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解析游戏系统设计中的经济学原理

发布时间:2011-07-29 10:42:01 Tags:,,,,

作者:Mike Birkhead

这只怪应该给多少经验?这个物品的掉落率应该定为多少?我们怎么知道两种功能相异的物品价值相当?

经济学研究的是稀缺条件下的抉择。探讨玩家动机的角度之一是,经济学。这种视角告诉我们,玩家在不断地做选择:玩游戏、玩你的游戏、练战士还是术士、在剑术上加5点还是在念力上加4点……资源是有限的,所以玩家如何做出一种选择而抛弃另一种选择?因为这种选择更有益;因为这种选译让角色更强大;因为这种选择能提升地位;因为这种选择让人开心。所有的奖励都可以用经济术语表达出来。通过学习经济理论的基础,你就可以回答关于玩家的奖励系统的重要问题。

玩家希望有种自己完成了不得的事的感觉——即他的努力成果必须得到确认——确认的方式之一是奖励玩家有形资本(新工具、金钱或药水等)、角色资本(新技能或经验点)、人力资本(声望、剧情片段或成就)。当系统以奖励(红魔法球)确认你的努力成果(杀死那些hoplites),你会对自己的努力感觉良好;你觉得你的行动有成效,你想再接再励。作为设计师的你甚至可以通过在奖励中添加随机元素使玩家的这种体验效果翻倍。

系统设计师不仅要理解导致成就的原因,还要回答关于系统的重要问题:物品价值多少、物品掉落率应该是多少和玩家投资点在哪里等等。这些问题的答案来自对经济学基础的充分理解。

economics(from ecocn.org)

economics(from ecocn.org)

扎实的基础

没有坚实的地基,就没有高楼大厦。所以我们必须打好基础。扎实的基础的基石之一是含义辞典——这是我们在设计中遇到的挑战,是借用某种(目前)有效的方式得到的益处。以下是一个术语及其含义清单:

消耗性商品:一经使用即报废的物品,如命值药水。

可靠性商品:使用后仍有持续效果的物品,但该物品会越来越贬值。某物贬值的速度越快,它就越接近消耗商品。

密封性商品:不具有消耗性、且不能贬值的物品。注:电子游戏中的大多数物品属于这一类。

有形资本(K):有形游戏物品对玩家是有价值的,能帮助玩家更有效地克服挑战。决定工具的重要性(游戏邦注:这里可引申至它对玩家生产活动的影响)是拥有该物带来的乐趣程度。

角色资本(A):这是给予玩家的抽象奖励,如新技能和能力。角色资本有价值,但在游戏世界中是没有实体表现的。这类物品不可交易,但与有形资本类似,施加在玩家身上的影响决定其重要性。

人力资本(H):玩家的知识也是生产能力的重要因素。虽然我们并不能直接从玩家身上交换来,但我们应该总是重视玩家日渐增长的知识和技术。熟练的玩家的生产速度和效率肯定超过菜鸟玩家。以《战神》为例:玩家从摧毁石化怪中能得到更多魔法球(知道的人不多),保持长时间攻击数可以获得额外的魔法球。这两种额外奖励,如果使用得当,可以极大地补充熟练玩家的生产能力(魔法球数量)。

生产能力(q):简而言之,给予流动资产、技术和一定量的劳动力资源(人力资本),玩家能够生产的数量,就叫作生产能力。对于游戏而言,这意味着玩家的杀怪速度、解疑速度、通关能力或者完成任务的速度,即完成所有给予玩家奖励的活动的能力。

小型开放性经济(SOE):这是由游戏玩家之间的交易而形成的市场(多人游戏)。这不同于玩家与NPC商人之间的交易,甚至与玩家和“外界世界”的交易(ebay)也不同。

世界市场(GM):这是由NPC商人定义的市场。在大多数游戏中,NPC商人出售一种无限供给品,他们能满足对特定物品的无限需求。无限供给品是自我控制的,所以在这种市场中的交易不会影响到玩家市场或NPC商人。

以下讨论会引用大量MMO游戏作为例子。尽管MMO对于本讨论是完美的测试案例,但绝不是唯一能运用到经济学的游戏。《战神》里有经济;《神秘海域》里有经济;《真人快打》里也有经济。只要玩家需要做出选择、只要你给予玩家奖励,你就是在市场上做生意。你和玩家之间存在交易。所以我会努力列举尽可能多的例子,如果你们不嫌我唠叨的话。

生产与报酬

我们现在所讨论的所有问题都源自一个基本前提:你可以对游戏中的商品赋值。一把剑有价值,好比一项技能有价值,你可以进行含义探讨,即选择一种而放弃另一种的优势。但在此之前,你必须克服两个主要障碍:游戏中的什么机制能赋予某物价值?这些价值的含义是什么?

