Battle Mechanics III: Why your opponent doesn’t matter

skill fierce loyaltyWelcome to part III in this Battle Mechanics series. In part I and II, we constructed the basic battle formula with buffs and debuffs, focusing specifically on gear buff and debuffs. Now it is time to chose the optimal set of gear. But before we get to that, we consider here our opponent. Many people still tell me that I have to take into account the opponent’s gear when choosing my own, in the sense that (usually), if an opponent has mostly debuffs, I should aim for buffs, and vice versa.

In part IV, we are going to (for the last time hopefully) discuss our own gear choices, taking Diminishing Returns into account, but here in part III, I will first briefly detail why you should never look at your opponent’s buffs and debuffs distribution.

>continued

To start of we will take the latest battle formula we derived at in parts I and II, formula (eq.19), again colored for both sides of a battle (orange=attack, blue=defense):

19-2

Now, to show why your opponent does not matter, we will be the defending party in the following example. So in order to calculate how we fare relatively, we fill in the bottom blue factors, while the opponent’s values go in the top orange factors.

For the orange opponent’s factors, you hardly ever know the exact values in PvP TK, but perhaps you kinda know from the shown gear what gear values they have. Whatever the case, the two orange factors are gonna result in certain numbers, regardless of what gear you have (just as the blue factors are based solely on your gear and not the opponent’s). For now, let’s replace these factors with constants A and B:

19a

The result when filled in, will tell you how many troops you will relatively lose (this number has no value in real combat outcomes, but will tell you how well a set of gear performs compared to another). Now here is the thing. Take an arbitrary (>1) number for A and B. In this example, let’s set the base life value for our troops to 1 for easy calculating, and let’s take 10 for A and B. We start with 0% attack debuff and 0% life buff. An enemy attacks us and kills X amount of troops. Remember, we don’t have all the numbers required to come to a precise prediction of troop lost, just the ability to compare on gear set relative to another. So the X number of troops killed will be our starting point.

lifeIn scenario 2, we add 100% life buff to our stats. Now the right hand division’s denominator becomes twice as large, and thus the division as a whole will get halved. Which means, we now lose X/2 troops, saving 50% compared to situation 1.

attack debuffIn scenario 3, we also add in 100% attack debuff. Same as above, the left hand side division also becomes twice as small, meaning we now lose (X/2)/2  = X/4 troops. We saved another 50% compared to situation 2. So for each consecutive situation, the number of troops we lose gets divided by 2:

  1. 0% life buff, 0% attack debuff = X troops lost
  2. 100% life buff, 0% attack debuff = X/2 troops lost
  3. 100% life buff, 100% attack debuff = X/4 troops lost

Now, IF it were the case that the opponent’s gear (symbolized by the terms A and B above) influenced our gear’s performance, we should be able to tinker with A and B, such that the results of situations 2 and 3 are NOT X/2 and X/4 respectively. Now I am not going to do the math to show you that this is not the case. If you really want to see for yourself, try different combinations for A and B (>1), get your X troops lost in situation 1, and see whether 2 and 3 still hold up as expected. They will!

And with that, I have shown that your opponent’s gear plays no role in how effective your own gear is. Yes, of course, if one opponent has better gear than another one, the first will get better ratio, but the point is is that your personal best set of gear, is ALWAYS your best set of gear (for defense or offense), regardless of enemy buffs/debuffs. So the next time someone tells you to apply more buff against enemies with primarily debuff (or vice versa) point them here to see why that is wrong.

And because the enemy gear (A and B) doesn’t matter, we can remove them from the equation:

19c

(note: 19B was a mistake I made so is left out)

Now, since we look for relative comparisons, our Life_base term in (eq.19C) is also unnecessary, and we can eliminate it, for example by making it equal 1, giving us:

20

And that is the end result as far as we are concerned right now. Equation 20 here is all you need to compare two (defensive) sets of gear. The higher the score, the better the set is. Simply add up the life buff and attack debuff from the gear pieces and Gems, and fill it in, for example in a spreadsheet. Of course one last addition should be the offensive equivalent of (eq.20), which is given below:21

So in short, if you want to compare defensive sets, use (eq.20), and when you want to compare offensive sets, use (eq.21).

Now we are left with one dreaded topic that needs addressing: Diminishing Returns. I’ve written on it in several articles, but installment IV in this series should really put an end to all discussions. See you there!

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12 thoughts on “Battle Mechanics III: Why your opponent doesn’t matter

  1. Pingback: Battle Mechanics – Steel Floss

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  3. If you can write out the whole battle equation for either Attack or Life I will know how diminishing returns is implemented. I simply need to know where the multiplications and where the additions are.

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  4. Beardmonkey good job!
    Do you think u can answer my question I wrote on battle mechanics II or maybe add me on Line/Touch (I’d: maxxxel/anti-kabam) and we can talk together.

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  5. I was wondering about the math. Your solution es absolutely perfect. But I was considering what if we sum up the buff and debuff instead of multiplying them. I know the best to do is to multiply them, however, for some players it may result hard to get if they are not used to mathing. So, I was thinking to explain them using a simple sum. My concern is if the sum could lead to a contradictory results, for instance, saying that a gear that is better than other one but actually it isn’t. In resume: Do you think the sum keeps the ordinality that the multiplication implies?

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    • No! The math is what it is and unfortunately, you cannot substitute a multiplication for an addition without the answer becoming meaningless. In this case, addition would even negate all DR and make balancing buffs and debuffs unnecessary, which is why it would be totally wrong. An explanation for kinda how this works will be included in part IV.

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      • Thanks! I checked it, your work is really great. Thanks for all the help. By the way, If you’re full in shield walls and city guardian, shouldn’t you consider to keep a higher debuff? Not much, just a bit. Considering that you have another sources for buff than for debuff.

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