[Balance Issue] Cooldown Reduction Mechanics

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Noetherian

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Senior Member

10-15-2009

Note: Not sure whether or not this is the right forum for this type of feedback, if the thread should be posted elsewhere please let me know.

Disclaimer:

I realize that the examples in this post are a gross oversimplification of combat in League of Legends. However, I also believe that they illustrate a very real balance problem in the game.

Background:

In a fight between two champion, every (combat) statistic in League of Legends can essentially be viewed as either increasing the defending champion's "effective Health" (or expected time to live) or else increasing the attacking champion's "average DPS" (or equivalently decreases his expected time to kill). In League of Legends virtually all combat statistics exhibit constant returns to scale. That is, each point of the statistic is worth just as much as the one before.

For example, consider a hypothetical fight between Champion A who uses a physical attack that deals 150 damage every 1.5 seconds, against a Champion B who has 1000 health. Assuming that Champion A has 0% critical strike and Champion B has no armor, then Champion A has 100 average DPS and Champion B has 1000 effective health (and thus Champion A kills Champion B in, roughly, 10 seconds).

Now if Champion B were to gain 10 armor, each of Champion A's attacks would deal only 136.36 damage, and so Champion B would have 1100 "effective health" (i.e., he would survive 11 seconds against 100 average DPS). If Champion B were to gain another 10 armor (20 total), then each of Champion A's attacks would deal only 125 damage and Champion B would have 1200 "effective health" (i.e., he would survive for 12 seconds against 100 average DPS). This occurs because Armor exhibits constant returns to scale (i.e., every 10 points of armor buys Champion B one additional second of life, or 100 effective hit points).

Now let's say that Champion A buys an item that increases his attack speed by 50% (and we'll go back to the case where B is unarmored). Then Champion A attacks once every second and thus Champion A would deal 150 "average DPS". If Champion A buys a second item that increases his attack damage by 50%, then he attacks once every 0.75 seconds and would deal 200 "average DPS". This occurs because Attack Speed exhibits constant returns to scale (i.e., every 50% attack speed buys Champion 50 average DPS).

Finally, let's consider an example where Champion X is attempting to kill Champion B with a magic spell. If the spell has 400 base damage and a 4 second cooldown, then Champion X has 100 "average DPS". (We assume for simplicity that Champion X is using only this one spell, but the math works out in essentially the same way if Champion X were using multiple spells or a combination of spells and auto-attacks.) If Champion B has no Magic Resistance (aka spell block), then Champion B has 1000 "effective health" against Champion X.

Let's suppose Champion X's spell has an ability power ratio of 3 ability power = 2 damage. Then if Champion X buys an item that increases his ability power by 30, his spell will do 420 damage and he will deal 105 "average DPS". If Champion X buys a second item that increases his attack damage by 30 ability power, then each spell deals . This occurs because Attack Speed exhibits constant returns to scale (i.e., every 50% attack speed buys Champion 50 average DPS).

Side Note: Throughout this discussion, I will assume that Champion X begins a fight at full mana and has enough mana to kill Champion B. (This is a reasonable assumption, most Champions who begin a fight at full mana have enough mana to win the fight without running out). Mana is somewhat different than statistics like Attack Speed or Ability Power in that more mana generally does not enable you to kill faster, but instead reduces downtime (i.e. time spent waiting between fights or making a trip back to base). In many ways, Mana is more similar to movement speed in that high mana enables your character to be able to participate in fights that you might otherwise miss out on.

The Problem with Cooldown Reduction:

The problem with cooldown reduction is that unlike other combat attributes, it exhibits increasing returns to scale! This means that every 10% cooldown reduction is worth more than the previous 10%.

Returning to our previous example, let's say that Champion X buys an item that reduces cooldowns by 10%. This means that he can cast his spell every 3.6 seconds, and he has 111 average DPS. Now let's say hebuys a second item that reduces cooldowns by 10% (20% total). Then Champion X can cast his spell every 3.2 seconds, and so he has 125 average DPS. This means that the second cooldown reduction item gave him 14 DPS, but the first only gave him 11. (Similar calculations would show that a third 10% reduction item would yield an additional 17 DPS and the fourth would yield 24 DPS.)

Why this is bad:

The fact that cooldown reduction provides increasing returns to scale means that it is infeasible to appropriately balance cooldown reduction items. If it is worthwhile for a Champion to buy the first cooldown reduction item, then it is worthwhile for him to keep buying cooldown reduction items until he hits the cap on cooldown reduction. That is, either the final cooldown reduction item (that brings the champion to the cap) is too expensive, or else the first one is too cheap. This problem is exacerbated by the 9% cooldown reduction available from Masteries, because any player who takes a cooldown reduction mastery has increased the value (to his champion) of all cooldown reduction items in the game. (That is either cooldown reduction items are overpriced for players who take the cooldown reduction masteries or they are underpriced for players who do not.)

If you are skeptical that there is a real problem here, go to the strategy forums and read the guides. Virtually every guide in the strategy forum either recommends that a player neglect cooldown reduction completely, or else recommends that the player acquire enough cooldown reduction to hit the cap. (There are a couple guides that recommend only a small amount of cooldown reduction, but I would argue that those guides are mistaken.)