第一个问题相对简单,如果你注意到我们已经定义过的答案:生产能力。

生产能力

简单地说(虽然实际上它没那么简单),生产能力是三种因素(资源、资本和劳动力)的相互作用。不过别把我的话当回事,真正的经济学家会怎么说呢?

在人工虚拟的世界里,产品(q)是一些对象——杀怪物掉落的战利品、精心制作的物品、来自任务的奖励。这些商品由花费自己的时间去获取的玩家生产出来。玩家获得这些商品的能力取决于四个因素:玩家技术(人力资本(H));角色技能等级或经验等级(角色资本(A));角色的装备(有形资本(K));怪物的数量、制作投入或由游戏世界提供的道具(资源(R))。

————Edward Castronova,《Synthic Worlds:The Business and Culture of Online Games》

由以上定义可以得出一个函数:

产品(q)=(劳动)(有形资本)(角色资本)(人力资本)(资源)

q=f(L,K,A,H,R)

任何因素的增加,都会导致玩家生产能力和玩家挣得的报酬的增加(即成正比关系)。如果我的装备(K)改善了,我的杀怪能力也会提高。如果我知道所有敌人的秘密弱点(H),那么我就能更快更容易地杀死他们。两名所有因素都相符的玩家(相等的劳动(L)、相当的知识(H)、相同的资源(R)),如果两名玩家都能够获得相同的报酬,那么我可以担保他们的K和A也是相等的。正是这种基本前提使得我们能够以有意义的方式比较物品的价值。

生产重要性

某物的价值是复杂的,特别是在现实世界。有些东西具有情感价值或能抬高物主的地位,这种东西是无法用理性分析的。在游戏中,物品和技能的价值却是有限的,此外还服务于增加玩家乐趣这个首要目标。我们之所以玩游戏,因为游戏能带来乐趣。打游戏的次要目标是通过努力完成某事,完成某事的速度取决于生产能力。

所以,可以说最大化生产能力就是最大化游戏乐趣。

但还不止于此。生产很重要,是因为它让我们进行有意义地比较和对比,相当无意义的说法是“嘿,我只是更喜欢这样武器。”对于用户,可能,除系统设计师以外,这样说可不太好。你必须知道,因为如果你不能判断两样武器的机会成本,那么玩家也不能;此外,如果玩家不能判断,你就会让玩家心生不满。

study_economics_production Stages(from flarkminator)

study_economics_production Stages(from flarkminator)

如何利用生产

现在我们拥有生产能力了,我们可开始对关于游戏的真正问题发问了。一个好问题,一个你应该不断问自己的问题是:“如果玩家行骗,那怎么办?”。简单,试想一下,行骗就是不公平地最大化生产中的任何因素。研究你的系统时,不妨思考一下,当有人拥有无限的资本(疯狂的装备)、无限的资源(复制物品)或无限的劳动力(自动脚本程序),会发生什么事。

如果这些情况完全破坏了系统的平衡,那么你可能得重建系统。那种特定投入的扩散力对资源和生产的影响非常大。

你可以问的另一个问题是,“以下玩家更想要什么:物品A、物品B、400经验点?”简短的答案是,对玩家的乐趣具有最大影响的物品。详尽答案就要回头考虑一下生产能力。如果我们确信最大化生产能力会最大化我们的乐趣,那么问题的答案取决于玩家当前的情形。物品A,从字面上看,比物品B更优越,但最重要的是它对玩家的价值。字面上看物品A只是一个临界升级,而物品B却是一个主要升级,所以实际上玩家考虑到自己的机会成本,会选择物品B,因为物品B对玩家的整体生产能力具有更大的影响。玩家可能不会在这些物品中看到总体生产能力,但在经济学辞典中就有所体现。

我没有办法这样慢慢讲下去,你可能会错过重要的点:如果玩家有知识去比较和对比他的选择,玩家能够只准确地做选择——有些人可能会有争议;并且,如果系统教他,玩家才能获得这种知识;最后也是重要的,如果作为设计师的你没有清楚地把这种知识融入游戏中,系统是无法教会玩家的。

开始价值

我们可以比较,但我们没有价值。所以我们从哪开始?下一步是找到游戏的运转基础。在《街头霸王》中,所有事物都是围绕着隆与古烈的战斗设计的。在《战神2》中,所有事物都是围绕着Skeletons设计的。在《战神:奥林匹斯之链》中,所有事物都是围绕着Hoplites设计的。任何游戏都有它的“隆”——它的基础。不要随便地把价值赋给所有事物。当所有事物的价值都来自基本角色,那么它们就成了这个基础中的可称量因素,所以当基础改变了,你就已经知道如何调整所有其他事物。它是一种一致的系统调整,而不是胡乱地尝试。

