A reoccurring fallacy in online gaming is the effect of reductions, specifically in the form of damage mitigation. I first came across this phenomenon in the World of Warcraft, and have striven since to help spread an accurate understanding on this mechanic.

At its heart, the question is: What does 5% damage reduction really do?

Obviously, the answer is: It reduces damage received by 5%.

This is typically as far as most players go in evaluating this mechanic. However, some players go on to try to evaluate how much armor is optimal by researching the amount of damage reduction achieved by different values of armor.

For Demigods the formula for armor mitigation is:

100 x (1 - (2500 / (2500 + Armor)))

Let’s put this into a table for easier reading.

The first column is the amount of armor, the second is the amount of damage reduction.

Armor  DR      Armor     DR    Armor     DR
   0           0    2100    0.46    4200    0.63
100      0.04    2200    0.47    4300    0.63
200      0.07    2300    0.48    4400    0.64
300      0.11    2400    0.49    4500    0.64
400      0.14    2500    0.50    4600    0.65
500      0.17    2600    0.51    4700    0.65
600      0.19    2700    0.52    4800    0.66
700      0.22    2800    0.53    4900    0.66
800      0.24    2900    0.54    5000    0.67
900      0.26    3000    0.55    5100    0.67
1000    0.29    3100    0.55    5200    0.68
1100    0.31    3200    0.56    5300    0.68
1200    0.32    3300    0.57    5400    0.68
1300    0.34    3400    0.58    5500    0.69
1400    0.36    3500    0.58    5600    0.69
1500    0.38    3600    0.59    5700    0.70
1600    0.39    3700    0.60    5800    0.70
1700    0.4      3800    0.60    5900    0.70
1800    0.42    3900    0.61    6000    0.71
1900    0.43    4000    0.62       
2000    0.44    4100    0.62

This table may seem familiar to many of you, this is the content of the table that is in the wiki too. We can also turn this into a chart for easier understanding.

At this point many players say, okay, given this information it looks like the amount of reduction starts off at 4% with 100 armor and then decreases, around 3600 the damage reduction is only about 0.5% per extra 100 points of armor, so that’s a good stopping value. This is the point wherein almost all players stop, and advice is generally given to focus on getting ~3600, anymore is a waste. Thus it is believed that damage reduction has diminishing returns, this is true and can be seen in the figure.

However, this is where the fallacy comes in. While the advice may be true (extra armor is not worth the cost beyond ~3600), the reasoning is completely wrong. The reasoning is wrong because it is based on an incomplete understanding of the mechanic.

Consider the following; is 1% damage reduction more beneficial when you already have 10% damage reduction, or when you have 90% damage reduction?

Think about it, seriously.

Have an answer?

Now, if we consider the argument described above, the answer should be that 1% damage mitigation is the same, regardless of your current value. This however is wrong. The answer is that a 1% damage reduction increase at 90% damage reduction is much, much better than at 10% damage reduction.

To see this, we have to understand Effective Health.

Effective health is the relative amount of health your demigod has when being attacked by damage that is affected by damage reduction (white damage, autoattack damage, attacks that are not skills, minion damage, tower damage, etc). If your demigod has 50% damage reduction, then it will take twice as many hits to kill your demigod when compared to a demigod with 0% damage reduction. Thus your effective life would be 200%.

The formula to calculate effective life is:

Life/(1 – damage reduction)

With 0 damage reduction (0 armor), effective life is the same as your life

With 10% damage reduction, effective life is 111% of your life.

With 11% damage reduction, effective life is 112% of your life.

With 50% damage reduction, effective life is 200% of your life.

With 90% damage reduction, effective life is 1000% of your life.

With 91% damage reduction, effective life is 1111% of your life.

Now going back to our problem, the difference between 10% & 11% damage reduction is an increase in 1% more effective life, whereas the difference between 90% and 91% damage reduction is 111% of your life. That’s a huge difference.

So, instead of looking at the effect of armor as damage reduction, looking at it in terms of effective health brings a much clearer picture of what is occurring. Going back to the same set of data we have the following table of armor, damage reduction, and effective life (ELife).

