The Index of Power and You - A Comprehensive FAQ [Warning: Math + Walls of Text]

  • Thread Originally Posted by Tiberiania, 08-18-2013 & Edited by Alexiel Lucien 09-23-2018.



    EDIT Note: Currently unfinished. It's 5:30 in the morning for me; I am going to sleep and when I return I shall finish this FAQ. There is plenty of information here for now, however, and I am sure you will learn a thing or ten. Chances are that you won't make it through the entire thing by the time I wake up anyways, seeing how long it is. And I sleep like 12 hours a day. =P

    Now in COLOUR

    Table of Contents:
    1. What if the Index of Power?
    2. The Formula
    Misconception 1. Army Size Matters
    Note on Basic Points
    3. Scenario 1: Applying the Formula
    4. Scenario 2: Building Upgrades
    Important Note
    5. Scenario 3: Not Gaining Enough Points
    Efficient Upgrades
    6. Scenario 4: Morale Part 1
    7. Scenario 5: Morale Part 2
    8. Scenario 6: Multiple Provinces
    ...
    999. Info About This FAQ + Other Misc. Details


    Hai, Tibs here.

    This FAQ is about the Index of Power (duh), the ranking system present in the DE that helps us evaluate the power of our opponents, and ultimately decide who wins the round. Despite being present in every game, I get the consensus that people don't really understand how the Index of Power ("IoP" from here on) calculates it's values, or how to improve your IoP score effectively. I'm going to do a step-by-step walk through of the IoP Formula so everyone can gain a better understanding, and maybe clarify some misconceptions along the way.

    1. What is the Index of Power?

    Simply put, the IoP shows you what percentage of the games Morale and Upgrades you control, except instead of being out of 100, the percentage is out of 2000 (Fun fact: If you want to know what percentage of the games morale and upgrades yo u have, divide your IoP points by 20). You gain basic points depending on how much morale your provinces have, and for building upgrades. Here's the formula for calculating your IoP points:

    2. The Formula

    WSda96I.png

    Link to the original document of the formula: Here


    Side Note: The weird 'E' is the Greek letter 'Σ', and is known as "sigma". Sigma is used in math to represent the Summation operation [Link to Wikipedia], but here it basically means "calculate the following number for every province (and on the bottom line, every province for every player), and add them all together." Don't worry, I'll go over it in detail.

    Here's a text version that I will use later (You don't need to read/comprehend it)

    IoP = [calculate the following for each province you own, and then add it together: ((16 * province morale / 100) - 4 + (Number of Upgrades / 2) + (6 if morale is > 98, 0 otherwise))] / [calculate the following for each province you own, and then add it together: [calculate the following for each province they own, and then add it together:
    ((16 * province morale / 100) - 4 + (Number of Upgrades / 2) + (6 if morale is > 98, 0 otherwise))]] * 2000

    You'll notice that the formula looks a lot like:

    MBHaBNB.png

    The formula for calculating percent.

    Except our formula is a lot more complicated. Still, it works the same, as we're measuring one player's points compared to everyone's points, and then multiplying by 2000 instead of 100.

    Misconception 1: Army Size Matters

    If you look at the formula, you'll see that there are only 3 factors that matter:
    -Amount of provinces a player owns (And this is only an indirect factor, because it effects the following factor)
    -Morale of each province
    -Amount of upgrades one has built

    It doesn't matter if you have an army size of 1 or 100.000, as army size has no (direct) effect on the IoP. Of course, having 100,000 units gives you a greater ability to take other provinces than having just 1.

    Note on Basic Points:

    In order to compare the strength of different nations, the game calculates numbers known as Basic Points for each province, of which the basic points are added and manipulated to calculate IoP. Basic points are calculated from the moral and amount of upgrades a province has using the following formula:

    Basic points = (16 * province morale / 100) - 4 + (Number of Upgrades / 2) + (6 if morale is > 98, 0 otherwise)

    You will note that this is the top (or bottom) half of the IoP equation, without the silly Summation Sigmas. I'm going to use basic points to simplify the IoP formula in to 2 simpler steps.

    3. Scenario 1: Applying the Formula

    Here's a pretend 1 vs 1 map. Let's calculate the IoP for both countries. In doing so, we'll explore some of the underlying features of the IoP formula.

