Discussion on the quantitative model of game combat effectiveness

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Combat effectiveness quantification is a very important part of the combat numerical design, which involves the balance of the combat value of the basic will be measured by the effectiveness of the standard. This paper takes the expression of role warfare force =ehp*edps as abstract model, attempts to quantify the combat ability of a single character, introduces the method of quantifying various attributes and character skills to combat effectiveness, and analyzes the accuracy and universality of the quantization method.

　 the establishment of abstract model

ehp=edps*time--This is the key equation for the balanced design of combat values and the core and starting point for the quantification of combat capability. Imagine A, b two characters, both shot at the same time, while death, there are the following expressions:

EHP (a)/edps (b) =time=ehp (b)/edps (a)

Thus, we can get an expression of the individual character's ability to fight:

Character Combat =ehp*edps

The quantification of the ability to combat a single character is the process of translating the attributes and abilities of each dimension of the role into EHP and EDPs.

It is worth clarifying that the purpose of quantifying combat capability is primarily to provide a basis for the ability of a character to better guide roles and professional design, rather than to mechanically balance the capabilities of various roles in an absolute manner. In general, "Features > balances" or "Balance > Features", depending on whether the game's core play is 1VS1 's single player, or multi-vs-Multiplayer teamwork, depends on whether the game's tone is more emphasis on strategy collocation or more emphasis on numerical competition. As far as personal preference is concerned, I prefer the game of strong professional distinction, and also prefer the numerical design of "characteristic > balance".

Note: The combat effectiveness expressed in the text refers to the abstract mathematical model of the actual combat ability of the character, rather than the role panel combat force displayed in the game.

transformation of various properties and abilities

1. General attack properties and defense properties

In general, when we measure the combat capability, we will convert the attack class attributes such as hit rate, critical chance and so on to EDPs, and convert the defensive class attributes, such as free-cut rate, dodge rate, Parry rate, to EHP. But a lot of planning in the property conversion of the formula is very random, and some even for each game has used a unified expression.

In the author's study of attack judgment process, we have already performed: The expressions of EHP and EDPs are different based on different attack determination processes. It is worth noting in advance that most of the EHP and EDPs expressions in this article are only examples when you apply the multiply damage formula.

Waterfall algorithm:

If hit Dodge points two times:

ehp=hp/(1-no injury rate)/(1-Parry rate)

Edps=dps* hit ratio *[1+ critical strike rate * (Critical damage Multiplier-1)]

If hit Dodge merge judgment:

ehp=hp/(1-free)/(enemy hit rate-dodge rate)/(1-Parry rate)

Edps=dps* (1+ critical Hit rate * (Critical damage Multiplier-1))

The Round Table algorithm:

ehp=hp/(1-no-harm rate)/(on Dodge rate-Parry rate)

Edps=dps*[hit ratio-enemy dodge rate-enemy Parry rate + critical hit rate * (Critical damage magnification-1)]

Note: Dodge, Parry > Crit > Normal hit, and the sum of the probabilities of each state does not exceed the round table size

When calculating the combat capability of a character, its calculation must match the attack judgment process, not all the EHP and EDPs calculations in all games have a uniform expression.

2. Skills

The character's attack attribute causes damage to enemy targets through the carrier of the skill (the general attack can also be understood as a skill). When quantifying a role's ability to attack, you can benchmark the skill of the benchmark output, or you can try to set a cast combination of character skills in a specific battle duration (for example: Mage casts 8 ice arrows, 4 fire strikes, 2 ice rings, and 1 ice picks in a 45-second PvP battle) The Warlock uses Chaos arrows, sacrifices, burns, lighted loops, etc. in a 5-minute pve battle, and constantly modifies a combination. The sum of the amount of damage provided by this skill set, divided by the duration of the battle, gives the EDPs ability of the character in the battle scenario.

In addition, the EDPs of a single skill can also be quantified by calculation.

(1), Benchmarking output skills

Whether the heroic blows of a warrior in World of Warcraft (version 60, 70) or the Savage's ancestor Hammer of Diablo 3, either attached to the next attack, or replaced with this skill, can be understood as a powerful version of a common attack:

edps= Skill damage/attack interval for a class of general attack skill

The ability to read the cast spells can also be used to abstract the EDPS within a unit of time:

edps= Skill Damage/cast time for read spell spells

It is worth thinking that the longer the cast, the more likely it will fail to cast (interrupted, the target runs out of the cast range, etc.), so the extra amount of damage, the so-called high-risk high return, is often replenished at design time. Therefore, in quantifying combat effectiveness, the same needs to be done to reduce the appropriate reduction.

