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1950’s Peruvian Coke and Gacha

October 3, 2017

In the 1950’s, Peruvian inflation forced Coca-Cola to charge more per bottle of Coke. Unfortunately, their vending machines required physical updating to accept a new and larger domination. Instead, Coke devised a probabilistic system: the machine would charge the same amount as before, but randomly refuse to give a bottle. This raises the expected price of a bottle Coke while forgoing any physical updating. But a miscellaneous software engineer has a better idea: raise the price of Coke, but instead randomly give the money back.

Our Surfer is ‘risk loving’

The increase in price for a given ‘bottle draw’ would equal the expected payoff of a lower priced ‘bottle draw’ that randomly refuses to give a bottle. This is an interesting solution to player frustrations in gacha (“I didn’t get anything of value when I opened a pack!”).

Anyone care to reckon which model one would perform better: Higher draw price but gives money back or lower draw price but sometimes doesn’t give anything?

Players Go to Their Highest Valued LTV: Ads Are Beautiful Pareto Exchanges

January 16, 2017

Markowitz is not 5′ 9′ Milton Friedman and he resists your attempts to call him that.

Previously, I wrote about ads as a way to monetize non-payers, but there’s more to the ad exchange and what I’ll coin as ‘portfolio pumping’. It’s like portfolio theory, but not really.

These terms reference two growing phenomenon in F2P games. King is at the forefront of portfolio pumping, in which a given firm pushes a player from game to game within the firm’s portfolio.

Match-3 games in the portfolio and get $$$, ???. Image credit: Eric Seufert

Unlike portfolio pumping, ad exchanges push players to another firm’s games. Companies like Scopely are more fond of ad exchanges.

Walking Dead ad in Yahtzee, interesting given Scopely has competing Walking Dead game.

Frequently, the ads being served are for competitor games. Why would a company show ads for its competitors? In addition, why would firms want players to move from one game in their portfolio to another? I argue the underlying explanation is Pareto Efficiency which is just a fancy term for trade.

Ads for competitor games only make sense to the ad-server if

$churned player LTV < ad revenue$
and to the advertiser if
$acquired player LTV > ad cost$

It tends to be the case that a given company will engage in both ad buying and selling. The outcome of these ad exchanges are migrations of players to the games in which they have the highest LTV; the initial allocation doesn’t matter. This process takes place in high-speed auctions where firms are constantly in the search for the maximizing the equations outlined above. The decision rule for portfolio pumping is similar, but we add some special conditions, mainly the probability of simultaneous play.

$P(rLTV_{i} + nLTV_{i}) + P(nLTV_{i}) > rLTV_{i}$

Where,
$P(rLTV_{i} + nLTV_{i})$ is the probability of playing both games simultaneously. We add up both of the LTVs in this case.
$rLTV_{i}$ is the remaining LTV in the old game for the ith player, while nLTV is the LTV for the new game for the ith player.

This must be bigger than $rLTV_{i}$ for profitability.

Of course, there are ways to play with this. Wooga tried altering portfolio game prompts during a player’s lifespan but found no effect.¹ King continues to portfolio pump but dropped ads in Candy Crush Saga.

It’s a goddamn gorgeous process that should litter econ textbooks like lighthouses and lemons.

Runge, Julian, et al. “Churn prediction for high-value players in casual social games.” 2014 IEEE Conference on Computational Intelligence and Games. IEEE, 2014.

Re-Rewriting Economic History

October 22, 2016

ediwm_3_5x5postcardfront_outlines-400x280

Will Luton argues on the dangers and solutions to F2P inflation over at gameindustry.biz.

While there are some missteps in the opening of the article, Will makes a powerful and elegant point:

…a sale can only be considered profitable if the net revenue from the start of the sale until resource equilibrium, and so demand, is restored is more than if the sale hadn’t been run. For well run sales in games with well balanced economies this should always be true.

Sales flood the economy with resources via shifts along the demand curve. Holding all else equal, this is modeled as a move from P1 to P2.

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The tricky part, not found in the textbook model, is time. Unlike say, refrigerators, a durable good, virtual currency is a consumable good. This means we expect repeat purchases, similar to say, gasoline. Sales in this sense pull revenue forward by changing purchase ‘schedules’ more so then a durable good. The sales are only profitable if the sale sinks resources players would have never sunk otherwise (net positive sink). In games, this is achieved this achieved via live ops. This model explains how Supercell runs their games; it’s no coincidence that Clash Royal is the first Supercell game to have sales and real live ops while their other titles have little of either. Introducing one without the other keeps net sink flat in the long run by shifting intertemporal time preferences rather than increasing the size of the ‘sink pie’ so to speak.