    (10 points to anyone who names the in-game names of these two provinces without having to check any of the Supremacy maps)

    OTbmP4e.jpg

    Red Player has the following province:
    A - 70% morale - 0 upgrades
    Blue Player has the following province:
    B - 70% morale - 0 upgrades

    The easiest way to start would be to calculate the basic points for each province:

    Province A:
    Basic points = (16 * province morale / 100) - 4 + (Number of Upgrades / 2) + (6 if morale is > 98, 0 otherwise)
    Basic points = (16 * 70 / 100) - 4 + (0 / 2) + (0, because 70 < 98)
    Basic points = 7.2

    Province B:
    Basic points = (16 * province morale / 100) - 4 + (Number of Upgrades / 2) + (6 if morale is > 98, 0 otherwise)
    Basic points = (16 * 70 / 100) - 4 + (0 / 2) + (0, because 70 < 98)
    Basic points = 7.2

    Then, we use these numbers to calculate each player's IoP:

    Player Red
    IoP = Sum of Red's province's basic points / total of all province's basic points * 2000
    IoP = basic points from A / (basic points from A + basic points from B) * 2000
    IoP = 7.2 / (7.2 + 7.2) * 2000
    IoP = 1000

    Here, Red's IoP is exactly 1000, which makes sense because Red controls half of the provinces, and their province has the exact same amount of upgrades and exact same morale of Blue. Blue has exactly 1000 points too. I think you're smart enough to figure out why, so I don't need to explain it to you.

    4. Scenario 2: Building Upgrades

    Same map, but Blue spent GM to build a fort.

    NzunKSQ.jpg

    Red Player has the following province:
    A - 70% morale - 0 upgrades
    Blue Player has the following province:
    B - 70% morale - 1 upgrade (level 1 fort)

    Again, we calculate the points for each province. Note that every building, from Recruiting Offices to Harbours are equal to exactly 1 upgrade per level. A level 2 Workshop would count as as many upgrades as a 2 Harbours, and a level 4 Factory would count as as many upgrades as 6 Railways (2 upgrades from workshop, 4 from factory).

    Province A:
    Basic points = (16 * province morale / 100) - 4 + (Number of Upgrades / 2) + (6 if morale is > 98, 0 otherwise)
    Basic points = (16 * 70 / 100) - 4 + (0 / 2) + (0, because 70 < 98)
    Basic points = 7.2

    Province B:
    Basic points = (16 * province morale / 100) - 4 + (Number of Upgrades / 2) + (6 if morale is > 98, 0 otherwise)
    Basic points = (16 * 70 / 100) - 4 + (1 / 2) + (0, because 70 < 98)
    Basic points = 7.7

    Note that the basic points for B have increased:

    Player Red
    IoP = Sum of Red's province's basic points / total of all province's basic points * 2000
    IoP = basic points from A / (basic points from A + basic points from B) * 2000
    IoP = 7.2 / (7.2 + 7.7) * 2000
    IoP = ~966

    Player Blue
    IoP = Sum of Blue's province's basic points / total of all province's basic points * 2000
    IoP = basic points from B / (basic points from A + basic points from B) * 2000
    IoP = 7.7 / (7.2 + 7.7) * 2000
    IoP = ~1034

    First of all, note that by building a fort, Blue's IoP went up.

    -=+=- IMPORTANT NOTE -=+=-

    Secondly, note that as Blue's IoP went up, Red's IoP went down. By building a fort, Blue captured more basic points than Red, so Blue was entitled to more IoP points which came from Red. If you do not gain basic points faster than average,you will lose points on the IoP.

    5. Scenario 3: Not Gaining Enough Points

    Same map as above, but Red decided to one-up Blue by a level 2 fortress, whereas Blue responded by upgrading his fort to level 3.

    [Lost attachment]

    Red Player has the following province:
    A - 70% morale - 2 upgrades (level 2 fort)
    Blue Player has the following province:
    B - 70% morale - 3 upgrades (level 3 fort)

    Province A:
    Basic points = (16 * 70 / 100) - 4 + (2 / 2) + (0, because 70 < 98)
    Basic points = 8.2

    Province B:
    Basic points = (16 * 70 / 100) - 4 + (3 / 2) + (0, because 70 < 98)
    Basic points = 8.7

    Player Red
    IoP = 8.2 / (8.2 + 8.7) * 2000
    IoP = ~970

    Player Blue
    IoP = 8.7 / (8.2 + 8.7) * 2000
    IoP = ~1030

    5 fortress levels were built during this day, 2.5 per nation, for an average gain of 1.25 basic points. Red only built 2 fortresses (2 levels = 1 basic point) and only gained 1 basic point, which is below average, so Red lost points on the IoP even though they built quite a lot of upgrades.

