User:Maximilianklein/Sandbox/Case Study

A Presentation of a deconstruction of Tiny Zoo Friends and Work Sample by Max Klein

=Tiny Zoo Friends Deconstruction=

Executive Summary
Presented are four aspects of Tiny Zoo Friends asserted in their areas of strength and need for improvement.
 * In the reach section, after contacting an expert for advice, methods are proposed to determine which animals are cutest and wackiest in an appeal to gamers, building on the already smart inclusion of Zombie-esque animals.
 * The discussion of retention commences with a model of the enjoyment of the game, factoring for the building delays and pricing structure. Then suggestions are made to both elaborate on, and maximise the enjoyment function.
 * On the heels of retention, the revenue section asks how related enjoyment is to revenue. Exponential regressions produced elucidate the best exchange rates for in-game currency, but it is questioned whether they are at the right price points.
 * In competition a verdict is pondered that while gameplay is mostly undifferentiated amongst its clones, supplementary tactics may be employed to crown as key differences.

Reach
The most simplistic definition of Reach is counted by the number of users of an application amongst a population per day and per month. Known as Daily Active Users (DAU) and Monthly Active Users (MAU), these metrics have risen to prominence with the advent of online and handheld casual gaming. Of recent they have come under scrutiny in their measure of a population, because they may double-count users when a company views it's summed DAU or MAU over a platform. The point of discounting platform-summed DAU and MAU as metrics is that one gamer playing two TinyCo titles is not as meaningful as two gamers playing two TinyCo titles (one each). It would seem to settle on unique per platform DAU and MAU, (normalized DAU and MAU) as metrics, yet after some time that turned out to not show the complete picture. In order to investigate further I secured a meeting with Zach Helke of Adomoti, an advertiser of casual games on social media outlets. In talking to him about Tiny Zoo Friends I started proposing the idea of counting DAU in the target demograhic and outside of it. He stopped me immediately and blurted, "Never assume your demographic." Expounding "This is a Zoo game right? Evidence has shown that the largest spenders on Zoo games are middle-aged women." Scratching my head in trying to understand the relationship, he helped by explaining the psychology, "Zoo games are about the cuteness of the animals, and about the actual animals themselves. People play because they want the [proverbial] Pink Koala." He advised me to read the forums, and having taken that advice I've watched youtube videos of Pokemaster0731 telling his community about his new Gargolyes, and importantly how he spent $60 buying his new Gargoyles which everyone else absolutely must get. If reach really is related to the actual animals, then it'd be important to find out which animals are the most desired. For example $$ max \left \{ \frac {\text{normalized DAU with promoted animal} \ x} {\text{base normalized DAU}} \right \}_{x=rabbit}^{monsters} $$. That is we search for the maximum increase in normalized DAU and MAU after in some way promoting different animals. This will allow the game's reach to be viewed under the basis of its content. In fact it's not necessary to identify the largest target demographic until we find in which ways the are most titillated first.

To answer the questions of where Tiny Friends Zoo excels and falls short in reach I would use the above proposed idea of identifying it's most valuable thematic content. It is my estimation that Tiny Zoo Friends already does well in expanding its reach by incorporating non-animal collectibles such as Zombies and Pegasi in its repertoire to broaden its appeal. The cross-breeding mechanism also goes far into creating zany combinations of animals that require work to be attained. These present features championing Tiny Zoo Friends, and can be fully realized by understanding statistically just which ones are most wanted. On the other hand Tiny Zoo Friends might score minuses in not allowing the animals cuteness, to be fully unleashed, having caged them to infrequently animated isometrically drawn stills. Unlockable video animations or even emulating the popularity of erstwhile animal fact books would be sample features to heighten the cuteness and hence reward of obtaining the animals. A way to mathematically determine if these features were beneficial would be to activate them randomly on different animals and see if their in-game attention raised accordingly.

