What’s so “Quantum” about that?

Now that we have an idea as to what our game is worth,  how do we got about constructing a business model that is more efficient at capturing its value.  This where the “Quantum” term enters the discussion.  The Quantum Economic analog to Heisenberg’s Uncertainty Principal is that it is impossible to know an individual players optimal monetization potential AND capture it.  The act of “observing” an individual players maximum value potential changes it… In other words it’s impossible to measure and capture the optimal value of individual players.  The mathematics of Quantum Mechanics deals with this problem by dealing with groups of quantum particles described by probability functions that determine their probable locations and energies but not their exact individual ones.  The entire groups behavior can be accurately described in this fashion without dealing with the absolute locations and energies of individual particles.  The same idea holds for Quantum Economic business models.  We can figure out the collective value of a game to a group of players but we cannot measure and maximize the value of individual players.  How then do we maximize the value of the group?  Not surprisingly the answer is to use probability functions…

When I was first struggling with these ideas to design a better business model for WildTangent I ran across a puzzle that gave me the insight I needed to solve the problem.  I’ll share that puzzle here as an introductory lesson in what I now call Quantum Pricing models.

You are given 10 red balls and 10 white balls and two buckets.  How would you distribute the balls between the two buckets such that if you were blindfolded and asked to randomly reach into a bucket and randomly select a ball from the bucket you would have the maximum probability of picking a red ball?

Obviously if you put 10 white balls into one bucket and 10 red balls in the other your odds of picking a red ball would be 50%.  Interestingly the result would be the same if you put 5 red balls and 5 white balls in each bucket.  The puzzle, however, does not require that you put exactly 10 balls in each bucket…  I’ll include the solution at the end of the blog, but take time to think about it.  The answer to this puzzle is also the answer to the question of how it is possible to nearly extract the maximum value of a game from an audience without knowing each individual in the group’s optimal price point.

To capture most of an individual’s optimal value we need a probability function that enables us to guess what that optimal value is very accurately without measuring it directly.  For example, if we know how to identify when somebody is playing as though they are hooked on a game AND if we know their time, date and local and we know the optimal conversion point in the game AND we know the games commerce friction co-efficient AND we know the games rough viral properties when it is free THEN we can calculate any individual users PROBABLE value state at the moment they are playing and make a heuristic decision about monetizing it.

EXAMPLE:  Joe Gamer started playing Gnome Wars eight days ago and has played five sessions in the past two days.  According to our addiction profile for Gnome Wars,  Joe Gamer is “addicted” to the game.  Joe Gamer is playing Gnome Wars NOW at 9:30am on a Monday morning… should we attempt our first commerce transaction with Joe?

Gnome Wars probability of converting an addicted player:  3.3%

Gnome Wars average first transaction size:  $25.75

Gnome Wars average LTV: $36.50

Probability of converting any addicted player to commerce on a Monday morning: -23%

Gnome Wars Addicted Player profile:   A Gnome Wars addicted player generally maintains close to peak addiction for 8-11 days with an 11% risk of losing the player during that period.

So let’s decide if we should ask Joe Gamer for money now, or at a different time;

Ask for Money now? 

(3.3% – (1.0 – .23))*$36.50 = $9.27

Ask for Money Later?

3.3%*36.50*91% = $10.96

Individually you risk losing Joe Gamers money if you wait to try to monetize him but collectively the patience heuristic will yield more money from the overall audience.  If you are trying to make payroll however the math may yield a different result…

Ask for Money now? 

(3.3% – (1.0 – .23))*$25.75 = $9.08

Ask for Money Later?

3.3%*$25.75 *91% = $7.73

One might quickly realize that the use of probabilistic pricing can give you control of your revenue recognition within a range of value.  It’s very useful when forecasting quarterly revenue results when you can tune your economy to bring revenue forward or push it back in time depending on what suits your accounting needs.  You can even calculate the price of bringing revenue forward and make a financial decision about doing so.  In this example, bringing revenue forward costs $10.96-$9.08 = $1.88 per transaction.

