AppData for Empires & Allies

AppData is a website that shows usage metrics for Facebook applications.  If you've visited the "Links" page of this blog, you might have noticed the link to the AppData for Empires & Allies.

The two major usage metrics are DAU and MAU:

• DAU = Daily Active Users; the number of Facebook-authenticated users who used a particular Facebook application at least once in a given day
• MAU = Monthly Active Users; the number of Facebook-authenticated users who used a particular Facebook application at least once in a given month

AppData uses DAU and MAU as reported by Facebook.

How much money does Zynga make from sales of Tier 8 units? #2

In my earlier article, "How much money does Zynga make from sales of Tier 8 Units?", I estimated how many total Triton Carriers were offered for sale and from that how much money Zynga makes from sales of these and other Tier 8 units.  Here is an update using data on the newest Tier 8 unit, the Artemis Infantry.

How much money does Zynga make from sales of Tier 8 units?

I was curious how many Tier 8 units were offered for sale--in particular, how many Triton Carriers since that's what's currently on sale.  To figure this out, I pieced together two pieces of information that I gathered at nearly the same time.

Data

First, the image above tells us that 44% of the total Triton Carriers offered for sale have been claimed.  That means 56% have been sold.

Second, I used Charles Proxy to find out how many Triton Carriers are currently available for sale.  The image below tells us that that number is 341.

Estimate of how many are for sale

It's critical that I got these two pieces of information less than one minute apart because that means they can be combined.  If 341 units are left, 44% have been claimed, and 56% have been sold, then that means approximately 341 / 0.56 ~  609 were originally offered for sale.

I repeated this procedure a few more times.  From all my data and from the fact that a nice, round number is more likely, I think it's safe to say that 600 Triton Carriers were originally offered for sale.


How much money does that make Zynga?

Each Triton costs 800 Empire Points, so 600 of them cost a total of 600 * 800 = 480,000 EP.  Let's say 1 EP = 0.10 USD.  Then each Triton costs 80 USD, and 600 of them cost 48,000 USD.

Assuming an average discount on EP purchase of 20%, the exchange rate is 1 EP = 0.08 USD.  Then each Triton costs 64 USD, and 600 of them cost 38,400 USD.  This assumes all EP used to buy Triton Carriers are paid for in USD or an equivalent rate in other currencies.

Assuming Zynga actually sells all 600 units, they earn around 38,400 USD.  This may not actually be the case as we know the Pegasus was only 87% claimed at the end of its offering period.

I don't know how many of the other Tier 8 units were offered for sale or how many of the future ones will be.  Let's assume 600 of each.  From all nine Tier 8 unit types, Zynga will take in revenue of around 9 * 38,400 = 345,600 USD.

I assumed the 600 units per Tier 8 unit class were for the whole world.  It's possible that it's just for the U.S. or for a particular set of game servers that I happen to be associated with.

World Domination Cheaters

Are you curious about how many players are possibly cheating in World Domination?  So was I...

Here are some statistics on the last 100 players I fought against in World Domination.  Players that I fought multiple times count only once each.  These battles occurred over the past week (March 14-20, 2012), but I took a break from World Domination for 3 of those days.  In that time period, my Dominance Rank progressed from 54 to 56.

This table shows the % of opponents that had a given number of Tier 8 units (the Chimera and its brethren):

# of T8 Units	% of Opponents
0	47%
1	9%
2	23%
3	20%
4	1%
5	0%

Basically, about half of my opponents used at least one Tier 8 unit in their World Domination Defense Force.

Here's a similar table that includes both* Tier 8 units and World Domination units that players definitely shouldn't have had access to (Phoenix Bomber, Sea Hive Carrier, etc.).  I excluded the Buzzard Autogyro since many players could have received them as rewards from an earlier quest.

# of Units*	% of Opponents
0	45%
1	5%
2	19%
3	29%
4	2%
5	0%

Keep in mind that probably some of these players actually paid for their Tier 8 units.  It would be interesting to know what percentage that actually is.  Well, we know that the ones with World Domination units they can't possibly have unlocked yet are definite cheaters.  That gives us a lower bound for how many cheaters there are.

# of Cheat Units	% of Opponents
0	87%
1	8%
2	4%
3	1%
4	0%
5	0%

We see that 13% of my opponents are definite cheaters.  The actual % might be as high as around 50%--it depends on how many of those Tier 8 units are legit.  It could be even higher since some people are tactful enough not to use illegal units in their World Domination Defense Force.