Retention
In order to begin analysis of Tiny Zoo Friends ability to retain users a simplified model of user Enjoyment is presented. Let us assume the most users are retained when the Enjoyment is maximised. The main element I propose that regulates Enjoyment ($$E$$) of the game is the time ($$t$$) in which takes to build objects. Therefore our basic enjoyment function is in the variable of time $$E(t)$$. To start understanding $$E$$ we make the assumptions that $$E(0)=0$$, so when it takes no time to build anything the game is just an editor; and that $$ \exists \ t_{enough} \ \text{s.t.} \ E(t_{enough})=0 $$, so there exists a certain time when things take too long to build and the game becomes unenjoyable. Somewhere in between, like $$t_0<t_{max}<t_{enough}$$ is the Maximum enjoyment point. One such satisfying elementary function is the parabolic function, here displayed $$E(t)=-(t-1)^2+1$$.



Yet there is a twist, the average time to build objects in game is actually a function of the pricing structure, because in Tiny Zoo Friends you can pay to avoid grinding. Defining $$p$$ as the average price in Dollars of either Zoo Bucks (ZB) or Zoo Coins (ZC) we try to sketch $$t(p)$$. The requirements for $$t(p)$$ are $$t(0)=0$$, that when ZB costs nothing the user can simply build as fast has s/he likes; and $$\lim_{p \to \infty}t=k$$, where $$k$$ is the time it would take if you had to grind all your in-game currency, so that if the cost of ZB was infinitely high users would just grind. Such a satisfying function would be $$t(p)=\frac{-1}{p - \frac{1}{k}} + k$$. Below is shown $$t(p)$$ where $$k=5$$. In reality k would be given by data already coded into the game.



And finally the fun part would come in, to substitute $$t(p)$$ into $$E(t(p))$$ so that Enjoyment would be model by price. Putting on our Calculus caps we would solve $${\operatorname{d}E(t(p))\over\operatorname{d}p}=0$$ to maximize the Enjoyment function. This of course give us an answer that is a price point, discussion of which I defer to the Revenue section.

Making the model more sophisticated will be the move to consider individual building times for objects $$T_i$$ rather than average building times of all objects $$t$$. With each $$T_i$$ will be a corresponding $$P_i$$ the price variable for the $$ith$$ object. This time some linear algebra could be utilised to make a closer fit to the actual enjoyment of the game. Define $$E(t(p)):= \sum_i c_i \cdot E(T_i(P_i))$$. And like an old repeating joke we will take derivatives as before.

Where does Tiny Zoo Friends do Well in terms of Retention? In the Android version leaving notification in my drawer that I have elephants to feed is a nice start. Yet what does it matter in all earnest to TinyCo if I am not a paying customer. The Industry standard tricks are present, to add time-sensitive deals urging to buy, and there is a cross-breeding end-game that helps to freshen gameplay after a while. The main question really comes into the pacing of the game; how quickly you level? At current there is still the feeling of an exponential leveling system which is undoubtedly proven to work, but not proven to be the best. I wonder if progress can't be faster, compensated by raising the cap of expensive animals? The goal is to hook people before they reach their quit threshold. If we define quitting the game as having not played for more than a week (available data) then that may be a good metric to track. That metric would be number of days from first play until quit, and it should be measure against $$l$$, the base of the exponential function that determines leveling (how exponential is leveling). Controlling the base of an exponential function is a theme that I will now explore in Revenue.

Revenue
The goal for TinyCo is to maximise revenue, but we will approach this first on a simple assumption. We assume that profit is linearly related to Enjoyment, that the more enjoyable the game is the more profit received, crucially in a monotonic manner. If such a monotonic relationship existed between profit and enjoyment then Enjoyment maximisation would also mean profit maximisation. However obvious this seems, it would infer a departure from the classical Economics perspective. The Economics Total Revenue calculation is not immediately relevant because a key assumption is broken. Total Revenue is defined as $$price \cdot Quantity(price)$$ where the pivotal assumption is that quantity sold is inversely related to price. This is not applicable here because the game can operate on an entirely free basis. Therefore quantity demanded is more related to a player's frustration and enjoyment interacting with price. An adapter piece on price could possibly nullify it's direct response to quantity. For an indication for the Total Revenue where we would modify the canonical function to $$TR=P_i \cdot E(T_i(P_i))$$. Maxmising $$TR$$ would require more calculus and could be done easily once the available data for each $$E_i$$ was calculated. What fact we can glean is that the in game currecnt is almost exponentially related to dollars. Consider the following graphs taken from Tiny Zoo Friends