As to the amount of damage, and the number of spells more than how much of the skill needs to be corrected, need to be repeated testing, not generalize, because it and other related design and game features closely related, such as: various occupations in the game, the number of disruptive skills and the frequency of the attack, whether the damage caused by casting delay, the type of game , the smoothness of the operation, the average delay time of the server, etc. In the same vein, there is a need to reduce the amount of combat effectiveness and may require multiple tests.

(2), instantaneous output skills

If there is no public CD setting, the EDPs increase of the instantaneous skill has the following expression:

edps= Skill Damage * (time/skill cd+1)/time

Note: The battle has just begun to be cast first

If there is a public CD setting, then:

edps= (Skill damage-Public CD duration * Benchmarking Skill EDPs) * (time/skill cd+1)/time

Note: Of course, you can also calculate the number of times set in the previously set skill cast combination.

(3), damage absorption skills

Obviously, the damage absorption skills can be easily converted to EHP:

Damage absorption skill EHP = damage absorption/(1-Role free injury rate)

Note: The damage is designed to be affected by the role of the first part of the exemption, of course, can also be designed to be exempt from

(4), control-based skills

Control skills can be understood as an extension of the duration of combat, that is, during the duration of the control skill, we suffer less damage and can even inflict damage on the enemy unilaterally. The expression of our ehp= enemy edps*time can be understood to weaken the enemy's EDPs, which in turn can increase our ehp in disguised form:

Conversion of our EHP increase = enemy edps* control skill weakening percentage * control duration

Note: The ability to reduce attack speed is equivalent to a percentage weakening the enemy's DPS, stun and other skills equivalent to the enemy's DPS dropped to 0 during this time period.

(5), Friendship tips

Skills can be quantified as combat capability, but in fact, in the conventional numerical design process, the role of combat forces should be the starting point for the design of skills. We can turn EHP into control skills and damage absorption skills, transforming EDPs into physical skills, various types of damage skills and instant spells with different cast times. In fact, the ability to combat similar properties template, through the characteristics of the skills of the design, can be derived from a number of distinct characteristics of the profession.

3, block properties of the calculation-fixed injury-free and percentage of injury-free

The common block properties are designed in two different ways:

A, the successful block after the percentage of injury-free

This block effect is equivalent to a part of self-injury, but the probability of triggering:

Waterfall algorithm:

ehp=hp/(1-no injury rate)/(1-Parry rate) (1-Block rate * block-free percentage)

The Round Table algorithm:

ehp=hp/(1-no injury rate)/(ratio of dodge-Parry rate-block rate * block-free percentage)

Application examples: World of Warcraft, Dragon Ball

B, the successful block after the reduction of fixed value damage

This block effect can be abstracted as the weakening of the enemy's EDPs, and can be converted to the increase of our EHP:

Enemy EDPs Weaken value = block-Free VALUE * block rate/enemy attack interval

Conversion of our EHP increase = block injury-Free value * block rate *time/enemy attack interval

Application Example: Diablo 3

Note: This algorithm can not be very rigorous, in extreme cases, block injury value is greater than the enemy's EDPs, overflow part is wasted. But most of the cases are still applicable.

It can be seen that not only the block properties, like the block effect of talent, passive injury-free skills, can be calculated according to this.

4, the calculation of HPS

The HPS mentioned here includes: Hot skills for continuous treatment, life response per second, hit life response, and so on. Such effects can also be abstracted as a weakening of the EDPs of the enemy:

Enemy EDPs weakening value = our HPS

The HPS can also be thought of as a life resilience, which is calculated as a ehp=edps*time balance equation:

Character hp=[enemy edps* (1-no injury rate) * (1-Parry rate)-hps]*time

Role ehp= [Enemy edps-hps/(1-free rate)/(1-Parry rate)]*time

Note: The attack decision process is the waterfall algorithm

Character ehp=[enemy Edps-ehps]*time

With this equation we can find some subtle situations:

The effect of HPS will be the character's protection against injury, avoidance and other defensive properties amplification, the design of its values must be taken into account, when necessary, should be added to reduce the treatment effect of the properties to deal with.