Progression is another confounding variable. Holding all else constant, a given item is worth less for each additional level a user is at. This is simply an artifact of rising difficulty (in the form of stronger enemies, more experience to level up etc). As a result, sales make late game players in different while making early game players better off.

Reproduced from the original article. Left: a game with constant difficulty. Right: a game with increasing marginal difficulty.

Reproduced from the original article. Left: player progression on a game with without sales. Right: a game with sales.

The insight Will offers is that sometimes this is an advantage by changing the progression path of newer players to a higher equilibrium then current late game players previously had. This allows new players to ‘catch-up’. This sounds a lot like the Solow model. Yes, that Solow model ¹. I don’t think Will models this correctly, however, as each player is not on a discrete curve as his graph on the left depicts. Even without inflation, the graph on the right is an accurate picture of a given game economy.

Consider two possible goods that could be put on sale (and thus inflated) from Clash of Clans: a builder or gold. The builder is a dramatically better purchase because it allows for more output per unit of gold or elixir (increase in technology). This shifts the growth rate of a given player up. On the other hand, the gold is a small one-time increase in capital stock that won’t scale with the game. For designers, this offers the chance to use sales as strategic instruments to alter the metagame. By offering Clash of Clan players discounts on a builder, players converge and then exceed the GDP of elder players. A sale of gold, however, merely ‘jumps’ the GDP of players without changing the long-run growth rate. This means designers can either jump the point along which new players are on the progression curve or they alter the new player curve entirely.

Sales jumps players along the curve, while a sale with 'technology' creates an entirely new curve. Also I have an S pen. Watch out art teams.

Sales jump players along the curve (A -> B), while a sale with ‘technology’ creates an entirely new curve. Also, I have an S pen. Watch out art team.

Back again

Known as ‘Destroyer of Toy Islands’ on Server 54G, Robert Lucas knows no mercy.

Unfortunately, this can deter some investment by changing inflation expectations. If players know a given dollar will have increased purchasing power later on, why make the investment now? Indeed, a 30+ paper written by Game of War players and subsequent boycotts attest to the negative side effects of perpetually trying to catch players up.

Careful consideration and analysis can make sales a valuable gameplay tool as much as they are a business one.

Solow, Robert M. (February 1956). “A contribution to the theory of economic growth”. Quarterly Journal of Economics. Oxford Journals.70 (1): 65–94. doi:10.2307/1884513. JSTOR 1884513. Pdf.

Eric Seufert’s Best F2P Blog Post Isn’t About F2P

September 17, 2016

screenshot-at-sep-17-20-28-48 Everyone’s favorite former Rovio employee is a prolific writer on F2P games; the closest we have to a Fukuyama. Seufert has covered a range of topics, but none more important than internal organization.

Seufert argues for a number of institutional policies to surround analysts with within an organization. Frequently, analytics and data are as much about the appearance of sophistication as they are actual value adds. This need not be the case. The confusion arises over where the value of data lies. Perhaps ironically, data’s value doesn’t lie in the data, but rather in the data analyst.

In most organizations, analytics reports to product teams, a mistake, Eric argues. Often product managers face the principal – agent problem: their incentives and the companies do not align. Product managers want to successfully manage products and will present the narrative they are doing so. This is inefficient for companies who often wish to assess the true performance and trajectory of a portfolio. When an analyst’s career path depend on a product manager their narratives will often match. With organizational independence from product teams, analyst’s incentives align closer to the companies, providing more objective analysis.

Not just an accountability watchdog, real analyst value revolves around the ability to drive product roadmaps. At it’s highest order, analytics is a forward looking discipline, not a backward looking one. By experimenting and studying human behavior, analysts find levers that pull certain responses. This creates opportunities to exploit these levers. Do currency pinches increase monetization? Are new gotcha characters or new levels driving revenue? Should we invest more in reducing load times or UI changes? Using theory driven empirical investigation analysts can move companies towards better outcomes than competitors. If organizations don’t allow analysts to pursue these questions, they’ll become cheerleaders for product teams. On the other hand, if first order information (RR, ARPU) is not accessible or automated, analysts will forever be running the hamster wheel of reporting. This is one of the more overlooked points Eric argues for.