Armor     DR    ELife   Armor     DR    ELife   Armor     DR   ELife
     0         0    100    2100    0.46    184    4200    0.63    268
  100    0.04    104    2200    0.47    188    4300    0.63    272
  200    0.07    108    2300    0.48    192    4400    0.64    276
  300    0.11    112    2400    0.49    196    4500    0.64    280
  400    0.14    116    2500    0.50    200    4600    0.65    284
  500    0.17    120    2600    0.51    204    4700    0.65    288
  600    0.19    124    2700    0.52    208    4800    0.66    292
  700    0.22    128    2800    0.53    212    4900    0.66    296
  800    0.24    132    2900    0.54    216    5000    0.67    300
  900    0.26    136    3000    0.55    220    5100    0.67    304
1000    0.29    140    3100    0.55    224    5200    0.68    308
1100    0.31    144    3200    0.56    228    5300    0.68    312
1200    0.32    148    3300    0.57    232    5400    0.68    316
1300    0.34    152    3400    0.58    236    5500    0.69    320
1400    0.36    156    3500    0.58    240    5600    0.69    324
1500    0.38    160    3600    0.59    244    5700    0.70    328
1600    0.39    164    3700    0.60    248    5800    0.70    332
1700    0.40    168    3800    0.60    252    5900    0.70    336
1800    0.42    172    3900    0.61    256    6000    0.71    340
1900    0.43    176    4000    0.62    260            
2000    0.44    180    4100    0.62    264            
 

And again turning this into a figure so we can understand it more easily.

The conclusion is that Armor has the same exact effect on life, regardless of how much you have. A good shorthand rule is that every 100 points of armor grants your demigod 4% more effective life.

Negative Armor

The QoT and Lord Erebus have abilities that lower the armor of the target for a period of time. These abilities really increase the amount of damage a target takes (again 4% more damage per 100 points of armor removed). Additionally, this damage effect skyrockets if you pass 0 armor and go into negative armor. The following table demonstrates how extreme this gets.

armor         damage multiplier  Effective life
-2300            12.50                  8
-2200             8.33                 12
-2100             6.25                 16
-2000             5.00                 20
-1900             4.17                 24
-1800             3.57                 28
-1700             3.12                 32
-1600             2.78                 36
-1500             2.50                 40
-1400             2.27                 44
-1300             2.08                 48
-1200             1.92                 52
-1100             1.79                 56
-1000             1.67                 60
 -900             1.56                 64
 -800             1.47                 68
 -700             1.39                 72
 -600             1.32                 76
 -500             1.25                 80
 -400             1.19                 84
 -300             1.14                 88
 -200             1.09                 92
 -100             1.04                 96
      0             1.00                100

Note that like regular armor damage reduction, this damage multiplier only functions on white damage. The QoT's armor reduction ability also functions on towers, and allows her to be very effective in removing them.

Bite
Level   Armor
  1      250
  2      400
  3      550
  4      700

Ground Spikes
Level Damage    Mana      Armor Reduction       Damage increase vs Towers   Damage increase vs Demigods
1         250         500             375                                  17%                                  15%      
2         375         500             750                                  43%                                  30%
3         500         675            1125                                 82%                                  45%
4         625         750            1500                                150%                                 60%

Before one gets up in arms about the inbalance in the QoT's ability to remove towers with her 'insane' damage increase, consider that the debuff lasts for 5 seconds and only functions with white damage. Compare this damage to the 1700 damage for a Hammer Slam rook or other similar maxed abilities and you'll find this is rather trivial. At early levels the boost in nice, but is also confounded with the QoT's melee dps (the lowest of all demigods) and the difficulty in communicating with other players that they should hit the tower after the pretty spikes go out.

The damage increase versus other players is also misleading. Consider this, how much would you pay for an item that increases minion damage by 60% for 5 seconds, but costs 750 mana per use? Also, contrast this to Oak's Penitence which increases all damage by 16% for 7 seconds, slows the target, does damage, and interupts.