In other words, when EHPS (the increased HPS) is larger than the EDPs of the enemy's character, the player's character will never die. As in the early versions of Diablo 3, the secret Engineer's ability to use the energy shield is paired with a high-second return, which is instantly full when not killed by seconds. Domestic games due to the emphasis on pay growth, when the super-R high defensive properties, the effect of the HPS is greatly amplified, it may make such attributes or can be treated too strong situation. The strategy should be considered in advance so as to avoid a serious breakdown of the occupational balance.

analysis of accuracy and universality of effectiveness quantification

In the last piece of content, we have transformed the attributes and capabilities of each dimension of the role into expressions related to EHP and EDPs, and at the time we are done, can we think of force majeure factors such as stripping operations, such as human factors, network delays, and so on, that each character's combat capability has been transformed into a precise digital expression?

It seems that under the cognitive of some numerical planning, the character combat ability = Role ehp* role EDPs This expression is only related to the attributes of the character, and can perfectly reflect the absolute combat effectiveness of a character. According to the author's observation, this kind of cognition is widely existed in the various forum's numerical section, but many game designers forum pushes "The depth good text" also does not seem to have explored this point deeply.

In this module, let's take a moment to get out of the illusion and examine the accuracy and universality of the combat effectiveness quantified by this model.

1. Participation calculation of adversarial attributes

In fact, a careful deduction can be found that in the characters EHP and EDPs expressions, there are a large number of enemy properties involved in the calculation. At this stage, the existence of antagonistic attributes is ubiquitous (critical strike and uprising, dodge and precision, armor and piercing, special attack and special defense, etc.). As long as there is the existence of a confrontation attribute, the expression of EHP or EDPs is bound to be related to the enemy's attributes, almost impossible to peel off, which means that the combat effectiveness of the player character changes with the enemy's attributes.

If there is a confrontation attribute in the numerical system of the game, the combat effectiveness of the character will change with the property of the target, and it is not universal.

2. Attack Judgment Process

Assuming that a numerical system without any adversarial attribute exists, can it be assumed that the character combat capability expressed in Ehp*edps is universal? Or not.

(1) Round Table algorithm

If the attack decision process uses the Round table algorithm, it is not possible to abstract EHP and EDPs that are related only to their own attributes. Because there is only one state decision, it is inevitable to peel off the properties of both sides, EHP and EDPs are dependent on the enemy properties.

The non-stripping attribute referred to here does not refer to the property of precision and evasion, critical strike and uprising, but refers to: our EHP calculation is related to the enemy hit rate, and our EDPS calculation is related to the enemy's defensive attributes.

Edps=dps* (hit ratio-enemy dodge rate-enemy Parry rate + critical hit rate * (Critical damage Multiplier-100%))

ehp=hp/(1-free)/(enemy hit rate-our evasion rate-our parry rate)

(2) Waterfall algorithm

Even if the waterfall algorithm is used, if the judgment of hit and Dodge is combined with dice (the ratio of hit rate and dodge ratio is calculated by combining the actual hitting probability and then the dice is determined), then the expression of our combat effectiveness is still not related to the enemy's attributes.

Edps=dps* (hit ratio-enemy dodge rate) (1+ critical strike rate * (Critical damage Multiplier-100%))

ehp=hp/(1-free)/(enemy hit rate-our dodge rate)

Every time the decision of the attack judgment process is not the attribute of the target to participate in the calculation, the role of the effectiveness of the quantification of the likelihood of universality.

3, Damage Calculation formula

If you do not design a confrontation attribute, at the same time choose the waterfall algorithm to attack the decision, a roll of dice only throw unilateral events, and do not mix against the target properties, then the quantification of its combat effectiveness is absolutely accurate? Still not necessarily.

(1), subtraction formula: Damage = Our attack-enemy defense

Obviously, if the game's damage calculation uses the subtraction formula, it must not be able to abstract the EHP or EDPs that are unrelated to the enemy's properties, and the damage = attack-Defense calculation process is related to the properties of the opposing parties.

(2), multiplication formula: damage = Our attack * (1-enemy injury-free rate)

In the system of multiplication formula, EDPs and EHP expressions which are independent of the enemy's properties can be obtained.

(3), Division formula: Damage = Our attack * Our attack/(our attack + enemy Defense)

In the system of the Division formula, the properties of the two sides are still mixed together in the damage calculation and cannot be peeled off.

If the damage formula is subtraction or division, the combat effectiveness of the character will change with the properties of the target and not be universal.

4. HPS Properties

The action mode of HPS property is equivalent to the damage calculation method of subtraction system, which is necessarily related to the enemy attribute.

When the utility of HPS is included in the calculation, the combat effectiveness of the character will change with the property of the target, and is not universal.

5. Control skills

Needless to repeat, the ability to quantify the combat capability of an enemy is not related to the enemy's attributes by controlling the skill of the opponent's effects.

If the control skill is considered, the combat effectiveness of the character will change with the ability to resist the target and not be universal.

