Note: This is part 4 of a section on Math and Scaling of item modifiers.
Let me describe..
. possible solutions to the points I've talked about in this series and some discussion about the results.
0. The "Safe" law about percent modifiers, if I didn't stress it enough..Reduction modifiers should stack
multiplicatively.Enhancement modifiers should stack
additively.
The reasoning being is that this is the safest way to ensure that things don't have exponential growth.
0b. Consider taking only the highest bonus or prevent things from stacking.
If you are *super* paranoid about things scaling out of control, consider using only the
highest reduction or enhancement of each category. Typically however, this will simply lead players to cherry pick a whole slew of other statistics and become well rounded.
This allows you to create a whole spectrum of gear without worrying about potentially dangerous interactions allowing for better ease and flexibility of reward.
For example, if they can only have one enhancement to critical strike then they will then choose to upgrade damage, accuracy, speed, etc. Since focusing on one statistic is useless they will choose to get bonuses in a variety of statistics.
(This may be a good thing.)
Note/Beware:
Make sure players understand only the highest bonus applies.
Note/Beware: Lots of nominally unrelated things can actually be related! Damage %, Attack Speed %, Number of hits, Accuracy %
all increase DPS! If you ensure that only the highest bonus takes effect,
be sure that you have as many offensive modifiers as defensive modifiers.
Otherwise, if there are more offensive modifiers, players that like to play defense won't be able to "catch up" or vice versa, if there are more defensive modifiers, players might not be able to do any damage.
1.
Cap reduction modifiers aggressively.Capping reduction modifiers (damage reduction, slows target, etc.) aggressively (to 50% or less) hinders their exponential growth
regardless of what kind of math model you use to accumulate reduction modifiers.
That is, if you cap all reduction modifiers to a maximum of below or equal 50% then you keep the marginal benefit of each additional percent of reduction roughly equal. This is due to the fact that in reductions each percentage has
increasing returns that is grows roughly exponentially.
For example, let's consider a speed reduction spell. If this spell reduces their attack speed by 10% players will survive 11% longer since his damage output will drop to 90% of what it was, a relative difference of 11%.
1/0.9 -> 1.11
1/0.8 -> 1.25
1/0.7 -> 1.42
1/0.6 -> 1.66
1/0.5 -> 2
You can see the exponential creep start here where the last 10% is 3 times as effective as the first 10% but after the 0.5 mark, it starts to climb to ridiculous levels, such as 1% being 10 to 20 times more effective at the 0.66 mark than the first 1%.
1b.
Consider compensating players for capped stats - Optional! Interesting!
If players are theoretically able to reach a percentage higher than your cap then compensate them in other ways in order. If players are not compensated for capped stats then you start to hit another odd phenomenon where players stack equipment to cap as many different statistics as possible.
For example, in WoW players reach a critical strike % cap at roughly 23% chance to critical. This causes players to go for hit % chance in order to increase their DPS, causing both statistics to be maxed by both players and making equipment diversity kind of useless. The problem is that players will want to optimize themselves and since the multiple capped statistics can are obtainable and maximizable then they will seek to maximize all of them and so everyone's bonus statistics looks the same.
If additional critical strike % had been converted to critical strike bonus damage %, this would be an interesting compensation that would allow players to have builds that are more critical focused with some loss in consistency by sacrifice hit rating.
Some Examples:Hit % Chance -> Critical Strike %
If they are able to hit a target 100% of the time then it makes sense that they could perform more deadly critical blow.
Debuff Target % -> Increased Hit % for Debuff
For example, if their ice bolt slows for the maximum 50% slow then compensate them by making the 50% slow more reliable by reducing the enemy's chance to resist the spell.
Resist Effect % -> Flat % Reduction if they fail to resist.
For example, if a character has a 50% resist against stun effects, if they go over the cap perhaps consider compensating them by making the stun they *fail* to resist last shorter.
2.
Have scaling flat bonus effects based on level.This is *similar* to having percentile effects but still allows equipment to grow obsolete when the player reaches a new tier of equipment.
A weapon could have +1 / damage per level of the player. This can, in theory, scale with the player like % effects... However, you are guaranteed that this bonus scales
linearly. If your health/defense factors scale
exponentially then this equipment is guaranteed to be relevant for a while
and still be outgrown and irrelevant after a number of levels without any other fact.
For example, let's say that at each level, our hero (and the monsters) gain 10% a level and our hero, receives, as a prize a sword that does 10 damage and +1 additional damage per level!
Level 1: 100 hp / 11 damage sword = 10 hits to die.
Level 2: 121 hp / 12 damage sword = 11 hits to die.
Level 3: 133 hp / 13 damage sword = 11 hits to die.
Level 4: 146 hp / 14 damage sword = 11 hits to die.
Level 5: 161 hp / 15 damage sword = 11 hits to die.
Level 6: 177 hp / 16 damage sword = 12 hits to die.
Level 7: 194 hp / 17 damage sword = 12 hits to die.
Level 8: 214 hp / 18 damage sword = 12 hits to die.
Level 9: 236 hp / 19 damage sword = 13 hits to die.
The sword is slowly becoming irrelevant. In a few more levels, the sword will have to be replaced because it kills monsters far too slowly. He will soon need to switch equipment thus allowing us to simultaneously give a
useful bonus and a bonus that will eventually
become irrelevant.
This is better than both flat bonus and % bonus to damage in terms of how it scales and how easy it is to gift. However, this works off the following assumptions:
1. Your bonus scales linearly. (In the above example, it was x * 1)
2. The thing it scales against rises exponentially (In the above example, it was a x^10% factor).
However, beware. If your bonus is
too large then you run the risk of players not bothering to replace their weapons for a long time because they don't need to. It scales "well enough" for them to skip an upgrade or two. This is good in a sense, in that players will never hit an equipment dead-end. This is bad in a sense, in that it encourages players not to upgrade.