理解你的生产能力及其对价值的控制,大有裨益,但此外,一旦你理清玩家的生产等级,你就可以开始计算对象的价值和它们进入(或退出)系统的比率。

计算掉落率

掉落物品,经验点和金币都是进入系统的价值(类比“金钱”)。你的目标是保证流入系统的金钱与流出系统的金钱持平,这是为了防止通货膨胀。这种价值流入市场就好比,有人快速打开水池的水龙头。我们可以把金钱流入系统的速率称作:Vf。这种价值在针对各类人(或针对玩家)的市场(水池)中呈螺旋式上涨,最终流出市场,同时将价值从经济体系中移除。我们可以称流出市场的速率为:Vd。这样,你可以得到以下等式:

Vf=Vd

在《战神》中,当我杀死一只怪,我就得到红色魔法球(Vf)。这些魔法球就是流入市场的价值。我不断积累魔法球,然后打开菜单,用这些魔法球升级东西(Vd)。从本质上说,我在世界市场中进行了交易,然后我就间接升级了我的角色资本。这种升级(我的魔法更强大了)增加了奎托斯(Kratos,《战神》主人公)的击杀能力,从而增加了Vf率。以下是环路图:

study_economics_inflation Cycle(from flarkminator)

study_economics_inflation Cycle(from flarkminator)

让我们在称之为“World of Flarks”的伪MMO(2013年秋)中进一步运用这个例子。所谓劳动力是指在工作的人数。根据怪的等级,我可以猜到劳动力资本(A和K)的一般等级。假设这些价值是固定的,那么我们可以任意改变其他变量以控制Vf,即像物品掉落率、怪的重刷率、怪的难度系数和怪的固定成本等这类东西。

我们来定义一些价值和样本怪。

《World of Flarks》:

服务器人数:2000

最高等级:20

不低于10级的人数:500

介于9-12级的人数:100

Flarkmaster之剑:

价值:10g

虚弱的Flinkar(Flinkar the Weakling):

位置:失败者森林(Forest of Losers)(世界刷出)

所在区数量:1

重刷率:5分钟

怪等级:10

难度:低

宝剑掉落率:50%

这里,虚弱的Flinkar持有Flarkmaster之剑。Flinkar是在世界刷出来的,所以杀死它是没有固定的成本的。他在游戏中只有一个,每小时刷出来12次。因为他属于低级怪,玩家的技术(H)就比较不成问题。因此,我会假定所有等级不低于10级的玩家可以利用到这个资源。因为有500个潜在玩家符合这个标准,所以我可以假设这个资源是绝对的消耗品(他一刷出就被“夺命掠财”)。简单地说,我可以确定每小时进入经济体系的价值率(Vf)。

Vf=(每小时击杀数)x(掉落率)x(宝剑价值)

60g=12×0.5x10g

每小时60g相当高了。即使不给关于理想的Vd信息,我也可以担保,我的经济目标还没达到。在此,我有几个选择。因为物品的价值和怪的等级是常数,我去掉变化的掉落率,补上固定的成本,或者改变怪刷出率。我们来试一下另一只怪:

study_economics_diabloceratops(from flarkminator)

study_economics_diabloceratops(from flarkminator)

恶魔龙小小(Dinky the Diabolical Dinosaur)

位置:Flarkmaster小树林(5人地下城副本)

所在区数量:任意BOSS(1)

召唤材料成本:1g

地下城平均长度:1小时

怪等级:10

难度:高

宝剑掉落率:X

通货膨胀上限:

0.5g/小时

这是一个更复杂的情况。怪现在位于地下城,召唤它需要付出代价,此外还是个难对储的怪。这次我们以理想的Vf(0.5g/小时)开始,解出我们的掉落率。

第一个困难是,我得确定玩家杀死这只怪要花多长时间。从世界统计信息看,我知道有100名玩家介于9-12级,这是闯荡这座地下城的理想等级范围。但是,恶魔龙小小是个强悍的家伙,确实要更强的技能和更好的装备。100名玩家中只有60名玩家达到顺利放倒恶魔龙小小所需的资本(H、K和A)

这是一座5人地下城,所以这60名玩家要分成12组;另外,这是一个副本地下城,所以这12只队伍可以同时进入这个地下城。但是这种假定需要60个人全程参与且总是彼此配合。根据文章《Alone Together》所说,玩家只花30-40%的时间参与团队,所以我们可以假设在任何给定时刻,只有3-4个团队同时活动。已知这是一只任意怪,我们可以把它减少到3。

要考虑的最后一个是固定成本。不计小小是否掉落宝剑,每个团队必须付出1g作为召唤小小的成本。最后,我可以得到新的等式:

Vf = ((击杀率) x (掉落率) x (宝剑价值)) – ((击杀率) x (固定成本))

0.5g = (3 x 掉落率 x 10g) – 3g

3.5g = 30g x 掉落率

0.117 = 掉落率

根据当前的怪、当前劳动力和这个理想的价值,理想的宝剑掉落率大约是12%。一个简单的案例,但是你可以看到像经济学家一样思考的力量所在。目前为止,我们已经关注过流入系统的金钱,但流出系统的金钱又是怎么样的一种情况呢?