I think this suggests a dual mandate of analysts: (1) accountability of features and (2) what features are worth developing. This creates a natural tension of not only playing the role of watchdog to product managers but partners as well. It is the duty of good analysts to navigate this relationship successfully.

F2P Demand Curves Are Weird, Just Ask Levitt

September 17, 2016

A paradigm forever changed, one man carries a dying tradition.

Steve Levitt, the last price theory samurai, and John List, future nobel prize winner, have published a paper on free to play economics.

In a textbook neoclassical experiment, Levitt alters the quantity of Candy Crush hard currency at a given price point. While economists generally think of price variation as the way of deriving demand curves, quantity variations are just as legitimate a tool.

Despite a sample size of over 15 million and a wide range of quantity convexity (80% variation across variants), all quantity discounting schemes produced similar revenue. Levitt concludes by commenting,

“…varying quantity discounts across an extremely wide range had almost no profit impact in the short term.”

The interesting and little explored result indicates that,

…almost all of the impact of the price changes was among those already making a purchase; radical price reductions induced almost no new customers to buy…

This suggests free to play games are made up of two groups of users: purchasers and non-purchasers. This means the decision of becoming a customer is exogenous, there is no ability to convert non-customers to customers i.e. this is decided outside of the game. Put another way, non-customers are perfectly price inelastic and customers are perfectly price elastic. Indeed, industry research collaborate this.²

Interesting, but is it actionable?

Were this to hold, it suggests a number of results. The first is that product manager’s ability to monetize non-customers (99%~ of users) will not come from IAP, but rather other forms. This may help explain why F2P ad revenue and incentivized video continues to show YoY growth.³ ⁴
Furthermore, product managers should consider experiments exploring the maxima point of ad frequency. Given that there’s a trade-off between retention and ad-frequency there exists an optimal ad frequency point.
attachment-1
With little chance of non-customers converting to customers, product managers should worry less about increased ad frequency turning off potential customers.

The final result suggests the ROI of trying to raise the LTV of customers exceeds that of trying to raise the new customer creation rate. Product managers should develop roadmaps in accordance.

http://venturebeat.com/2014/02/26/only-0-15-of-mobile-gamers-account-for-50-percent-of-all-in-game-revenue-exclusive/ [/note ¹ http://www.gamesindustry.biz/articles/2013-08-22-two-thirds-of-whales-are-males
https://www.chartboost.com/blog/2015/04/mr-jump-20-000-day-mobile-game-ads/
http://www.pocketgamer.biz/news/63994/giftgamings-lift-deuls-daily-revenues-by-up-to-38/

How to Measure Whales

May 21, 2016

“$10.00 LTV am I right?”

You’ve soft launched your game, done a UA push, and a string of hope appears. Against all odds, a dominant cohorted ARPU curve emerges! Is this this an anomaly or have you caught a whale?

The first way to examine this is to perform cointegration tests between the cohorted ARPU curves, testing for stastistical significance. It may be true the difference in the curves are real, but that doesn’t answer if you’ve caught a whale.

In 1905, Michael Lorenz developed a method for measuring relative inequality between nations known as the Lorenz curve.

Just keep saying what % of the population owns what % of the wealth and it’ll make sense.

The F2P application is to define wealth as revenue (either on a daily or game level) and players as the population in the context of free to play games. By measuring how bent inwards a cohorted Lorenz curve is relative to other cohorted Lorenz curves we can measure the ‘whali-ness’™ of different cohorts. Even better is how this reduces to a single metric – the gini coefficient. A gini coefficient of zero indicates a perfectly equal distribution of income, 10% of the population owns 10% of the wealth, 20% of the population owns 20% of the wealth and so on and so forth. A gini coefficient of 1 is the exact opposite – a single person owns 100% of the wealth.

This translates to what % of players are responsible what % of the revenue. Measuring gini coefficients across games rather than cohorts gives more insight into how a particular game monetizes – whether it’d be whale, dolphin, or minow driven.

Actionable insights might include how effective introducing ads could be. A high gini coefficient (very few players are responsible for revenue) might mean there’s a more fertile base to monetize on.

The main insight, however, is further understanding. It’s clear that success can come about in drastically different ways in free to play games, the gini coefficient is simple way to measure that.

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