The percentage of players with Tier 8 units who are definite cheaters is approximately (11 / 53) * 100% = 21%.  I'd bet the actual % is far higher.

This may or may not be a good estimate for how prevalent cheating is in Empires & Allies.  Keep in mind that this analysis was for players who were matched up with me; they had Domination Rank in the mid-50's and most of them had Attack Wins close to mine.  There is probably far less cheating among lower-level players, and greater amounts of cheating among higher-level players.

Red Rampage 10 - Weak Units

Since when does Elite = Weak?

Why are some of the new Elite units weaker than their regular counterparts?

Red Rampage 10 was just released on March 19-20, 2012 (depends on your time zone).  It introduced 5 new units:

• Elite Mantis Infantry (720 Strength)
• Elite Tarantula Artillery (760)
• Elite Badger Tank (720)
• Elite Sea Hive Carrier (645)
• Elite Yamato III (780)

These are the corresponding regular units:

• Mantis Infantry (700 Strength) (unlocked at Domination Rank 44)
• Tarantula Artillery (750) (DR 59)
• Badger Tank (800) (DR 74)
• Sea Hive Carrier (750) (DR 64)
• Yamato III (800) (DR 79)

The Elite Mantis Infantry has 20 more Strength than its regular counterpart, and the Elite Tarantula Artillery has 10 more Strength than its regular counterpart.  These are meager improvements, but improvements nonetheless.

On the other hand, the other 3 Elite units actually have lower strength than their regular counterparts.  Even more perplexing, the Elite Sea Hive Carrier is 1 Tier lower than the regular Sea Hive Carrier.

What's going on!?

There are several factors at play here:

1. You can purchase these Elite units, while the regular ones need to be unlocked by gaining sufficiently high Dominance Rank in World Domination.  (Let's ignore hacking.)  The Elite units that are stronger than their regular versions are the two with the lowest Domination Rank requirements.  If you could purchase the Elite versions and they were stronger than the ones unlocked by World Domination, then World Domination would lose much of its appeal.
2. There's not much wiggle room between the Strengths of the existing Tier 7 units and the Tier 8 units (the Chimera and its ilk).
3. These Elite units are buildable, while Tier 8 units are not.  (Ignoring hacking again.)
4. Tier 8 units are much more expensive than Tier 7 units.  (Ignoring hacking again.)

Tier 7 vs. Tier 8 Units

Let's take a closer look at the second factor.  Consider the Elite Badger Tank.  The regular Badger Tank has a base Strength of 800, while the Cerberus has a base Strength of 850.  When fully upgraded, these two units have Strengths of 960 and 1020, respectively.  There's not much wiggle room in between these two tanks.  If the Elite Badger Tank came with a base Strength between 800-800, then when fully upgraded, it would rival the Cerberus in Strength.  Even then, the Elite Badger Tank would be one tier lower, but most players notice Strength, not Tier.  Players who had bought the Cerberus would not be too happy about their purchases if the Elite Badger Tank came out too strong.

Similarly, the Yamato III has a base strength of 800, while the Poseidon USV has a base Strength of 850. So the same lack of wiggle room between 800 and 850 exists here.

What about the Elite Sea Hive Carrier?  No Tier 8 Carrier has been released yet, but we can expect one soon.  The regular Sea Hive Carrier has only 750 Strength.  We can expect the Tier 8 Carrier to have base Strength of 800 (more likely) or 850.   The same restrictive Strength range exists here.  It wouldn't be good for the sales of this future Tier 8 Carrier if the Elite Sea Hive Carrier already existed with nearly the same Strength.  Perhaps this explains why the Elite Sea Hive Carrier is the weakest of the Red Rampage 10 bunch in terms of Strength and the is only one that's a lower Tier than its regular counterpart.

Why does the Elite Sea Hive Carrier have to be so weak when:

• It matches the existing Elite Sea Horse Carrier (which just came out) in Tier and Strength;
• It Is outmatched by the existing Elite Leviathan Carrier, which is Tier 7, has base Strength of 675, and has a level requirement of only 50;
• The Albatross Carrier is Tier 7, has base Strength of 700, and has a level requirement of 70?

The Elite Sea Hive Carrier doesn't have to be so especially weak!  It would be a bit more reasonable for it to be Tier 7 and have base Strength around 700, making it a bit stronger than the recently released Elite Sea Horse Carrier--even if that doesn't make it stronger than the regular Sea Hive Carrier, which after all needs to be unlocked through World Domination.