通货膨胀VS通货紧缩

玩家做出的几乎所有活动都属于一类通货膨胀行为。玩家不断地把钱投入市场,如杀死《战神》中的怪所得的红魔法球,或者《魔兽世界》的Nefarion掉落的战利品。怪物并不创造这些物品和资源,所以只有玩家才能创造出价值。现在你的任务是找到把钱退出系统的方法。虽然你可能从这些物品中联想到通货紧缩,但像“升级树”的这类设计基本上是为了让玩家制造通货紧缩的。

把钱从经流体系中移除,有三个有效的方法,且每个方法都有不同的、可以用于增加或减少效力的程度。第一个方法是把交易推入世界市场中,第二个是税收,第三个是通过市场风险创造社会流动性。

世界市场

从游戏中移除金钱的最有效方法是让世界市场提供一个特有的、高使用率、消耗性产品,这种产品对玩家的生产能力影响极小——听起来很复杂,其实理解起来不难。任何时候玩家从GM中购买商品,都是将金钱从SOE中移除的机会。玩家与GM的交易越多(或产品越昂贵),从玩家经济体系中流出的就越多。因为GM的供给是无险的,需求是无限的,价格是由设计师把持的,所以无论玩家消耗多少,价格都不会改变,且玩家可以出售或购买任意数量。让我们回想一下这种必需品:为什么它是特有的,为什么让它可消耗,它对生产能力意味着什么?

特有物品:所谓特有,就是它不存在于SOE中。这使得交易必须转向GM,且该商品的价格只能按GM(游戏设计师)的要求调整。

消耗性:玩家必须不断返回GM把金钱流出来。如果商品供给是可靠的(甚至是密封性的),那么无论该物品的成本多么紧缩,玩家的渐进通货膨胀行为也会克服购买该物品的需要。非常昂贵的可靠性产品是将大量金钱从市场中快速流出的最佳办法(想一下《魔兽》的情况),但对于长期防止市场通货膨胀,这并不是一个有效的方法。

生产:GM是供应的产品对绝大部分玩家的生产能力不存在影响。正如我们已经讨论的,我杀怪的效率越高,我的生产就越多。所以,如果在GM上供应的通货紧缩的产品让我成为更有效率的生产者,那么我实际上增加了通货膨胀率(不做紧缩它的努力!)。

好吧,这听起来很棒,但并非所有物品都是可消耗的。可靠性产品怎么样?渗透性产品如何?我们是不是完全被骗了?谢天谢地,不是这样的。我们的知识来自一个相当卑劣的现代社会。第二个方法当然来源于生活:税收。

税收

从市场上流出金钱的第二个最有效的方法(虽然有时候不流行)是提供一种我们想要的服务,然后对此收费,富人多收,穷人少收——这也叫作“累进税”。本范例要求你的魔兽盔甲参与。任何时候受到怪物攻击,你的盔甲耐用度就减少。如果你死了,你也要失去大量盔甲耐用度。如果耐用度减少到零,你可能就不会再用了。修补的唯一方法是花钱找NPC商人。你穿的盔甲耐用度越高,修补它的费用也越高。有趣的是,第一眼看到这个物品会以为它是“可靠的”,且会贬值。这是不对的。因为直到崩坏的那一刻,它们都是100%有效的;一旦修复,它们又恢复100%的效力。这些物品实际上并不会贬值。它们从你买来(或做出来)的那天起就一直是那么好。它们实际上是密封的,但有一个周期的的使有税(你甚至没有意识到吧!)

风险

移除金钱的另一个方法是使玩家的花费有风险。游戏中的普遍问题,特别是在MMO中,是一旦富人掌握了财富大权,他们就一直很富有。他们没地方挥霍,所以他们的财富就被丢在一边,或者他们买下一整个拍卖行来囤积居奇。想像一下,有这么一个系统,我可以在中世纪的世界购入各种商品的股票。例如,我相信卡利姆多小麦的价值是一只风险股,但我认为它是一个增长市场。然而第二天,一群来自北方的龙族把产小麦乡村夷为平地。接下来有三件事发生了:一,因为卡利姆多小麦的交易大跌,所以金钱(可能是大量金钱)流出市场;二,杀手们涌进市场交易。我可以召集好友,然后在这群龙造成更大的破坏前将其一网打尽。三,鼓励玩家关注游戏的内外状况。如,游戏以网络方式告诉我要关注游戏内市场商品的行情。更甚的是,如果这些龙族周期性“关顾”我的小麦地,怎么办?这样,卡利姆多小麦就是一种高风险、高回报的生意了。

