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So, I’m an Ornn OTP, and I’ve been debating whether to purchase health versus resistances in order to maximize your effective HP. I’ve seen a number of calculators and spreadsheets, as well as a few articles with recommendations for successful builds in certain seasons, but I needed something that 1) is a fast rule of thumb that I can remember and use in game, and 2) takes into account the gold cost of each stat. In other words, I was searching for a fast estimate of how to obtain the most efficient HP increase with the gold I had on hand.
Before we go into the math, there are a few things to keep in mind. To begin, these estimates are only useful if you’re primarily concerned with a particular kind of harm. I did my hardest to include physical, magical, and true damage, but doing so algebraically is a pain (I may revisit this with some python code at some point). Essentially, if you’re dealing with mixed damage, HP will be more important than this article suggests. Second, it doesn’t account for penetration (though you may compensate if you’re fast with mental calculations and pay close attention to opponent things).
The Fundamentals
For those who don’t know, damage reduction in league is calculated using the following formula:
Pre-Mitigation Damage=100/(100+Resist) Post-Mitigation Damage=100/(100+Resist)
More lucid math
So, if you have no armor, you will take 100% of the incoming physical damage, if you have 100 armor, you will take 50%, if you have 900 armor, you will take 10%, and so on. This is where the phrase “resistances have diminishing returns” originates from, but it’s a little deceptive since what you really care about is effective health, not damage reduction in percentage. The following is the formula for good health:
(1+R/100) H E=H N
More lucid math
HN is for nominal health (the figure on your HP bar), and R stands for the resistance in question (armor or MR). This equation shows that one additional point of resistance improves your effective health by 1% of your nominal health, regardless of how much health or resistance you presently have (no diminishing returns).
The Investigation
“How much does my effective health improve when I raise each stat?” was my initial inquiry. This is equivalent to calculating the derivative of effective health with respect to either nominal health or resistance, but we can also do it manually by raising the stat of interest by 1 and subtracting the old effective health from the new one, as illustrated here:
H (E,H N )=(H N+1)(1+R/100) H (E,H N )=(H N+1)(1+R/100) H (E,H N )= -H N (1+R/100)=(1+R/100)=(1+R/100)=(1+R/100)=(1+R/100)=(
H (E,R)=H N (1+(R+1)/100) H (E,R)=H N (1+(R+1)/100) H (E,R)=H N H N (1+R/100)=H N/100 -H N (1+R/100)=H N/100
More lucid math
So far, we’ve established that each resistance increases our effective health by 1% of our nominal health, regardless of our current resistance, and we now have a similar expression for increasing our nominal health (which increases by 1 + 1% of our resistance, which is kind of cute and makes sense).
These expressions indicate how much of an effective health increase we receive each point we spend on a new defensive stat, but we must spend gold on them, because health and resistances have distinct gold values. Each point of health is 2.67 grams, each point of armor is 20 grams, and each point of MR is 18 grams. For the sake of simplicity, I’ll assume that each resist costs 20 g per point.
I really want to know the answers to the questions “How much does my effective health rise if I purchase 1 gold’s worth of resistance?” and “How much does my effective health increase if I buy 1 gold’s worth of resistance?” before I pick which I should buy. “How much does buying 1 gold worth of nominal health improve my effective health?” These are simple problems today, since we can just divide the aforementioned formulas by the cost of the relevant stat:
g (H N)= ((1+R/100)/2.67 Effective Health Gain per Gold Spent on Health=g (H N)= ((1+R/100)/2.67 Effective Health Gain per Gold Spent on Health=g (H N)=
g R= H N/2000 = Effective Health Gain per Gold Spent on Resistance
More lucid math
We’re almost there! Now we can make these rates equal to each other to obtain an expression that will be true when spending money on health or resistances is equally effective. Now all we have to do is simplify:
H N/2000=((1+R/100))/2.67
H N=750(1+R/100)
H N=750+7.5R
More lucid math
That concludes our discussion. Although multiplying by 7.5 is inconvenient, estimations are your best friend here. And the only information you need is that which appears in your game’s stats box. If your HP is more than 750 + 7.5R, you need purchase additional resistances. Buy additional health if it’s less.
Obviously, if you’re dealing with mixed damage, this guideline won’t help you as much (and buying health will be better than this rule suggests because health increases your effective health against all kinds of damage).
Thank you for sticking with me through this long article; I hope you find it useful!
TL;DR: If your current health is less than 750 +, you may become tankier for the same gold by purchasing health (7.5 X Resistance). If your present health is better than that, purchasing resistances is a better option. Only applies if you’re fighting mainly one kind of damage; if you’re fighting mixed damage, put a little more emphasis on health.
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