    -=+=- Efficient Upgrades -=+=-

    If you build the following upgrades:
    -Recruiting Office
    -Aerodrome (GM and Air-Pack games only)
    -Harbour
    -Railway
    -Level 2 Barracks
    -Level 4 Factory
    -Level 5 Fortress
    You will gain (1 + 1 + 1 + 1 + 2 + 2 + 4 + 5) = 17 upgrades = 8.5 basic points

    Upgrade Cost (Iron + Lumber only) Cost (All Resources)
    Recruiting Office 500 500
    Aerodrome 2000 4000
    Harbour 10000 10000
    Railway 8000 9000
    Barracks 1500 3000
    Workshop 1000 1500
    Factory 5000 7500
    Fortress 2000 2000

    Recruiting Offices, Workshops, and Fortresses are all very cheap and efficient ways to boost IoP using upgrades. Instead of a paragraph of text comparing Forts and Workshops, have a chart:

    Workshops
    Fortresses
    Cost less Cost more
    Requires oil Only requires iron
    Build very quickly Build slowly
    No boost to morale Boost to morale
    Only upgrades twice Upgrades 5 times
    Conclusion:
    Best built at end-game, or whenever a fast boost to IoP is required
    Conclusion:
    Building forts is a more long-term strategy for maximising IoP

    6. Scenario 4: Morale Part 1


    Sorry about that, I seem to have described some fairly complex stuff without finishing off the basics. Luckily, morale has the same effect on basic points as upgrades; you simply substitute different morale values in to the formula.

    Here, A has 75% morale, B has 50% morale.

    [Lost attachment]

    Red Player has the following province: A - 75% morale - 0 upgrades
    Blue Player has the following province: B - 50% morale - 0 upgrades

    Province A: Basic points = (16 * 75 / 100) - 4 + (0 / 2) + (0, because 75 < 98) = 8
    Province B: Basic points = (16 * 50 / 100) - 4 + (0 / 2) + (0, because 50 < 98) = 4

    Player Red IoP = 8 / (8 + 4) * 2000 = ~ 1333
    Player Blue IoP = 4 / (8 + 4) * 2000 = ~ 667

    Note that A has 50% more morale than B, but twice as many basic points. This is because the point in which one gets 0 points from morale is at 25%, not 0 percent. If you have less than 25% morale in a city, you actually lose basic points:

    Green Player has the following province: C - 10% morale - 0 upgrades
    Province C: Basic points = (16 * 10 / 100) - 4 + (0 / 2) + (0, because 10 < 98) = - 2.4

    Even though you can have a negative amount of basic points, you can not go below 0 IoP points.

    7. Scenario 5: Morale Part 2

    Here, province A has 99% morale, and province B has 98% morale -- only a 1% difference in morale.

    [Lost attachment]

    Red Player has the following province: A - 99% morale - 0 upgrades
    Blue Player has the following province: B - 98% morale - 0 upgrades

    Province A: Basic points = (16 * 99 / 100) - 4 + (0 / 2) + (6, because 99 > 98) = 17.84
    Province B: Basic points = (16 * 98 / 100) - 4 + (0 / 2) + (0, because 98 = 98) = 11.68

    Player Red IoP = 17.84 / (17.84 + 11.68) * 2000 = ~ 1209
    Player Blue IoP = 11.68 / (17.84 + 11.68) * 2000 = ~ 791

    Reaching 99% or higher morale in a province gives you a bonus of 6 basic points to your total -- which is a pretty hefty bonus when you can only get 12 from morale and 8.5 (8 in non-GM or Air-Pa ck games). Because of this, upgrades that boost morale (Harbours, Railways, Forts, Factories) are very useful for maximising IoP points if you can push a province's morale to 100%. Again, due to their fast contruction times, morale boost, and low cost, fortresses prove excellent at maximising IoP points.

    8. Scenario 6: Multiple Provinces

    999. Info About This FAQ + Other Misc. Details

    Current word count: ~2400
    Hours spent writing: 6
    Computer crashes directly caused by this document: 1

    Congladurations for reaching the bottom~! Now go back up and actually read through the FAQ, instead of just scrollng down and hoping you see something interesting.

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