Evasion

Another problematic mechanic is Evasion or dodge. Many players consider it to be rather useless and avoid it, typically because of the belief that evasion is additive or multiplicative. Both of these statements are somewhat wrong.

Evasion works as follows:

For all white damage there is a chance (your evasion %) of that attack missing entirely. That means a 5% evasion rate decreases the amount of damage you take by 5%. However evasion and armor work in a subtle way, they are not strictly additive or multiplicative. The formula for the average amount of damage taken as a function of evasion is:

Average Damage = (1 – evasion )*(2500 / (2500 + armor))

Now working through this formula may be confusing, so I’ve written up the following to help you understand what it means, and not necessarily calculate it out. First off, the effects of evasion and armor work in two different steps. Damage is first avoided by evasion and then only damage that is not avoided is reduced by your armor value. This does cause some randomness, but we can remove this by working on averages, which is how I created the above formula. Now that we have average damage, we can convert this into effective life.

Effective life = Life /( (1 – evasion )*(2500 / (2500 + armor)))

This formula is even worse than the last one, isn’t it? Don’t worry, stick with me and at the end this will make sense. Now again, evasion does not add with armor to directly increase effective life, nor does it strictly multiple the effect of armor. What we can do though is to convert evasion into a multiplier of effective life after we calculate effective life from armor. In other words, calculate effective life from armor as normal, and then multiply by a converted evasion number.

The converted evasion number comes from the formula:

Converted evasion = 1/(1-evasion)

Or we can grab an approximate value from the following table

Evasion    Converted Value
  5%             105.26%
10%             111.11%
15%             117.64%
20%             125.00%
25%             133.33%
30%             142.86%

Let’s do an example:

With 1000 armor, we have 29% damage reduction, and 140% effective life.

Adding in 10% evasion we have 155.4% effective life (140%*111%).

So in this case, adding 10% more evasion gives us an extra 15.4% life. This is very different from an estimate if we believed that evasion was simply additive or multiplicative.

You can also see that with 30% evasion, effective life increasing almost by half. That’s huge. As a side note, 30% evasion is also the maximum amount of evasion available; so don’t try to get more of it.

So, which is better armor or dodge? Well it depends really. Again going back to our shortcut, 100 armor gives you 4% more effective life, whereas the amount of effective life you gain from evasion is dependent upon your current armor value.

As you can see in the chart, the amount of effective health you gain increases as your armor increases, however we can still provide a shorthand rule. Looking at the following table, find your current armor on the armor column (left column), and then find the % Evasion you are considering along the top. Where these two columns and rows meet is how many armor points that item is worth.

                    Evasion           
Armor   5%     10%   15%     20%     25%    30%
1000    184    388     617      875     1166    1500
2000    236    500     794     1125    1500    1928
3000    289    611     970     1375    1833    2357
4000    342    722    1147    1625    2166    2785
5000    394    833    1323    1875    2500    3214
6000    447    944    1500    2125    2833    3642

Examples:

I have 2000 armor and am considering an item that grants 10% evasion. Crossing the two I find that this is the equivalent of 500 points of armor.

Now, later in the same game I have 4000 armor and again consider that same item with 10% evasion. The item is now worth 722 points of armor.

So, I hope that helps out people with their strategies. At this point I should comment about the effects of armor, evasion, health, and health regeneration.

Short version, it is complicated.

Long version: It is complicated.

Damage reduction only works against white damage. Skills, the major source of spike damage, are NOT affected by damage reduction. This means that stacking damage reduction is very good for staying in a lane or denying your opponent access to areas of the map. However it is very bad when used to directly face a demigod in combat, especially if they have high amounts of spike damage. The converse is true for stacking health. When staying in a lane or kiting an opponent, health is okay (The problem is that health regeneration takes so long). However, when you directly engage in demigod combat health is very good.

This means against a slam rook stacking armor instead of life is suicide, however against an autoattacking regulus it is the optimal choice.