一旦你明白经济学探讨的要义,你就可以提出新问题。添加一种精巧的系统到游戏中怎么样?该系统的服务目的是什么?物品的品质从掉落起就一直那么好吗?经济学能帮你回答这些问题!这些本身也是值得公开探讨的,也许我得让我酸痛的手腕休息一下,才有办法处理它们吧。

如果你认为本文的话题很有意思,不妨去读读我刚才引文出处的那本书《Synthetic Worlds: the business and culture of online games》。该书对游戏中的经济学解释得更加精辟清晰,确实值得所有人阅读。(本文为游戏邦/gamerboom.com编译,如需转载请联系:游戏邦

Every System Designer Must Study Economics

by Mike Birkhead

How much experience should this monster give? What drop rate should we set on this item? How do we know two functionally distinct items are worth the same amount?

Economics is the study of choice under scarcity, and one of many ways to discuss player motivation is to view it through the lens of economics. This lens shows us that the player is constantly making choices: to play a game, to play YOUR game, to be a fighter instead of a wizard, or to take that +5 to slaying instead of that +4 to thinking. Her resources are limited, so how does she choose one over the other? Because one is more rewarding; because it makes her avatar stronger; because it enhances her status; because it makes her happy. All rewards can be expressed within economic terms, and by understanding the basics of economic theory you can answer important questions about your player’s reward system.

Players want to feel they have accomplished great things — i.e. her work product must be validated — and one way we do this is by rewarding her with Physical Capital (new gear, money, or potions), with Avatar Capital (new abilities and experience points), and with Human Goods (Fame, Story moments, or Achievements). When a system validates your work product (killing those hoplites) with rewards (red orbs) you feel good about your work; you feel your actions had purpose, and you want to keep going. You can even double the effect by adding a randomized element to the reward.

It is the system designer’s job to not only understand what drives accomplishment, but also to answer very important questions about their system: what are items worth, what drop rate should an item have, and what do the players spend their money on? The answers to all these questions comes from a good, strong understanding of the basics of Economics.

A Strong Foundation

You cannot build without a strong base, so before we analyze we must lay the foundation. One of the cornerstones of a sturdy foundation is a meaningful lexicon — something we struggle with in design, and is one of the benefits of borrowing from one that does (for now). The following is a short list of terms and their definitions.

Consumable Product — products that are destroyed after being used for the first time. Such as a health potion.

Dependable Product — products that persist after being used, but they depreciate in value over time. The quicker something depreciates in value the more it begins to act like a consumable.

Permeable Product — products that are never consumed, and also never depreciate in value over time. Hint: most items in a video game.

Physical Capital (K) — physical games objects of value to the player, which help the character overcome challenges in a more efficient manner. Deciding the importance of gear (and by extension it’s affect on the player’s production function) is going to drive the amount of enjoyment they get from receiving it.

Avatar Capital (A) — these are the abstract rewards we give the player. New skills and abilities. They have value, but they have no physical manifestation in the world. These are things that cannot be traded, but like Physical Capital, the impact on the player’s production function will drive their importance.

Human Capital (H) — the knowledge of our player is also a factor in the production function, and while we do not directly trade this to the player, we should always try and take into account the player’s growing knowledge and skills. A master player is going to produce at a much faster and more efficient rate than a novice. Take the example of God of War: you receive more orbs for destroying a stone’d monster (not something widely known), and you receive bonus orbs for maintaining long hit counts. These two bonuses could, if not handled well, drastically offset the production (number of orbs) of a master player.

Production Function (q) — in short, this is a function that expresses how much someone can produce given their current assets, skills, and resources with a certain amount of labor. For a game, this means how quickly they kill monsters, how quickly they solve puzzles, how easily they access new areas of the game, or how quickly they finish quests — all actions that grant them rewards.
Small Open Economy (SOE) — this is the market defined by trade among players of the game, if your game is multiplayer. This is in contrast to trade between players and NPC merchants, or even players and the “outside world” (ebay).

Global Market (GM) — the market defined by NPC Merchants. In most games NPC Merchants provide an infinite supply, they consume an infinite demand for any given item, and they are self contained so that trading within that market has no impact on either the player market or the NPC merchants.

A lot of the following discussion will use MMO’s as the example. Though they make perfect test cases for dissection, they are by no means the sole domain where this can be applied. God of War has an economy; Uncharted has an economy; Mortal Kombat has an economy. As long as the player is making choices with their time, and as long as you are giving them rewards, then you are dealing in the market of their time. You are trading with them. So I will attempt, while mindful of verbosity, to relate with as many examples as possible.

