by the above data, the 20% Resource Package is actually the most efficient Resource Package offered during this event. Each point of Glory spent on the 20% Resource Package is worth 0.0202% of your Total Warehouse Capacity. As we move forward with the calculations, it is important to note that Total Warehouse Capacity is calculated by adding up how much of each resource your warehouses can store in all your villages. Average Warehouse Capacity is calculated by dividing the Total Warehouse Capacity by the number of villages you have, outputting the average capacity of the warehouses in your villages.

    To find the best item to buy during this event, I compared the resources gained from every other reward to the resources gained from buying the 20% Resource Package. Whether or not the reward is worth buying is determined by figuring out how much each Glory is worth, and comparing that to the value of Glory spent on the 20% Resource Package. Let's compare!

    Raid Booster
    Grants +10% Haul Capacity for 48 hours -- 200 Glory

    Multiplying the Glory cost of each item by the efficiency of the 20% Resource Package returns the minimum of how much Total Warehouse Capacity in resources this item has to grant for it to be worth more than the 20% Resource Package.

    200 Glory x 0.02020 Total Warehouse Capacity/Glory = 4.040% Total Warehouse Capacity

    So for the Raid Booster to be worth more than the 20% Resource Package, it has to generate at least 4.040% of your Total Warehouse Capacity in resources.

    (4.040 x 10)/2 = 20.20% Total Warehouse Capacity in farming per day

    Since this item is a +10% boost to hauls and lasts 48 hours, this item is worth more than the 20% Resource Package only if you farm 20.20% of your Total Warehouse Capacity per day AND all of your hauls are full hauls.

    With a Total Warehouse Capacity of 1 million, I would have to farm 202,000 of each resource per day in only full hauls, or 606,000 total resources for this to be worth more than the 20% Resource Package.


    Flamboyant Speech

    Grants a resource package worth half the cost of a noble for every noble produced for 24 hours-- 880 Glory

    880 Glory x 0.02020 = 17.777% Total Warehouse Capacity to be worth more than 20% Resource Package

    17.777% x 2 = 35.555% Total Warehouse Capacity

    In order for this item to be worth more than the 20% Resource Package, it would have to generate 17.777% of your Total Warehouse Capacity, meaning you would have to spend at least 35.55555% of your Total Warehouse Capacity on nobles while under its effect.

    Noble cost = 46666.666 Average per resource
    Nobles > (Total Warehouse Capacity x 0.355555)/46666.666

    This reward is worth more than the 20% Resource Package only if you produce this many nobles in the 24 hours: Number of Nobles > Total Warehouse Capacity/131250

    With a Total Warehouse Capacity of 1 million, I would have to produce 8 nobles for this item to be worth more than the 20% Resources Package.


    Noble Decree
    Decreases the cost of Gold Coins by 10% for 24 hours -- 1100 glory

    1100 Glory x 0.02020 = 22.222% Total Warehouse Capacity to be worth more than 20% Resource Package

    22.222% x 10 = 222.22% Total Warehouse Capacity

    For the Noble Decree to be worth more than the 20% Resource Package, you have to spend at least 222.22222% of your Total Warehouse Capacity on Coins.

    Coin Cost = 27667 Average per resource
    Coins > (Total Warehouse Capacity x 2.222)/27666.666

    The Noble Decree is worth more than the 20% Resource Package only if you mint this many coins in the 24 hours: Number of Coins > Total Warehouse Capacity/12451

    With a Total Warehouse Capacity of 1 million, I would have to mint 81 Coins for this item to be worth more than the 20% Resource Package.


    War Effort
    +30% Base Production of each resource for 48 hours -- 1380 Glory

    1380 Glory x 0.02020 = 27.8787% Total Warehouse Capacity to be worth more than 20% Resource Package

    27.8787% / 2 = 13.9393% Total Warehouse Capacity/day
    13.9393% / 24 = 0.5808% Total Warehouse Capacity/hour

    For the War Effort to be worth more than the 20% Resource Package, it will have to produce at least 0.5808% of your Total Warehouse Capacity every hour.

