14 January 2018

The Concept of Magic Find - The Stat

The controversy about the magic find is high. Is it useful? Is it useless? What does it even do? Is it overpowered? Is it under-powered? Maybe these questions are something everyone should know for themselves.

What Is Magic Find?

Magic find is most commonly known as the stat that increases your chance of finding rare loot. So let's say we have a boss that drops an extremely rare weapon and the chance of this weapon is 0.2%. Now we have a player and we say he has a 100% magic find. We define magic find to increase the chance of rare drops. So having this rare weapon with a 0.2% drop rate to drop 100% more often it now drops with a chance of 0.4%. 

But That Doesn't Make Sense

If magic find doubles your drop chance some items will have a chance of 100%. That doesn't make sense. So let's say we have an enemy that drops:
  • a bottle full of dirt
  • some armor
  • common weapon
  • crafting material
  • rare weapon
So there's a 1/5 chance to get either. However, drop chances are not equal some are more rare others are less rare. So currently each item has a 20% drop chance. If we decrease the chance of the rare weapon the drop chance of all others increases. As it always has to stay 100%. One way to do this we could say each item has a 2/10 chance to drop. Which is still a 20% chance. Now we can say the last item has a 1/10 chance and the bottle full of dirt has a 3/10 chance. What happens is we get this loot table now:
  • bottle full of dirt - 3/10 = 30%
  • some armor - 2/10 = 20%
  • common weapon - 2/10 = 20%
  • crafting material - 2/10 = 20%
  • rare weapon = 1/10 = 10%
We can continue to increase your divisions and split the odds to the items until we're happy with the drop chances:
  • bottle full of dirt 15/50 = 30%
  • some armor - 11/50 = 22%
  • common weapon - 11/50 = 22%
  • crafting material - 12/50 = 24%
  • rare weapon = 1/50 = 2%
Now the problem we have is if we say we have 100% magic find our drop chances are:
  • a bottle full of dirt: 60%
  • some armor: 44%
  • common weapon: 44%
  • crafting material: 48%
  • rare weapon: 4%
If we sum up the drop rates we get 200%. This does not add up, except if we're now expecting to get 2 items instead of one. So something we can do is, we can say rare items become more common. We can do this by evening out the difference of each. 20% is the drop chance that makes every item equal if 100% magic-find doubles our chance to find rare loot we double everything that's below 20% and half everything above 20%. Doing this we will get these:
  • a bottle full of dirt: 15%
  • some armor: 11%
  • common weapon: 11%
  • crafting material: 12%
  • rare weapon: 4%
Summing it up gives us 53%. Hm, that's a bummer. We need 100%. What we can do instead is we can see how many numbers are above 20%, that's four. Okay, how many items are below 20%? That's one. So what's the chance of that one? It's 2%. If we double it we have 4%. Now we need to remove 2% of the numbers that are above 20%. Since we have 4 numbers we need to remove 2% / 4% = 0.5% of each. So our drop chances actually are:
  • a bottle full of dirt: 29.5%
  • some armor: 21.5%
  • common weapon: 21.5%
  • crafting material: 23.5%
  • rare weapon: 4%
At some point, you have the same chance for anything from this. That's one way to do it. Another way you could do it would be to say we have rarities of items. Like drop rarities.

Shift Instead of Equalize

An alternative this way would be to increase the chance to find the rarest item and decrease the chance to find the most common item by the same amount. So if we say we double our chance to find the rarest item our loot table will look like this:
  • a bottle full of dirt: 28%
  • some armor:  23%
  • common weapon: 23%
  • crafting material: 23%
  • rare weapon: 4%
What happens if we continue is that the chances are going to be swapped. In the end, our bottle full of dirt has a 4% chance and our rare weapon will have a 30% chance of dropping.

Even More Magic Find

If we want rare items to drop more often than that we need to reduce the chance of less rare items to have them drop less. The problem we have here is that items of common rarity may not be encountered at some point. If there's no cap on magic find you won't get materials from enemies anymore. You will only see the rarest of rare items. Every time. So as you can see we have a problem if we go further than equalizing the drop rates.

Adding a Puffer

Another way would be to add a puffer. Let's say the enemy has a 40% chance of not dropping an item. We still have our normal loot table with our bottle full of dirt, some armor, common weapon, crafting material and rare weapon. Getting our other items is a 60% chance. So each of these items has its chance to drop from this 60% chance. How do we calculate this? Like that:
  • Nothing: 40%
  • bottle full of dirt: 30% * 60% = 18%
  • some armor: 22% * 60% = 13.2%
  • common weapon: 22% * 60% = 13.2%
  • crafting material: 24% * 60% = 14.4%
  • rare weapon: 2% * 60% = 1.2%
Now thanks to the puffer of 40% if we say we increase rare items we can do this by taking half of the puffer like this:
  • Nothing: 20%
  • bottle full of dirt: 30% * 80% = 24%
  • some armor: 22% * 80% = 17.6%
  • common weapon: 22% * 80% = 17.6%
  • crafting material: 24% * 80% = 19.2%
  • rare weapon: 2% * 80% = 1.6%

Magic Find Combined With Loot Tables

Some games like Guild Wars 2 take a different approach to the whole topic of magic find. They're using loot tables that are affected by magic find. If we say we have a loot table for common drops, uncommon drops, rare drops, and special drops and we say magic find does not increase your chance for a common drop but your chance for a higher loot table we can put items we still want the player to be able to drop in that table. Even better we can balance magic find out.

Let's say our loot tables look like this:

Common Loot Table
  • a bottle full of dirt 32%
  • common armor 16%
  • common weapon 16%
  • uncommon gear 10%
  • crafting material 16%
Uncommon Loot Table
  • tooth of the enemy 32%
  • uncommon armor 16%
  • uncommon weapon 16%
  • rare gear 10%
  • uncommon crafting material 16%
Rare Loot Table
  • gold ring of the enemy 32%
  • rare armor 16%
  • rare weapon 16%
  • uncommon gear 10%
  • rare crafting material 16%
And so on. So what happened here? You can still find trash items in the more rare loot tables, however, they're worth more. This also balances out magic find. We can have as much magic find as you want you will still find trash to sell and materials or whatever you want the player to find on the enemy. At the same time, the loot the player gets is still rarer.

If you kill an enemy as an example you might roll like this now:

  • nothing: 33%
  • Common Loot Table: 33%
  • Uncommon Loot Table: 16.5%
  • Rare Loot Table: 8.25%
So our chance to find a rare weapon without magic find is 8.25% * 16% = 1.32%. If we want to increase our chance on the rare loot table we can use the techniques as mentioned above. Maybe you could even combine all of the techniques. Puffer, equalizing, rarity-dependent loot tables and an over capping technique?

Conclusion

It's important to make sure how much magic find the player will get and what magic find should do and how it should work. Do you really want the player to get a common item no longer or do you want him to have the same chance to get any item in the end? Do you want the player to still be able to get certain items if he has maxed out his magic find or do you want him to find a rarer version of the same item that is worth more but can be used for the prior and better things?

In the end, it's your game and your choice. Either way, think about it.
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