$ vs. Zoo Bucks



$ vs. Zoo Coins

Remarkably the plots look very similar, and testifying to that is that both fits have $$R^2=.97$$. I would conjecture then that the same function is being used to determine these price points for both currencies at TinyCo. Yet the lower price points are beneath the exponential regression, and later exceed it. This would mean that the lower price points give the consumer a worse-than-exponential exchange rate, while high pricing gives better-than-exponential rates. All this points to an attempt to shift purchases to the higher end, but is that really where Revenue is maximised? TinyZoo does well to use the traditional incentive of bulk, but could be push harder by exagerating the intensity. Prices I suggest could follow a more agressively growing exponential. In fact if you review the online presence of Tiny Zoo on youtube consumers are very aware of purchasing at their best value, as Pokemaster0731 opines and advises in his postings. So an exploration of highly exponential pricing might be warranted.

Competition
The success of resource management games rests in their ability to exalt the user as a master resource manager, and reward them the phenomenon of a well run infrastructure. Capitalising on this sought after emotion in the player, requires the balance of feeding gamer his or her craving, and yet also frustrating his or her development with the optional resolution of paying some cash. In the summer months of 2011 pining for the glory days of Sim City I download a TinyCo competitor application in Paradise Island and played it obsessively as a respite and escapism from the pressures of exams and life in general. Eventually though I reached my breaking point, and vehemently, as a self-intervention uninstalled the application from my phone and erased my saved data. Having never poured any money into it's open, salivating mouth it would seem that I got the better of the game, but that would be to miss the point. The addiction was strong enough to cause mental upheaval to the point where my better side felt it necessary to command a format operation on my SD card, and that is a powerful grasp indeed. What can we learn? In short the importance of demographics and a rabbit hole. Each demographic has it's theme. While I'd never play Tiny Zoo Friends for its boasted juvenility, there was nothing impeding Paradise Island's inviting tentacles. Yet this isn't an opportunity lost for TinyCo, quite rightly Tap Resort Party is there for the taking. And I would have played Tap Resort Party if two conditions were met: I'd known about it, and it required less grind. A long term pursual of competing on the basis of less grind would seem to imply a race to the bottom which is unfavourable to all the games makers. This would be abundantly true to an uncreative mind. Why couldn't hours of waiting be shaved on the condition of looking at advertising? Not directly of course (that'd be insulting), but by earning hours-saving codes at the TinyCo website which has an ad-barrier. Maybe by playing TinyCo games simultaneously. Whatever you make me do to run more code, I was already drifting down the rabbit hole. All of this goes to say that the clones that exist stay true to their pejorative—they are convincing clones. Not all hope is lost though, owing to the nature of the gameplay, being spaced sparsely over days, there is time to insert additional complementing structures. These could be added social interaction (maybe player-to-player resource trading), or exterior activities that confer in-game benefits.

=Work Sample= Slowly boiling in my life has always been the inexplicable and inexorable influence of the The Free Encyclopedia. On the path form skeptic to advocate I was approached about participating in their Education Program as a test-bed when I was teaching a student-lead course. The program's simplistic goal was to replace traditional college assignments and term papers with Wikipedia editing on the same topic, helping both parties at once. That is student motivation by doing something cool, and an expanded Wikipedia. Soon after accepting I found myself at their offices being handed a drink and interrogated as a focus group of one.