    ((Average Wood Output + Average Clay Output + Average Iron Output)/3)*0.3 > Average Warehouse Capacity*0.005808

    The War Effort is worth more than the 20% Resource Package only if your average base resource output per resource (not including other buffs like the +20% premium) is this high: Average Resource Output > Average Warehouse Capacity/51.65

    With an Average Warehouse Capacity of 200,000, my average resource output per resource would have to be at least 3873 resources/hour. Note that for this reward, Average Warehouse Capacity is used, not Total Warehouse Capacity. Also 'Average Resource Output' represents the average output of each resource production building in every village across your empire, and so is a value between 60 and 4800. If your Average Warehouse Capacity is greater than 247,920, this reward will never be worth more than the 20% Resource Package.


    Privilege
    Instantly creates a nobleman in the selected village if requirements have been met -- 1740 Glory

    1740 Glory x 0.02020 = 35.151% Total Warehouse Capacity to be worth more than 20% Resource Package

    Noble Cost = 46667 Average per resource
    Total Warehouse Capacity = 46667/0.351

    The Privilege reward is worth more than the 20% Resource Package only if your Total Warehouse Capacity is less than 132,954

    If I had a Total Warehouse Capacity of 1 million, it would not be worth getting this reward, as the 20% Resource Package is better.


    Improved Mine Carts
    Permanently improves iron production in one village by 10% -- 1950 Glory

    This reward produces the most resources in this list because its effects are permanent, however the resources take a long time to pay off.

    1950 Glory x 0.02020 = 39.3939% Total Warehouse Capacity to be worth more than 20% Resource Package

    Hours to Pay Off = (Total Warehouse Capacity * 0.393939)/((Selected Village Iron Output*0.1)/3)

    Improved Mine Carts are worth more than the 20% Resource Package after this many hours: Number of Hours = 11.81 x (Total Warehouse Capacity / Selected Village Iron Output)

    If I had a Total Warehouse Capacity of 1 million and an iron output of 2254 (Iron Mine level 25), it would take 5240 Hours, or 218 Days, to be worth more than the 20% Resource Package.


    War Chest
    Instantly mints one gold coin for every village you have -- 2180 Glory

    2180 Glory x 0.02020 = 44.0404% Total Warehouse Capacity to be worth more than 20% Resource Package

    Coin Cost = 27667 Average per resource
    Average Warehouse Capacity = 27667/0.440404

    The War Chest reward is worth more than the 20% Resource Package only if your Average Warehouse Capacity is less than 62,821

    If my Average Warehouse Capacity was 200,000, it would not be worth getting this reward, as the 20% Resource Package is better.




    The bolded subsections of each reward describe when that reward is worth more than the 20% Resource Package. Inputting your own Total Warehouse Capacity into that calculation will tell you whether or not it is worthwhile buying that reward. For large accounts, the 20% Resource Package is easily the best reward. Reminder that Total Warehouse Capacity is the sum of all your warehouse capacities per resource, so a level 30 warehouse adds 400,000 to the Total Warehouse Capacity. An account with 2 level 30 warehouses has a Total Warehouse Capacity of 800,000.

    Additionally, this only takes resource generation into account. Many of the other resources provide combat bonuses or other benefits that cannot be accurately measured through the use of resources. This quantitative analysis only takes those rewards that generate resources, or are directly linked to resources into account.

    TLDR: Use the bolded equation under each reward to determine the best reward to buy on your account. If your account is large (Has a lot of high level warehouses) the 20% Resource Package is almost always the best bet.
     
  2. Novembre

    Novembre Forum Personality 2016

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    Excellent work mate. I appreciate your effort :)
     
    rickyson1 likes this.
  3. daredeviler

    daredeviler Non-stop Poster

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    tl:dr 20% res package is OP.
     
  4. HumbleRevolution

    HumbleRevolution Non-stop Poster

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    Nate you the man.
     
  5. Seven Devils

    Seven Devils Non-stop Poster

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    Enjoyed the read.
     
  6. Player not found.

    Player not found. Still Going Strong

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    I enjoyed the read, and I hate long walls of text.
     
  7. King Banana

    King Banana Non-stop Poster

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    Nice post, but I can't see you even mentioning double flag bonus, which is the best IMO.