Production And Wages

Everything we now discuss derives from the basic premise that you can assign value to a commodity in the game. A sword has a value much like a skill has a value, and you can have meaningful discussions about the merits of choosing one over the other. For this to occur, however, you must overcome two major hurdles: what mechanics in the game assign value to something, and what do those values mean.

The former is simple, and if you have been paying attention we have already defined the answer: the Production Function.

The Production Function

To put it simply (though, in practice it is not) the production function is the interaction of three factors (resources, capital, and labor). But don’t take my word for it, what does a real economist have to say?

In synthetic worlds, output (q) is going to be some object—pieces of loot from a hunted monster, items that have been crafted, rewards from quests. This good is produced by the player, who expends her own time (L) to get it. Her ability to get the good depends on four other factors: her skills as a player, or human capital, H; her avatar’s skill levels or experience levels, or avatar capital, A; her avatar’s gear, or physical capital, K; and the number of monsters, crafting inputs, or quests provided by the world, or resources, R

-Edward Castronova, Synthic Worlds: The Business and Culture of Online Games

This definition gives us a function.

Product (q) = (Labor)(PhysicalCapital)(AvatarCapital)(HumanCapital)(Resources)

q = f(L,K,A,H,R)

Now, items that are produced have some value and can be sold for a price (p). The player’s wages (w) are now expressed in a new function.

w = p x f(L,K,A,H,R)

As any factor increases, so does the player’s ability to produce, and by extension her earned wages. If my gear (K) improves , my ability to kill monsters increases. If I know the secret weakness to every enemy (H), then I kill them quicker and easier. All things being equal between two players (same labor, L; same knowledge, H; same resources, R), if two players are able to earn the same wages, then it is safe to say that their K and A are equivalent, and it is this basic premise that allows us to compare value of items in a meaningful way.

Production Matters

The value of something –especially in the real world– is complicated. Something can have sentimental value or confer status, which overrides any kind of rational analysis. In a game, however, items and skills have limited value, besides serving the ultimate goal of increasing someone’s fun.  We play games because they are fun. Progression to the secondary goal of beating a game is accomplished by working, and the speed of that is controlled by the production function.

So one could say that to maximize your production function is to maximize your fun.

But it is more than that. Production matters, because it lets us compare and contrast choice in a meaningful way — quite the opposite of saying, “gee, I just like this weapon more.” That’s not good enough. To a user, maybe, but not to a System Designer. You must know, because if you can’t judge the opportunity cost of two weapons, than neither can the player; moreover, if the player cannot judge, then you will leave them dissatisfied.

How To Use Production

Once we have the function we can begin to ask real questions about the game. A good question, and one that you should constantly be asking yourself: “What happens if the player cheats?”. Simple, think of cheating as unfairly maximizing any of the factors of production. When studying your system try and consider what happens when someone has infinite capital (insane gear), infinite resources (duplicating items), or infinite labor (automated scripts). If any of these situations throws the entire system out of balance, then you should probably restructure the system. That particular input steam might have too much influence on resources and production.

Another question you can ask, “what would players want more: Item A, Item B, or 400 experience points.” The short answer is the item that has the greatest impact on the player’s fun. The long answer returns us back to the Production Function. If we assume that maximizing the Production Function maximizes our fun, then the answer depends on the player’s current context. Item A, on paper, is superior to Item B, but it is the value to the player that matters. Contextually Item A is only a marginal upgrade, while item B is a major upgrade, so the player, judging his opportunity costs effectively, chooses item B, as it will have the greater impact on the player’s overall production capabilities. He might not see it those terms, but that is how it is expressed in the lexicon of economics.

Without the ability to break it down this way, you might miss the crucial point: He can only make that choice accurately–some might argue happily–if he is given the knowledge to compare and contrast his choices, and he can only gain this knowledge if the system teaches him, and lastly, but most importantly, the system cannot teach him if it is not expressly designed into the game by you — by the designer.

Starting Values

We can compare, but we have no value. So where do we start? The next step is to find your Ryu, your grunt. In Street Fighter everything was designed around Ryu fighting Guile. In God of War 2 everything was designed around the Skeletons. In Chains of Olympus it was the Hoplites. Every game has its Ryu – its base. Do not go randomly assigning values to everything. You see, when everything’s value is derived from the base character, then they are scalable factors of the base, so when the base changes you already know how to adjust everything else. It is a system adjusting in concert, as opposed to wild stabbing.

Understanding your production function and its control over value is good, but what’s more, once you have a strong understanding of the production level of your player(s), you can begin to calculate not only the value of objects, but also the rate they should enter (or exit) the system.

