Balancing Theory

Subject: Balancing Theory Sun Dec 13, 2009 10:36 pm

Nome wrote:

The Law of Concessions
This is not a real law--it's something I made up for this article. However, it is something you should follow at all times when using this method of balancing. To be exact, when building a skill from a balanced baseline, for everything you add, you must take something away. For example, if you add damage, then you must increase mana cost. If you remove cooldown, then you must decrease stun duration. On the other hand, if you increase damage, but lower cooldown, you create a direct imbalance in usefulness. Note however that there are certain exceptions to the rule--Magebane's Flash far outclasses Wretched Hag's Flash of Darkness in every respect. This stresses the importance of context--while Magebane is a single-target DPS survivalist carry, Wretched hag is a spell-casting DPS monster.

To illustrate the concept of the Law of Concessions, let's take a look at DotA's Sven the Rogue knight and Leoric the Skeleton King. DotA is used because there exists a large amount of redundancy in the skills, though IceFrog has been trying to differentiate heroes lately. Because DotA has been through years of playtesting and balancing, we can use its numbers as a baseline for what we wish to do. Historically, the two heroes played foil to one another. Both were strength melee DPS characters who shared an identical stun skill and heavy reliance on passive abilities and damage amps.

Rogue Knight's Storm Bolt: single-target AoE, high cooldown, high damage.
Skeleton King's Hellfire Blast: single-target, low cooldown, medium damage.

Older DotA players may remember that both the Rogue Knight and Skeleton King had Storm Bolt at one point, though the actual spell mechanics were identical to the current Hellfire Blast, while Rogue Knight's version was eventually changed to its current incarnation. Therefore, we take Hellfire Blast as the baseline, and balance from there.

The Rogue Knight previously had only one AoE spell, which was [URL="http://www.playdota.com/heroes/rogue-knight#skill126"]Great Cleave[/URL]. Therefore, his stun was given an AoE effect in order to synergize with the cleave and make him an effective group damage dealer.
The AoE is a huge buff, as it allows for the Rogue Knight to disable a group of heroes. Therefore, we must use the Law of Concessions--the cooldown is much higher, and to keep up his total DPS, the damage is also increased to make up for the much less frequent use of the spell.

These changes in effect make the two heroes incredibly different. Hellfire Blast remains a great ganking tool, as the effective cooldown is only 6 seconds. That means that if you fight a high-mana Leoric, you are effectively disabled 25% of the time. Storm Bolt on the other hand becomes much for useful as a team-fighting skill. Paired with heroes that can clump up enemies like Enigma or Magnus, it equates to a powerful full-team disable and damage. In effect, this change shakes up the roles of each character. Storm Bolt gained damage and AoE and conceded cooldown. The Skeleton King remains a single-target DPS with amazing tanking, while the Rogue Knight gains powerful physical and magical AoE capabilities, yet the overall balance remains sensible.

Let's make our own example now. Let's say we want to give our hero a big hero-killing ultimate meganuke. We have two baseline references for this:

Pyromancer's Blazing Strike
Witch Slayer's Silver Bullet

But we don't want to just add yet another big one-off nuke, do we? That's unoriginal. Let's say we already designed his other skills--he's going to be a tankish hero that does a ton of damage both to himself and to his enemies. We come up with a cool concept...

Vengeance: Deals X + Y*(%HP missing) in damage. Cap of Z total damage.

This skill essentially does more damage the more health you're missing. To make things simple, let's balance for LVL3 only. Silver Bullet does 850 magic damage at 55 second cooldown. Blazing Strike does 950 damage at 55 second cooldown. We may, for the purposes of this example, disregard mana, as these heroes are both INT and can largely be assumed to have a big enough mana pool to be able to use their ultimates at will. We must also remember that our two baseline references are INT, which means they become less effective as the game moves on. To spice things up, let's make our hero an AGI, which means he actually becomes more effective as the game moves on. Now let's begin to use the Law of Concessions to create and balance our skill.

Pyromancer's Blazing Strike deals more damage than Silver Bullet because Witch Slayer has a superior suite of disables, which become more effective the longer the game goes on. Because our AGI hero scales better as the game moves on, the absolute cap should max out at 850 for now, which is Silver Bullet's unboosted max.
Vengeance: Deals X + Y*(%HP missing) in damage. Cap of 850 total damage.
However, we don't want Vengeance to be doing THAT much damage all the time. Yet we don't want it to be worthless either. So let's give it 350 base damage--that is, if you're at full HP, it will do that much. 350 is a decent number, because it's just as good as a normal nuke, but stresses the fact that if you don't use it under the perfect conditions, it's just as bad as a normal nuke as well.
Vengeance: Deals 350 + Y*(%HP missing) in damage. Cap of 850 total damage.
Now for the multiplier, which depends on a hidden variable--the minimum HP reward. The maximum bonus damage is 500. However, you do not want to present the maximum reward at the minimum HP (1%). Heroes that are at 1% HP should not be rewarded any more than a heroes at 2%--this is because it presents a frustrating case for the enemies hitting him. Therefore, we want to set a minimum cap. 25% HP is a good one--heroes at 25% are considered low, but not so dangerously low that using Vengeance would make his opponents cry bull. Now that we have that, it's easy to set the multiplier and tweak the equation.
Vengeance: Deals 350 + 6.6*(%HP missing) in damage. Cap of 850 total damage.
But why stop there? Let's take it further. Not only do we want Vengeance to deal damage, but we want it to heal *you* for a portion of the damage dealt. To gain this immensely powerful effect, we must make concessions. First, we must acknowledge that the healing effect is worthless when you're at full HP--therefore, we should base it entirely on the bonus portion of the damage. Next, we should consider that if we add a healing effect, it shouldn't do as much damage, because that would make it too powerful. Therefore, we must lower the multiplier and the cap. We don't want to make the heal too low, but we don't want to make it too high either, and because we are lowering the multiplier and the cap, we can make the heal multiplier be 100% of the bonus damage. The most powerful single-target heal in the game belongs to Jeraziah, who heals and deals 360 true damage, and can be cast on anyone. Vengeance only affects your target and yourself. Because it is also an ultimate, it should be higher. Therefore, we come up with this:

Vengeance: Deals 350 + 5.0*(%HP missing) in damage. Cap of 725 total damage. Heals yourself for 100% of the bonus damage inflicted.

Hope you enjoyed the read, and happy suggesting!

What do you guys think about this? I mean, he has a point... but I'm not so sure his math nor his concepts are true.

Subject: Re: Balancing Theory Mon Dec 14, 2009 12:18 am

It's something so basic that I thought it was understood by everyone. Adding math to it without any actual proofs of the math is pure conjecture.

Subject: Re: Balancing Theory Mon Dec 14, 2009 12:23 am

Too hard. Relativity, context etc. are important factors and those are very often subjective more than objective.

For example - how much range = damage? Is it fair to off-set the same base skill by 25 damage for 100 range? Or should it be 50? Or 75? Or 100? How much mana is one damage worth? All of this matters - but can only be answered in context, and subjectively.

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