This brings us to the fascinating subject of dynamic pricing.  Is it possible to sell the same product to two different users at different prices?  The success of microcurrency based business models illustrates at least one example where the answer appears to be YES!  Some people will pay hundreds of dollars/month to play Zynga Poker while others will pay nothing.  However this example is not exactly fair, although paying and non-paying players are consuming the same game, the paying players ARE getting a different experience.   Microcurrency based economies do not, in fact, charge people different prices for the SAME experience.  Suppose I have two people making an in-game item purchasing decision in the same game, at the same point in the game, at the same moment in time, in the same market?  The only difference between the two players is that the value the good differently from one another.  Is it possible to charge them each the optimal price the virtual good is worth to them without them discovering that they paid more or less than somebody else and getting angry?  The answer to this puzzle is very similar to the solution to the ball puzzle I described earlier.

Solution to the Ball Puzzle:

Place all the white balls and 9 of the 10 red balls in one bucket, place one red ball in the remaining empty bucket.  Now the odds of me randomly drawing a red ball from either of the two buckets approaches 75%, a 25% improvement over distributing the balls uniformly between the buckets.  The key is the realization that given 10 balls of each color to distribute instead of one ball of each color it is possible to mix the ratio of balls in different combinations between the buckets to achieve different probability ratios for drawing a red ball!  In a single microcurrency based social game with many virtual goods or in a portfolio of MANY games there are usually MANY monetization opportunities for the consumer not just one.  Probabilistic pricing distributed across many  monetization opportunities makes it possible to dynamically adjust the aggregate price of all virtual goods in the game to approach each players optimal monetization level without regard to the actual price of individual goods.

Hybrid Auction

Now that we have shown that we can assign a price to virality, a price to the advertising value of an audience and a price to the current and future commerce value of an audience then we can answer the question of how to monetize any arbitrary player in the game at any moment in time by running a quick heuristic auction between the three payment methods.  Joe Gamer has clicked on the purchase button for the Gnome Slayers Sword.   We can ask him for money, show an ad or ask him to invite friends, we calculate the heuristic value of each transaction option, compare them to one another and the greatest valued option wins the auction and is presented to Joe Gamer.  Simple!

Not so fast, we haven’t done our Quantum Economic arithmetic correctly yet.  The magic idea of Quantum Economics is that, with a little perspective and good analytics, it’s often possible to capture MOST of the value of a system, not be forced to choose one over another.  By choosing between prices presented by three different payment methods, the implication is that the money available from the other two options must be left on the table in order to capture the greatest value of one of them.  This is NOT actually true.  The uncaptured value of some payment methods can often be deferred to a different occasion where the value is recovered later.  Just because an available payment option was delayed does not mean the value was lost.  Advertising value is the only kind of instantaneous value that is hard to deferr.  If you don’t take an advertising opportunity immediately, it is largely lost.  Virality and commerce opportunities can often be deferred without substantial loss of value.

The user perceives that the ad is worth a quarter since a session of gameplay ordinarily costs a quarter even though less than 5% of consumers ever purchase. Interestingly advertisers ALSO perceive that they are getting a $250CPM placement here. The consumer gets a free session of play, the advertiser is happy to pay a higher CPM for this placement, we make more money! Everyone is magically happy somehow?

Quantum Economics makes it possible to “store” or “borrow” revenue from the future.

My first first-hand experience with this phenomenon was at WildTangent when we faced a difficult business decision during an executive meeting.  Kraft foods wanted to pay us a seven figure sum of money in advertising dollars to make our entire network of games free for a month sponsored by their various food brands.  The hybrid calculation on total revenue yield showed that we would lose as much revenue in commerce dollars as the ad campaign was worth to us.  What was the point in doing that?  Of course our commission based ad sales team pointed out that Kraft was a HUGE account to win and this was a HUGE premium ad buy.  If we were going to turn down deals like that, why be in the business of selling premium ads at all?  I reluctantly decided at the time that although it might be a huge waste of commerce revenue, it was a huge advertising win for us and would lock in the revenue for that month.  We took the deal.  The campaign ran for a month, our gaming traffic DOUBLED because the games all became entirely free, when the campaign ended and the commerce option kicked back in, 80% of the lost commerce revenue arrived in a wave as all of the existing free players and new free players that the campaign had gotten deeply engaged in games, started paying.   We subsequently realized that running waves of free ad supported play followed by lulls generated MORE revenue than choosing advertising over commerce or simply smoothly blending between them.  We also found that oscillating our models also reduced the tendency of the audience to “learn” our heuristics to avoid paying.  We called the practice whiplashing.