Calculating Drop Rates

Dropped items, experience points, and even gold pieces are Value (think “money”) entering the system. Your goal is to keep the money entering the system equal to the money leaving a system. Otherwise known as preventing inflation. This Value entering the market is like someone quickly turning on a faucet in a sink. Let’s call the rate of money coming into the system: Vf. This Value spirals around inside the market (sink) to various people (or just stays with the player), and eventually drains out of the market removing Value from the economy. Let’s call the total rate of Value coming out of the market as: Vd. Thus, you want the following equation to hold true:

Vf = Vd

In God of War, when I kill a monster it gives me Red Orbs (Vf). These orbs are Value entering the system. I accumulate Orbs over time, and then I open the menu and I spend these orbs to upgrade something (Vd). I have essentially traded on the Global Market, and in return I get to upgrade my Avatar Capital. This upgrade (my magic is more powerful) increases Kratos’s ability to kill, and in turn increases the rate of Vf. See how it’s all connected?

Let’s take this example further with a fake MMO we are going to call: “World of Flarks” (COMING FALL 2013). The labor force is the number of people on a server, and due to the level of the mob I can guess the general level of Capital (A and K) of the labor force. Assuming those values are fixed, then we are free to play with other variables in an effect to control our Vf. Things like the drop rate of the item, the spawn rate of the mob, the difficulty of the mob, and the Fixed Cost of the mob.

Let’s define some values, and a sample mob.

World of Flarks

Server Population: 2,000

Max Level: 20

Population at or above level 10: 500

Population between levels 9-12: 100

Sword of the Flarkmaster

Value: 10g

Flinkar the Weakling

Location: Forest of Losers (World Spawn)

Quantity in Zone: 1

Spawn Rate: 5 Minutes

Mob Level: 10

Difficulty: Low

Sword Drop Rate: 50%

Here we have Flinkar the Weakling, who has managed to acquire the Flarkmaster’s Sword. Oh Flinkar, you crafty little scamp you. He spawns in the world, so there are no fixed costs associated with killing him. He’s the only one of his kind in the game, and he spawns 12 times an hour. Since he is a low difficulty mob, player skill (H) is less of an issue. Therefore, I will assume that all players at (or above) level 10 can use this resource. Since there are 500 potential users that match this criteria I can assume that this resource is being Perfectly Consumed (he is killed and looted as soon as he spawns). Given this simple set up, I can determine the rate of value (Vf) entering the economy every hour.

Vf = (Kills Per Hours) x (Drop Rate) x (Sword Value)

60g = 12 x 0.5 x 10g

60g an hour is pretty high. Even given no information about our desired Vd, I think it’s safe to say that my economic goals are not being met. I have several options here. Since the value of the item and level of the mob are constant, I am left with changing the drop rate, adding fixed costs, or altering the mob spawn rate. Let’s try a different mob:

Dinky the Diabolical Dinosaur

Location: Flarkmaster’s Grove (Instanced, 5 Man Dungeon)

Quantity in Zone: Optional Boss (1)

Summoning Materials Cost: 1g

Average Dungeon Length: 1 hour

Mob Level: 10

Difficulty: High

Sword Drop Rate: X

Inflation Ceiling

0.5g / hour

This is a more complicated scenario. The mob is now located in a dungeon, he has a cost for summoning him that must be paid, and he’s a difficult mob to boot. Also, this time we are going to start with a desired Vf (0.5g / hour), and solve for our drop rate.

The first new wrinkle is that I need to determine how quickly people are going to be killing this mob. From looking at the world statistics I see that the there are 100 players between the levels of 9 and 12, which feels like a good range for people that would be running this dungeon. However, Dinky is a pretty tough –it does say diabolical– Dino who requires more skill and better gear. Only 60 of those 100 players have the required Capital (H, K, and A) to effectively take down Dinky.

This is a 5 man dungeon, so those 60 players are grouped into 12 groups; additionally, it is an Instanced dungeon, which means that those 12 groups can all be running this dungeon at the same time. This assumes, however, that all 60 of those people are playing all the time, and they are always perfectly grouped with each other. From the article “Alone Together” (http://is.gd/gcqWT) it was shown that players only spend about 30-40% of their time in groups, so for the sake of this we can assume that only 3 to 4 groups are running concurrently at any given moment. Given that this is an optional boss we can reduce it to 3.

The last consideration is the Fixed Cost. Regardless of whether Dinky drops that sweet sword, every group must pay a fee of 1g in order to summon him. With this final bit I can finally draw up the new equation:

Vf = ((Kill Rate) x (Drop Rate) x (Sword Value)) – ((Kill Rate) x (Fixed Cost))

0.5g = (3 x DropRate x 10g) – 3g

3.5g = 30g x DropRate

0.117 = Drop Rate

Given this current mob, this current labor force, and this desired faucet value, the desired drop rate for this item is around 12%. A simple case, but you can see the power of thinking like an economist. So far we have focused on money coming INTO a system, but what about money LEAVING a system?