One Possible Solution:

Change the way cooldown reduction stacks to make it more like attack speed. If a champion has a basic attack that fires 0.5 times per second, then each 10% attack speed that a player acquires makes the attack fire an additional 0.05 times per second. (That is, if a champion attacks once every 2 seconds, with 50% increased attack speed he attacks 1.5 times every 2 seconds ... or once every 1.33 seconds).

Similarly, if a champion can use an ability (i.e., cast a spell) once every 4 seconds (i.e., the spell has a 4 second cooldown), then equivalently, the champion can use the ability 0.25 times per second. Therefore, in a matter analogous to attack speed, each 10% cooldown reduction (i.e., 10% ability use speed) should increase the use rate of the ability by 0.025 times per second. That is, with 20% cooldown reduction (i.e., 20% ability use speed) the champion should be able to use the ability 0.3 times per second, which equates to a cooldown of 3.33 seconds.

Note: Obviously, such a change would require re-pricing all cooldown reduction items. However, it would at lease enable the creation of a pricing structure that is consistent with the pricing of other item statistics in the game. Additionally, with such a change it would not longer be necessary to have such a low cap on the amount of cooldown reduction a champion can use. (That is, the fact that cooldown reduction needs to be capped at 40% or 50% ... I forget which ... is a symptom of the increasing returns to scale problem discussed in this post!)

TL;DR

Every 10% reduction in cooldowns is worth more to your champion than the previous 10% cooldown reduction. This means that every champion either wants no cooldown reduction or wants to hit the cooldown reduction cap. This is a bad thing and makes it infeasible to fairly price cooldown reduction items. The mechanics underlying cooldown reduction stacking should be changed.


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Stormiy

Senior Member

10-16-2009

HaHa. Your are comparing in very biased way. There is no way that in the time when someones spell hits 400 dmg melee char would have 100 damage. Also you miss the calculation about AP vs Cooldown reduction


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The Johninator

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Senior Member

10-16-2009

Interesting post, but I'm sure this is a large part of the reason cd reduction caps at 40%, whereas most other stats do not have a hard cap.


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Brains

Adjudicator

10-16-2009

You have a good point, but just because something is more expensive for different people doesn't mean its improperly balanced. You are saying that runes and masteries make cooldown items more valuable, and I think thats intended. The same way +ap runes would make the +ap% item more valuable.

Its still a plausable strategy to get some cooldown reduction (not max at 40%), because there is a certain point where it is better to pay for other stats. For example, you are dying every five seconds, so you buy some health and armor instead of cooldown.

You are also saying that the cooldown items get cheaper as you buy them, but in reality you can only buy a maximum of four of these items, with cooldowns and masteries you would be crazy to buy three or more. This makes the cost balance problem pretty irrelevant.

Basically i'm pretty sure riot was aware of this when the implemented cooldown reduction items. They want a hard cap, because some abilities would be impossible to balance if they had to take into account potential 70-80% cd reduction.


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ERazER

Senior Member

10-16-2009

Yeah, it would be better if dodge and cooldown reduction have the same EHP and DPS gains with multiple items.


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Thinkaman

Senior Member

10-16-2009

The key here is that different mathematical scales of returns isn't bad. In fact, quite the opposite: It's what makes the game interesting. The hard cap on cooldown reduction shows the design thought that went into this.

Though if you think cooldown reduction in general has good scaling, check out Zilean...


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Logo

Senior Member

10-16-2009

I think you missing important parts in your discussion

Quote:
Every 10% reduction in cooldowns is worth more to your champion than the previous 10% cooldown reduction. This means that every champion either wants no cooldown reduction or wants to hit the cooldown reduction cap. This is a bad thing and makes it infeasible to fairly price cooldown reduction items. The mechanics underlying cooldown reduction stacking should be changed.
1. Every 10% reduction in cooldown ALSO makes +AP (or attack stats) more valuable as well. Since the AP to Damage ratio doesn't change with reduced cooldown adding 1 AP to a spell with 40% cooldown is worth more than adding 1 AP to a spell with 0% cooldown.

2. The DPS benefits of CD reduction in a real situation are rounded. You can't cast 2 and 1/2 Fireballs. Either you cast 2 or your cast 3. If reduced cooldown on an ability doesn't provide you the opportunity to get another spell off in a fight then its not boosting your DPS for that fight. Likewise the CD reduction of long cooldown spells is harder to determine. Take Heimdinger for instance, he's effective with CD but how much is enough? At some point between 0% and 40% the extra CD reduction isn't going to help him, once he can get 2x abilities off during a fight the rest of the -CD reduction isn't a factor.

3. You somewhat assume there's a direct Gold -> CD reduction item (implicitly). There isn't, each CD item is bundled with other stats meaning that the value of getting a CD reduction item is going to change based on how much you need the 2ndary stats coming with it. Some items like the Brutalizer stack and work great with a cheap 2ndary stat but that's an exception more than a rule.

There are a bunch of champs where I like some but not necessarily 40% cd reduction like Annie and Heimdinger.


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Kingreaper

Senior Member

10-16-2009

Can someone please confirm for me whether or not they've put the diminishing returns they promised for CD reduction into play? (multiplicative stacking to a cap of 75%)


I remember them saying they would, but people keep saying things which suggest they haven't...


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Epocx

Senior Member

10-17-2009

CD reduction is capped at 40% And is additive.


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ERazER

Senior Member

10-17-2009

The cap is still 40% reduction, but the stacking is not additive anymore and you need like 45% to reach the cap.