Conclusion

Ultimately, this whole mess stems from greed and poor planning.  This resulted in the introduction of too many units and thus conflicts between:

• The strengths of the Tier 8 units being set around 1000--probably related to Tactical Nuke I dealing 1000 damage per unit.
• The release of the Tier 7 units with most base Strengths around 700-800 and upgraded Strengths around 840-960, which comes close to the Tier 8 units.
• The units unlocked by World Domination.
• The regularly timed release of Elite units, which are usually slightly stronger than their regular counterparts.

Do Enemy Units Have an Unfair Advantage?

Awhile back, I posted an article titled "Sweet Spot Theory Debunked."  It was an example of confirmation bias--people tending to find confirmation in beliefs they already hold.  General Dogsworth linked this theory of sweet spots with another popular players' theory: that enemy units have a better chance of scoring direct or critical hits than players do.  Here's a quote from the General:

I hope you ALSO bear this in mind the next time you run into someone who is insisting that the AI has a better chance of inflicting Direct or Critical Hits than you do.  

However, there has been no evidence offered up in support of this fair-play stance--in fact, just the opposite.  Many players are convinced from personal experience that enemy units have an unfair advantage in battle, and some have provided limited evidence of this.  Here is a thread on the official Zynga E&A forums where players are complaining about this unfairness.

Two Scenarios

Here's a scenario: a player pits 5 Talon Tanks versus 5 Kodiak EXO Infantry.  Who wins?  At first thought, Talon Tanks should win because tanks are "great" versus infantry, while infantry are "poor" versus tanks.  However, Talon Tanks are only tier 6 while Kodiaks are tier 7, giving a tier edge to the Kodiaks.  Furthermore, Kodiaks have base strength of 650, while Talon Tanks have base strength of 550.  Thus, the battle is not as clear cut as first thought.  Which factors are more important here: being "great" versus another unit type or having tier and strength advantages?

An easier scenario: 5 Talon Tanks versus 5 Advanced Soldiers.  Here, both unit types are tier 6, and Talon Tanks have a strength advantage over Advanced Soldiers by 550 to 350.  Surely, the Talon Tanks should demolish the Advanced Soldiers without taking much damage in return.  Try it yourself and see what happens.

Here's an example of how one player, Tamiyah, fared when she invaded a neighbor.  When she pitted 5 Talons versus 5 Kodiaks, she destroyed all Kodiaks but lost 3 Talons.  Is that reasonable?

Fairness

These scenarios don't really address fairness.  The first scenario concerns what factors are more important in battle, while the second concerns whether the game battle logic makes sense and to what degree.

For fairness, the key question is: What happens if we reverse the units for player and computer AI?  If I pitted my own Kodiaks or Advanced Soldiers versus the computer AI's Talons, would the results of the battle be flipped?  As a side note, does it matter whether the computer AI is controlling another player's units (like in PVP or World Domination) or other units (like in quests and Campaign Mastery)?

Back to Tamiyah's example above.  When the player reversed the situation, she failed to destroy any Talons and lost all her Kodiaks.  Not quite the same result as before, huh?  Of course, this is just one example.

I'll follow my own battles more closely to see whether the General's fair-play stance holds and report my results.

Unfairness

Suppose things really are unfair.  It would be an outrage to players, some of whom presumably fork over real hard-earned cash for Empire Points.  Why would Zynga do this?

If you've played Empires & Allies for long and have a mind for business, technology, and conspiracies, perhaps you've contemplated whether some of the puzzling things going on in the game are due to plain incompetence or planned profit maximization.  Most likely a blend of both, I believe--this is a topic I'll expand upon greatly in the future.

You might call it Zynga's Planned Incompetence for Profit Maximization, PIPM.  That sounds like one of those many acronyms for U.S. government bailout programs (TAF, TARP, PPIP, anyone?).  A simpler acronym is PIPs, Planned Incompetence for Profits.  A somewhat "inappropriate" but yet-so-appropriate acronym is PIMPs, Planned Incompetence for Making Profits.

Why would Zynga do this?  The company must think the vast majority of players are too oblivious, distracted, or stupid to notice the unfairness.  They must think that enough players--especially the "whales"--develop feelings of frustration and military inadequacy enough to the point of spending more Empire Points to get better fighting units and upgrades.