6, the summary of cold water

Only in cases where the expression of EHP and EDPs is related to the property of one's own, the character combat capability quantified by the method described in this paper is the most universal and accurate absolute value; other times, the character's EHP and EDPs calculations are basically a reference value based on a predetermined enemy.

The EHP and EDPs expressions are only necessary if they are related to their own properties:

In the attack decision process, only one single roll of DICE is involved in the calculation of the attributes.

The damage settlement formula is a multiplication system.

Application Example: Diablo 3 attack decision process using waterfall algorithm, the damage formula is the multiplication formula, and there is no adversarial attribute, in the case of the return, second return, etc. as a reply ability (EHPS), the player role of the EHP and EDPs only related to their own properties, so it can be displayed in the panel, To facilitate the player to select equipment and compare attribute values.

See here, is there a despair and sadness in my heart? Commonly used EHP and EDPs expressions, the quantified combat capability is a reference value based on a particular enemy and is almost never universal. This is not the model itself caused by the shortcomings, in fact, in the author's cognition, the quantitative model has been the most applicable, but also the most accurate simulation.

Note: If you know more accurate and versatile ways to quantify your combat capability, please do not hesitate to enlighten me.

7, warm heart of chicken soup

We have concluded that in the vast majority of cases, the quantification of the ability to combat a character requires a reference to a predetermined enemy, and the calculated value is only a guideline. So, is the calculation of character combat ability futile, and is there any need for it?

The answer is very definite--very necessary! Because even if the reference value, as long as set up the appropriate frame of reference, it is of great significance. As the value of the designer, we can not control the behavior of the player, can not guarantee that the player in accordance with our expectations of the game, nature will not be able to ensure that the character of the player's characters in accordance with the design of the plan to grow steadily.

While we have no control over how the player's character will experience each battle during the growth process, we can control the limits of the player's ability to fight. Through the control of player character EHP, EDPs, Ehps limit value, we can limit the ability range of players in different stages, we can control the ability gap between RMB players and free players, we can guarantee the player's behavior, cannot cross the border.

At any time, we should be firmly in control of the attributes and skill limits. As the designer of combat values, we should not only ensure that the role capability is put at a definite limit, but also clearly simulate the combat situation when the character gets the ultimate battle force. And this is the actual application value of the quantitative model of combat effectiveness.

The use of this extreme design method may not be able to achieve the precise customization of the player experience, but at least the stability and order of the numerical system can be ensured.

8, a little spit groove

Have seen a lot of teaching in the forum, will EHP and EDPs algorithm speak vividly, but no mention of the corresponding attack judgment process design. Have seen a lot of numerical planning, and even did not understand a game of the overall numerical architecture, using a unified EHP, EDPS calculation of the role of combat effectiveness analysis. This kind of article and this kind of culture in fact the harm is shallow, also made me blinders not see Tarzan.

I do not deny that there are some experienced big guy only by feeling can design a good experience of the game values, but most of us ordinary people, whether should put down this indefinitely scholarship attitude, interrogation, think carefully, discern.


written in the last

I just entered the first half a year ago, browsing around the game design site value area of the article, found an interesting phenomenon: those superficial vague to not worth reading articles, often have majestic grand title, at the same time the text of the lines are revealed as the rules of the faint pride of the rule-makers. This may be due to the domestic market income-oriented environment, the importance of the game's pay-for-value design has been raised to unprecedented heights.

But those really valuable articles, instead of the most peaceful wording, passed through the actual practice of baptism to come to the insight. With the deepening of the understanding of numerical design, I feel more and more valuable experience of predecessors. Its value is not only in the continuous practice of repeated verification of the classic model and mature design, but also in the design concept of innovation and remodeling.

At the beginning of the entry, my leader said to me:

If the numerical design only stays in the Excel table, can never have the big act.

When I first began to glimpse the gateway, my leader said to me:

As a numerical planner, there are few things that can be controlled. But it would be enough if you could really hold those things firmly in your hands.

A remarkable numerical plan, it is clear to understand that they can not omniscient, only to build a virtual world of solid boundaries.

It is under such guidance that I clearly recognize the limitations of theoretical deduction, and understand that no good model can accurately simulate everything; knowing that all good projects have gone through countless cycles from measured to modified models.

The value is just a tool, it relies on the system, also serves the system. Since in the service industry, it is better to abandon the "value above all" pride, pick up the basic quality of the service industry-a humble heart.

Trying to control everything, but just delusion.

Discussion on the quantitative model of game combat effectiveness