Math and Difficulty: Percentile and Fixed Scaling: Part 1, Introduction

Note: Duh. Incredibly intuitive article about math and games. Unless you like considering the implications of mechanics, I'd advise you to steer clear.

Itemization, the bonuses that players can achieve, matters in games with a heavy equipment/numerical component.They appeal Johnny's mechanical driver to tinker. A flashy item appeals to Timmy's desire to feel power. The fact that items can be compared numerically give Spikes a hard goal. Numbers matter in game balance.

However, numbers are not to be trifled with. A poor understanding of what makes an item effective or good can throw off the game's gameplay balance ridiculously to the point where the game becomes a complete cakewalk (Bad because players then become bored) or much too hard (Bad because players then must grind excessively which can get boring.)

In this series of posts, I'm going to talk about the following topics:

1. Small percentile bonuses are insignificant early on and become oversignificant later on.
1% of 1 damage is trivial and insignificant.

2. Small fixed bonuses are over-significant early on and become trivial later on.
+1 damage to 1 damage is insane.

3. The order of operations matters.
+1 damage then +100% damage is 4. +100% damage then +1 damage is 3.

4. Percentiles are very hard to give to players in the correct porportions.
+ 1% to damage? Is that a good reward? Does that even do anything? What's the players damage right now? It could give him 10 damage or it might give him 1000. How about reduction? -1% to damage taken? How much damage taken does he have?

5. Percentile bonuses that can accrue are dangerous. Percentile bonuses out of 100 that can accrue are doubly dangerous.
+400% to a statistics at late game dwarfs everything else. A small insignificant +1 damage suddenly becomes worth 5 times the initial worth. A +1% critical bonus at the beginning of the game might be worthwhile until you realize that you can't give away more than 1% or 2% because by end game, players will reach 100%.

6. Not all percentiles are equal: Reduction and additions are and must work differently.
If I have 90% damage reduction and I get a mere 5% more reduction additively; I don't take 5% less damage. I take 50% less damage because now I'm at 95% reduction. Alternatively if I have 100% bonus to damage and I get 50% more bonus to damage additively, I don't do 50% more damage, I only do a mere 20% more damage because now I'm at 150% bonus damage.