Inflation Versus Deflation

Almost every action the player makes is some kind of inflationary act. They are constantly bringing money into the market, such as red orbs from killing monsters in God of War, or sweet loots dropping off Nefarion in WoW. Monsters do not work to create these items and resources, therefore it is some Value that is being created solely for the player, which is fine. Your job, now, is to find ways for money to exit the system. Though you may not think of it in these terms, things like “upgrade trees” are essentially designed to be deflationary actions for the player to take.

There are three effective means of removing money from an economy, and each of these has various degrees with which it can be applied to increase or decrease its effectiveness. The first method is by pushing trade onto the Global Market, the second is by using Taxes and the last is by creating social mobility through market Risk.

Global Markets

The most effective means of removing money from a game is to provide unique, high-use, consumable products on the global market, which will have minimal impact on the player’s production function — sounds a mouthful, but it’s simple to understand. Any time a player purchases something from the GM it is an opportunity to remove money from the SOE. The more often they do this (or the more expensive the product) the more money will be drained from the player economy. Since the GM has infinite supply, infinite demand, and the price is controlled by the designers, the price will not change regardless of how much the players consume, and the players can sell or buy as much as they want. Let’s return to our requirements. Why is it unique, why make it consumable, and what’s this about the production function?

Unique – By making the product unique it means that it is a product that is unavailable in the SOE. This drives trade onto the GM, and the price of the object can be adjusted as the GM (the game designer) sees fit.

Consumable — By making it a consumable product the players will have to keep returning to this market to drain money out. If the product provided is a dependable (or even worse a permeable), then no matter how deflationary the cost of the item, the gradual inflationary acts of the player will overcome the buying of this one item. Very expensive dependables are a great means to dump LARGE amounts of money out of the market very quickly (think mounts in WoW), but they are not effective means of keeping the market from inflating over the long term.

Production – The product provided on the GM must be something that does not impact the production function of the player in a major way. As we have discussed, the more effective I am at killing the more I produce. Therefore if the deflationary product provided on the GM makes me a more effective producer, then I am essentially increasing the inflation rate (and undoing the work of trying to deflate it!)

Well, this all sounds great, but not every item can be a consumable. What about dependables? What about permeables? Are we totally fucked? Thankfully, no. Our savoir comes from a pretty dirty word in modern society. The second half of all that is certain in life: taxes.

Taxes

The second most effective (though sometimes unpopular) means of removing money from the market is to provide a desired service that charges the rich more than the poor. This is also known as “progressive taxation.” The classic example of this is repairing your armor in WoW. Whenever a monster hits you, your armor’s durability is reduced. If you die you also lose a large chunk of your armor durability. If the durability is reduced to zero you may no longer use this item. The only way to repair this gear is to go to an NPC merchant and pay them to repair it. The better quality the armor that you wear, the more expensive it is to repair. An interesting point is that at first glance this may have the appearance that these items are “dependable” and simply depreciating in value. This is incorrect. Since they are 100% effective up until the moment they break and when they are repaired they return to 100% effectiveness, these products have actually not depreciated. They are just as good as the day you bought them (or made them). These are actually permeable, but have a periodic usage tax (and you didn’t even realize it!)

Risk

Another method of removing money from the system is by providing Risk based ventures for people to spend their money on. A common problem in games, particularly in MMOs, is that once the rich acquire massive wealth they stay wealthy. They have nothing to spend their large amounts of money on, so their wealth gets dumped onto mules, or they buy out the entire auction house to corner the market. Imagine a system where I could buy stock in various commodities in a medieval world. I believe in the worth of the Kalimdor wheat, a risky bet, but I think it’s a growth market. The following day, however, a horde of dragons swoop in from the north and raze the countryside. Three things have happened here. One, money (possibly lots of money) has been taken from the market, as the trade in Kalimdor wheat plummets. Two, the killers have been brought into the market trade. I can gather some friends together, and we can try to kill the dragons before they do too much damage – possibly salvaging the price. Three, users are encouraged to pay attention to the state of the game on both the inside and the outside. Say the game provided a web-based means for me to check the current prices on the in-game commodities market. Even better, what if these dragons make it a regular thing to come swooping down and screwing with my wheat? This turns the Kalimdor wheat into a high risk, but high yield commodity.

I can keep going.

But I won’t, even though there is so much to say. Once you understand the importance of economic discussions, you can move onto new questions. How about adding a crafting system to your game. What purpose does it serve? Should the items be as good as drops? Economics got you back! These are posts in their own right, and maybe once I give my wrists a break I can tackle them.

If you have found this at all interesting, you owe it to yourself to read the following book: Synthetic Worlds: the business and culture of online games. It explains this better and clearer than I ever could, and it should be read by everyone.(source:flarkminator


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