To summarize, a proper Quantum Economic value auction between different abstract payment types needs to take into consideration the future value of deferred transactions in order to price them correctly by subtracting the immediate value of lost ad revenue from the deferred value of commerce and virality.  Using the Kraft ad campaign example above the math might look like this;

Users instantaneous commerce value = $1

Deferred commerce value = $1*80% = $.80

Non-deferrable ad value = $.36

Instantaneous commerce value adjusted for lost ad revenue = $1 – $.36 = $.64

Since the future commerce value is greater than the present one and the ad revenue is non-deferrable the optimal decision is to show the $.36 ad NOW and initiate the commerce transaction for $.80 in the future for a total of $1.16 in hybrid revenue.  The COST of not including TIME in your pricing is $.16 per transaction…

*Note that the video ad actually plays while the user is making their choice… we get the ad revenue no matter what the user chooses… “Magician’s Choice”

In this example a Full Energy Refill Pack may have a $1 retail price.  Anybody can buy this pack for $1 at any time… however… in this example a user clicking on this item has been offered it for free in exchange for watching a Coke ad.  By serving an ad to make this item free to users 50% of the time, the “effective” Quantum price of the item is $.50 cents.  If we know that users playing this game will engage in dozens of commerce transactions over their lifetime we can blend the probability of serving a free item offer with a paid purchase offer to the user over their lifetime to generate an aggregate commerce revenue yield from them that may be completely different from the commerce goal for another player consuming the same game under the same circumstances and buying the same virtual goods.

Kids are a great concrete example of a meaningful application of dynamic pricing.  Social game developers are often seeking “whale” players who will spends hundreds of dollars a month on virtual goods without a care.  The trouble with this approach to monetization is that it can be difficult to differentiate a mature adult whale gamer from a kid going crazy with his mother’s credit card.  If Jr. runs up a $200 commerce bill on his mom’s card the game will get a commerce charge-back and an angry support call from an outraged parent at the end of the month.  Credit card thieves will also spend money on a social game without regard to cost.  How do you balance the business cost of handling angry parents and credit-card chargebacks against the benefit of having a small subset of users spend tons of money on a game?  Using dynamic pricing you might change your monetization goal for these players to generate no more than $40 in commerce revenue from them during the first 30 days of play and retain them long into subsequent months by increasing the ratio of free ad sponsored items to paid ones such that new payers are not able to spend more than $40 in commerce expense their first month, no matter how they play.  Once you are confident that the credit card is legitimate and the bill is paid you can gradually turn down the free ad supported item server to increase revenue.

Now we enter the realm of really exotic Quantum Pricing models.  We’ve demonstrated how to think about maximizing commerce value, we’ve shown that it is not only possible but powerful to mix advertising with paid commerce as a way of dynamically pricing virtual goods to maximize revenue.  Finally we take a look at the idea of substituting social messaging instead of currency OR advertising as a form of payment.  Here the user has been offered the opportunity to invite friends or connect to other social networks as an ALTERNATIVE to paying for a virtual good.  Look carefully at the images and notice that the OPTION to pay is always available to the consumer.  The result of positioning payment as an option is to constantly remind the consumer that they are in control and can decide if and when they want to see ads or invite friends INSTEAD of engaging in a commerce transaction.  It also reminds the consumer that the goods they are getting for free have a real cost, they just happen to be getting a deal on them.

Putting it all together

The idea that sets Quantum Economics apart from conventional microeconomic pricing models is the realization that when a good has negligible cost to deliver and support, a huge new range of economic options become possible that do not exist for goods with tangible value.   One of the most pronounced observations is that is possible to replace fixed pricing and fixed business models for probability based hybrid models that are many times more efficient at monetizing an audience across a virtual service than any simple business model can be alone.

We have shown that it is possible to calculate a games optimal value and use that information to calculate the monetary value of the games virality.  We have also shown a Quantum Economic way of treating advertising as an equivalent alternative to commerce in the same context and price its value relative to commerce correctly.  This means that mathematically speaking, commerce, advertising and virality can all be priced and treated the same as money and incorporated into the same business model without having to choose or compromise between them.  Let’s look at an example that puts all of these ideas together.

In this example Joe Gamer clicked “purchase” on a Full Energy Refill Pack in this social game.  Instead of going straight to a commerce page the game served a free alternative to paying for the item… why?  Let’s calculate the “probable” value of different monetization options for this event in the game and determine what we think the user will do here.