Problem Statement
At first I didn't realize why exactly I had been chosen for this scrutinizing interview, but it was because I was in a unparalleled position to answer their question. As an instructor and Campus Ambassador. The team in charge of promoting the program to Universities wanted my help in responding to a common question they received: how do you rate someone's work on Wikipedia? The difficulty is that invariably the individual effort becomes deeply intertwingled with that of the community. Wikipedia is not built to recognize singular efforts but that of the whole. As a teacher in a class I validated this need, but the student in me took over: what was the point in grading anyway? One question from myself as well as one from them.

Methodology
The answer is to spur learning and better work. To punish and to incentivise. We wanted better work truly, and not a grading system, because better work from students would reduce the need for a grading system. One of the best reasons colleges produce quality research I was musing at the time was to outdo one another. So I adapted and replied to the team, "let's build a metric and let the students compete inter-collegiately." This was heralded as a great idea, because it started to give momentum to automatically checking student's work and also helped motivate them at the same time. Developing what factors to include in the metric became an pedagogical argument amongst the Wikimedia team and the outside Campus Ambassador community. Finally the metric came to, through stalemate, a simplistic bytes-added to the articlespace which had it's criticisms. Were mine and other contribution in creating pages on Non-Euclidean Geometry equivalent to the rewording and copy-editing of other students? Given the subjective nature, were all bytes equal, or were some more equal than others? That's was an awful question to ask. Nevertheless the equal-byte leaderboard page went live, and I flashed it to my students and tutees, knowing that in order for it to have meaning it would have to derive it's value from a viral standpoint. In the meantime I kept scribbling my notes for version 2 of the metric.

Result
After the first gusts of baseless fanboy enthsiasm the balmly reality came to haunt me. I was worried that the competition mechanism wasn't going to catch alight, and then we'd have no grading system, and no good results to counterpoint the shift away from institutionalism. On pure bravado I walked into my courses and told my students that they were fomenting a revolution, they got a chance to make not only history but the lives of curious readers that bit better. Wikipedia prepared pre-made lectures to deliver on how to edit, which I threw away immediately much to the despair of my co-Ambassadors. We had to distance working on Wikipedia from the current academic ways, I couldn't even consider opening Powerpoint. I didn't do anything but demo live, and I would always illustrate points be leaving errors in my edits. One statistic that people overlook is that most long-time editors started with vandalism, or cleaning vandalism of some sort. I used only carrots of praise and recognition since we had the big secret that we couldn't really grade anyone accurately, and a Steve Jobs-esque insanely great new wave rhetoric. And although I got nervous when I walked out of the door for appearing pretentiously revlutionary, I finished the semester with pudding from which the proof leaps. View the Leaderboard. I was responsible for two courses at both Berkeley and San Francisco State, and they finished in the top two places of 29 classes. More than me being able to brag there is much more reliable and accurate information freely available to all on the topics of Internet Law, Piracy, and Environmental Policy. When I started to see that my classes would win the tops spots of the competition I had helped to create, like any mathematician, I wondered if had inadvertently biased them in some way. In progress is still the adoption of my latest proposition to switch to something that will account for referencing and how reverted your edits are. For instance

$$\left ( \frac{\text{net bytes added}} {1} \right ) \cdot \left ( \frac {\text{user references}} {\text{byte}} - \frac {\text{avg. reference}} {\text{byte}} \right ) \cdot \left ( \frac{\text{unreverted edits}} {\text{total edits}} \right )$$

as a metric. Which is a standard I again hope to create and exceed.

Reason
The reason for exemplifying this story that is displays a tactic, known in chess as, removing the defender. When deadlock is reach by some blocking obstacle, methodology shifts to attack the obstacle. Simple but less practiced. In this case I did away with bureaucracy and still created 12 reams worth of high quality content on-wiki, as was extolled later at Wikimedia summit where I was recognised. It epitomises my views on engineering, that as I silently show I am a mathematician at heart but it is only half of civilisation alone. As Churchill waxed lyrically, "scientists should be on tap, not on top." But that is not an insult, it is a reminder to be both Churchill and the scientist that Churchill would consult, all in one.

=References=