Sweet Spot Theory Debunked

There has been a theory going around that enemy units have sweet spots that you can aim at to get a higher chance of critical hits.  For instance, the sweet spot for soldiers would be their heads.  Many players believe in and practice applying this theory in their games.  

Long, heated discussions on the Sweet Spot Theory have taken place, including on the official Zynga Empires & Allies forum.  In a recent post in one such discussion, a poster by the name of Zu Nim delivered the coup de grâce to the theory:

Nothing wrong with telling folks to "put up or shut up" if they're going to make a claim. They never could. No surprise, really, because it was all in their heads. (Confirmation Bias says Hello!)
I don't want to get into the technical here in case it violates some of Zynga's terms. But long after this topic had run its course, I learned much about the game works as part of adding information to the wiki. And:

• No information is passed from the client about the location of a hit, only which player unit strikes which enemy unit

• The client relies on Zynga's servers to tell it how much damage was done to an enemy unit

• The client is told all kinds of minute information about the units, but no information about hit boxes (sweet spots)

There are no sweet spots.
The folks at Zynga must laugh hard when they see what people can convince themselves of. Laugh all the way to the bank... 

Original post: Sweet Spot Theory Debunked - Zu Nim

Assuming Zu Nim's technical investigation was thorough, no evidence can be more convincing than this against the Sweet Spot Theory.  Another possible piece of evidence would be a statistical analysis pitting combat using sweet spots versus combat using random aiming.  It would be difficult, however, to gather the data manually for such an analysis due to the enemy units constantly moving around.

On the same thread, General Dogsworth had this response:

I hope you ALSO bear this in mind the next time you run into someone who is insisting that the AI has a better chance of inflicting Direct or Critical Hits than you do. 

The General was referencing Enemy AI Hit Rates, another theory by players that exemplifies confirmation bias.

How Big Are the Islands?

How big are the islands exactly?  How much land vs. water is there?

Most beginners to Empires & Allies probably think the Central Island--the island they start on--is the biggest one.  How Home-Island-centric!  It turns out that the Home Island is the 2nd smallest one.  The biggest one is actually the West Island.

As part of a larger project, I actually measured how big each island is.  Here are the results, by decreasing size:

Island	# blocks	# cells
West Island	168	672
East Island	152	608
South Island	144	576
Central Island	138	552
North Island	132	528
TOTAL	734	2,936

A block is how big a house is.  A cell is how big one piece of road is.  A block is made of 4 cells.  In the counts above, I included only the blocks where you could actually build houses on.  Put another way, I excluded the shore.

Expansions

An expansion is 4 x 4 = 16 blocks, or 8 x 8 = 64 cells.  The game world has 196 total expansions.  You start out the game with 6 "expansions", and need 190 more to fully expand.  The number of expansions that include some non-shore land is 100, while 96 expansions are purely water/shore.  Thus, you need an additional 94 expansions from the 6 you start out with in order to cover all the land in the game.

To see how many expansions you currently have, use the table in my article on Expansions.  Keep in mind that "# Current Expansions" from the article does not include the original 6 "expansions" you start out the game with.  Your total # of expansions is 6 plus what you derive from the table.

Land vs. Water/Shore

As a bonus, here's the breakdown of the game world by land and water/shore:

Region Type	# blocks	# cells	%
Land	734	2,936	23.4%
Water/shore	2,402	9,608	76.6%
Game world	3,136	12,544

The E&A game world has 14 x 14 = 196 expansions, 56 x 56 = 3,136 blocks, or 112 x 112 = 12,544 cells.

The game world is 23.4% non-shore land and 76.6% water/shore.  The land % is higher than 23.4% if we include the shore. [Maybe I'll count the shore separately in the future.]  Taking the shore correctly into account, these percentages are not far off from the make-up of the Earth's surface, which is 71% covered by salt water oceans.

Maps

No, I didn't actually count all the blocks and cells one by one.  That would be a bit too tedious, even for me.  I actually mapped out the blocks in Excel and used a trick to count the blocks.

In the future, I may release the map(s) that I've made if I figure out how to present them nicely.

I mentioned above that this was part of a larger project.  I actually got sidetracked into all this counting.  Originally, I was trying to calculate the bonus effects of decors like Petroleum Refineries.  At first, I did the calculations on fake, square islands.  I thought it would be more accurate to create models of the game world.

I'm still in the middle of this project, but I'll try to write something on it later.  I'm sure there are other applications to all this work I'm doing...