Aug 052011

Armour and Magic Resistance (MR) provide a percentage of damage reduction (DR) against physical and magical attacks; respectively. The percentage is neither direct nor is it linear. In other words, 10 armour or MR doesn’t provide 10% DR. Moreover, adding 10 armour or MR doesn’t increase DR by 10%.

Taking the damage multiplier (DM) for armour and magic resistance from the League of Legends Wiki, the equation behind damage reduction is DR = (1 – DM)*100 <=> DR = (1 – (100/(100 + V)))*100; where V equals the value of armour or magic reduction and DR is the percentage of damage that is reduced.

In-game values verify this formula: for V = 30 armour or MR then DR = 23.08% damage reduction. Table 1 shows the corresponding DR for values of V from 10 to 1000 with increments of 10.

Table 1:

League of Legends Armour Magic Resistance Damage Reduction Table

Curiousity prompts the question of what value of V ensures a DR of 100%. Table 2 shows that the armour or MR necessary to reach damage immunity is a value of two million; well away of anything feasible.

Table 2:

League of Legends Armour Magic Resistance Damage Reduction Maximum Table

Regardless, Table 2 makes obvious the lessened impact of huge amounts of armour and MR. Copious amount of any stat give diminishing returns: the higher the value the less the effect from a further increase.

Graph 1:

League of Legends Armour Magic Resistance Damage Reduction Graph

Graph 1 shows the behaviour of DR as V increases. The diminishing returns we discussed are plainly evident. Then, the question becomes: how much armour or MR is worth getting?. To answer the question we should check how a change in the value of V affects DR.

The second column on Table 1 shows the values of the gradient or slope on each value of V. This shows the rate of change of DR, taken as a function of V: DR(V), as V changes. The differential of DR(V) = (1 – (100/(100 + V)))*100 is DR'(V) = (100/(100 + V))^2.

To be precise, the differential DR'(V) represents the change in DR(V), the dependent variable, with respect to the change in V, the independent variable. This allows to clearly see the effect that an increase in the value of V has on DR.

Graph 2:

League of Legends Armour Magic Resistance Damage Reduction Gradient Graph

An increse of V from 200 to 210 only increases DR in 1.08%. Besides, for values higher than 220 an increase of 10 armour or MR is not enough to modify DR by more than 1.0%; because the gradient continues decreasing. Therefore, we can conclude that armour or MR with a value higher of 200 is undesirable because of it meager incidence on damage reduction.

We hope you found the article useful and that it wasn’t too much math for your tastes. If you see a mistake or part that isn’t understandable just leave a comment. Positive feedback is welcome too.

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