Probability of engaging in a $1 commerce transaction at this point in the game:  1.7% = $.017

CPM value of serving a video ad to this user at this point in the game: $20CPM/1000 = $.02

Viral Value of asking Joe Gamer who has no friends in the game yet of inviting friends:  $.03/DAU * .76 virality = $.023

Huh… the MOST valuable PROBABLE transaction Joe Gamer can initiate here is to invite friends, the second most valuable transaction is to view an ad and the least valuable action is to ask Joe Gamer for money…  When Joe Gamers is asked to choose between getting the item for free in exchange for viewing a video ad and paying $1 for the item, which choice is Joe MOST LIKELY to make?  96% of the time, Joe will choose free… as a result of not getting blocked in the game, Joe will play more AND be more likely to invite friends resulting in a net greater value to the game playing for free on this occasion than being asked to pay… Giving Joe Gamer the choice between commerce and an ad, or commerce and inviting is called Magicians choice.  The consumer is offered a choice that doesn’t matter… if our heuristic was wrong about Joe and he ends up making a commerce transaction we didn’t expect, GREAT!

In general, after running Hi5.com, a social network with 60MMU and hundreds of social games, we found that when Quantum Economic probability profiles are used, in general the most valuable thing to ask a user for early in a game is virality, the second most valuable thing is commerce and the third most valuable thing is advertising revenue.  Generally, however, the optimal point of monetization in a social game is much deeper into the game than most game developers realized, substituting advertising to get users further engaged with social games before triggering commerce demands, increased the commerce revenue for many games we tested it with by 30%-80% in part because the MORE free versions of the game were MORE viral and had attracted and retained a larger audience by the time commerce demands started kicking in.

*Note that it was not necessarily incorrect for games to price themselves the way they did if they had no advertising model alternative available to compensate for instantaneous potential commerce revenue losses they would incur in order to defer commerce transactions deeper into their games.  The risk of losing the player in the future exceeded the value of the potentially greater commerce yield from the remaining players at a later date.  Substituting video ads for commerce transactions took the risk out of that financial decision by providing the game developer with a smooth stream of ad revenue during the longer trial period before players were asked for commerce.

Conclusion:

The ball puzzle contains one other important insight, the greater the number of balls and buckets considered in the puzzle the finer control you have over the precise probability of picking any specified color.  In other words the efficiency of extracting ALL of the potential value from an audience increases with more audience and more games.  Moreover as many many hours of deep analytics and data mining has shown me over the years, when you learn to treat a body of content and a large audience as fuzzy probability profiles the need for massive analytics infrastructure seemingly disappears.  You don’t need to track everybody’s individual personal information and behavior to devise a monetization system that captures all of their potential value.  Once you understand the overall structure of an audience’s behavior within a body of content, it is more efficient to treat the entire system as a Quantum Mechanics like probability distribution function and ignore the individuals.  As stated earlier, it isn’t possible to know an individual’s value state and capture it simultaneously.

Track and analyze trillions of individual social events and mine it all for meaning
OR…

x^2+y^2 = z^2
Fire the analytics team…

This insight is analogous to trying to predict how individual gas molecules crashing around randomly in the interior of a balloon will behave.  If you tried to track every single one of trillions of molecules and predict every collision and interaction between every particle in real-time in order to predict their future movements you would need an analytics infrastructure larger than all of the computers available on Earth.  If, however, you stepped back and realized that the collective behavior of the entire system can be described by the one line equation for a sphere’s diameter governed by the gases temperature and the balloons elasticity, you would know everything that mattered about predicting the systems future behavior with minimal analytical requirements.  Did the temperature increase?  Then the balloon’s diameter will increase proportionately… end of calculation…

I’ve had the same experience on several occasions, after months of pain staking data mining and massive data accumulation; I would hit on an insight that described the entire system, once that insight happened, the need for the monumental amount of data and analysis seemingly disappeared because a simple observation was often enough to characterize the system.  I don’t need to know where all the particles are in the balloon anymore, just tell me the temperature and I’ll tell you the balloons diameter.

I made this slide in 2007 to illustrate that a hybrid currency model was a superset of all known downloadable game business models at the time. After Hi5.com I subsequently demonstrated ways to price virality as a form of commerce but I haven’t made a slide showing that symmetry recently

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